Номер 10, страница 45, часть 2 - гдз по физике 9 класс учебник Генденштейн, Булатова

Авторы: Генденштейн Л. Э., Булатова А. А., Корнильев И. Н., Кошкина А. В.

Тип: Учебник

Издательство: Бином

Год издания: 2016 - 2026

Часть: 2

Цвет обложки: бирюзовый

ISBN: 978-5-9963-3062-1

Часть 2. Строение и эволюция вселенной. Глава VII. Солнечная система. Параграф 28. Планеты, астероиды и кометы - номер 10, страница 45.

App\Models\Task {#1030 // resources/views/models/task/default.blade.php
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                            "name" => "Бином"
                            "field_cases" => null
                            "field_translit" => "binom"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1132
                      #items: array:4 [
                        0 => App\Models\Term {#1133
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 4104
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Генденштейн"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Лев"
                            "field_patronymic" => "Элевич"
                            "field_surname_rp" => "Генденштейна"
                          ]
                          #original: array:12 [
                            "id" => 4104
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Генденштейн"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Лев"
                            "field_patronymic" => "Элевич"
                            "field_surname_rp" => "Генденштейна"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                        1 => App\Models\Term {#1134
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 3936
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Булатова"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Альбина"
                            "field_patronymic" => "Александрова"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 3936
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Булатова"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Альбина"
                            "field_patronymic" => "Александрова"
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                        2 => App\Models\Term {#1135
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 4679
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Корнильев"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Игорь"
                            "field_patronymic" => "Николаевич"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 4679
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Корнильев"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Игорь"
                            "field_patronymic" => "Николаевич"
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                        3 => App\Models\Term {#1136
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 4758
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Кошкина"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Анжелика"
                            "field_patronymic" => "Васильевна"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 4758
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Кошкина"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Анжелика"
                            "field_patronymic" => "Васильевна"
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1137
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1138
                      #items: array:1 [
                        0 => App\Models\Term {#1139
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6671
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Учебник"
                            "field_book_type_foreign" => null
                            "field_cases" => array:6 [ …6]
                            "field_plural_form" => null
                            "field_short_name" => null
                            "field_short_name_foreign" => null
                            "field_translit" => "uchebnik"
                          ]
                          #original: array:10 [
                            "id" => 6671
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Учебник"
                            "field_book_type_foreign" => null
                            "field_cases" => array:6 [ …6]
                            "field_plural_form" => null
                            "field_short_name" => null
                            "field_short_name_foreign" => null
                            "field_translit" => "uchebnik"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1140
                      #items: array:1 [
                        0 => App\Models\Term {#1141
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 9
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Россия"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "rossiya"
                          ]
                          #original: array:6 [
                            "id" => 9
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Россия"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "rossiya"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1142
                      #items: array:1 [
                        0 => App\Models\Term {#1143
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "moskva"
                          ]
                          #original: array:6 [
                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                             …4
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1144
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1145
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1146
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1147
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_publication_number" => null
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1148
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1149
                      #items: array:1 [
                        0 => App\Models\Term {#1150
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [ …12]
                          #original: array:12 [ …12]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2016"
                    "field_publication_year_until" => null
                    "field_part" => "1, 2"
                    "field_part_writing" => "Часть"
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное издание"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "1111"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_09/gendenshtejn-u/"
                    "field_isbn" => "978-5-9963-3062-1"
                    "field_cover" => array:2 [
                      0 => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052"
                      1 => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052"
                    ]
                    "field_cover_alts" => array:2 [
                      0 => ""
                      1 => ""
                    ]
                    "field_covers" => array:2 [
                      0 => array:4 [
                        "path" => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052"
                        "alt" => ""
                        "width" => "1863"
                        "height" => "2813"
                      ]
                      1 => array:4 [
                        "path" => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052"
                        "alt" => ""
                        "width" => "1863"
                        "height" => "2809"
                      ]
                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1151
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1152
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1153
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1154
                      #items: array:1 [
                        0 => App\Models\Term {#1155
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [ …6]
                          #original: array:6 [ …6]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 380
                      "subject" => 556
                      "class_subject" => 493
                    ]
                  ]
                  #original: array:50 [
                    "id" => 2980
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
                    "field_pages_status" => null
                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1127}
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1128}
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1130}
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1132}
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1137}
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1138}
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1140}
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1142}
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1144}
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1145}
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1146}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1147}
                    "field_publication_number" => null
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1148}
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1149}
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2016"
                    "field_publication_year_until" => null
                    "field_part" => "1, 2"
                    "field_part_writing" => "Часть"
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное издание"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "1111"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_09/gendenshtejn-u/"
                    "field_isbn" => "978-5-9963-3062-1"
                    "field_cover" => array:2 [
                      0 => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052"
                      1 => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052"
                    ]
                    "field_cover_alts" => array:2 [
                      0 => ""
                      1 => ""
                    ]
                    "field_covers" => array:2 [
                      0 => array:4 [
                        "path" => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052"
                        "alt" => ""
                        "width" => "1863"
                        "height" => "2813"
                      ]
                      1 => array:4 [
                        "path" => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052"
                        "alt" => ""
                        "width" => "1863"
                        "height" => "2809"
                      ]
                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1151}
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1152}
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1153}
                    "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1154}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 380
                      "subject" => 556
                      "class_subject" => 493
                    ]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1156
              #items: []
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1433262
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => null
            "field_branch_order" => "2"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1126}
            "field_page_start" => "4"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1158}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1156}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        1 => App\Models\Branch {#1157
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 1433270
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Строение и эволюция вселенной"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1159
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "38"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1160
              #items: array:1 [
                0 => App\Models\Book {#1125}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1161
              #items: array:1 [
                0 => App\Models\Branch {#1034}
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1433270
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Строение и эволюция вселенной"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1159}
            "field_page_start" => "38"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1160}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1161}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        2 => App\Models\Branch {#1162
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 1434384
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Солнечная система"
            "field_branch_order" => "VII"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1166
              #items: array:1 [
                0 => App\Models\Term {#1163
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #original: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "38"
            "field_branch_display" => "0"
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            "field_display_branch_in_title" => "1"
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            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1165
              #items: array:1 [
                0 => App\Models\Book {#1125}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1174
              #items: array:1 [
                0 => App\Models\Branch {#1173
                  #connection: "mysql"
                  #table: "branches"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 1433270
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Строение и эволюция вселенной"
                    "field_branch_order" => null
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1175 …2}
                    "field_page_start" => "38"
                    "field_branch_display" => "0"
                    "field_branch_expanded" => "0"
                    "field_display_branch_in_title" => "1"
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                    "field_display_branch_page" => "1"
                    "field_branch_title_in_content" => "0"
                    "field_navigation_title" => null
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1176 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1177 …2}
                  ]
                  #original: array:24 [
                    "id" => 1433270
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Строение и эволюция вселенной"
                    "field_branch_order" => null
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1175 …2}
                    "field_page_start" => "38"
                    "field_branch_display" => "0"
                    "field_branch_expanded" => "0"
                    "field_display_branch_in_title" => "1"
                    "field_display_task_interval" => "0"
                    "field_display_branch_page" => "1"
                    "field_branch_title_in_content" => "0"
                    "field_navigation_title" => null
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1176 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1177 …2}
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1434384
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Солнечная система"
            "field_branch_order" => "VII"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1166}
            "field_page_start" => "38"
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            "field_display_branch_in_title" => "1"
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            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1165}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1174}
          ]
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          #attributeCastCache: []
          #dateFormat: null
          #appends: []
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          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        3 => App\Models\Branch {#1167
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 1434386
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Планеты, астероиды и кометы"
            "field_branch_order" => "28"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1171
              #items: array:1 [
                0 => App\Models\Term {#1164
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
                    "id" => 32
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Параграф"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => "§"
                  ]
                  #original: array:7 [
                    "id" => 32
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Параграф"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => "§"
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "41"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1168
              #items: array:1 [
                0 => App\Models\Book {#1125}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1184
              #items: array:1 [
                0 => App\Models\Branch {#1183
                  #connection: "mysql"
                  #table: "branches"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 1434384
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Солнечная система"
                    "field_branch_order" => "VII"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1185 …2}
                    "field_page_start" => "38"
                    "field_branch_display" => "0"
                    "field_branch_expanded" => "0"
                    "field_display_branch_in_title" => "1"
                    "field_display_task_interval" => "0"
                    "field_display_branch_page" => "1"
                    "field_branch_title_in_content" => "0"
                    "field_navigation_title" => null
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1186 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1187 …2}
                  ]
                  #original: array:24 [
                    "id" => 1434384
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Солнечная система"
                    "field_branch_order" => "VII"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1185 …2}
                    "field_page_start" => "38"
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                    "field_display_branch_in_title" => "1"
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                    "field_display_branch_page" => "1"
                    "field_branch_title_in_content" => "0"
                    "field_navigation_title" => null
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1186 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1187 …2}
                  ]
                  #changes: []
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                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
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                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1434386
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Планеты, астероиды и кометы"
            "field_branch_order" => "28"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1171}
            "field_page_start" => "41"
            "field_branch_display" => "0"
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            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1168}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1184}
          ]
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          #attributeCastCache: []
          #dateFormat: null
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          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
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          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "content" => Illuminate\Database\Eloquent\Collection {#1073
      #items: array:2 [
        0 => App\Models\Element {#1102
          #connection: "mysql"
          #table: "elements"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:7 [
            "id" => 1696753
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1093
              #items: array:1 [
                0 => App\Models\Edition {#1103
                  #connection: "mysql"
                  #table: "editions"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:21 [
                    "id" => 6168
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
                    "field_order" => "1"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1100 …2}
                    "field_content_type" => "free"
                    "field_content_mode" => "text, image"
                    "field_page_content_mode" => "image"
                    "field_content_text_checked" => "0"
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Автор"
                    "field_moderator" => "stas"
                    "field_edition_type" => "statement"
                    "field_root_dir" => "0-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1099 …2}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1098 …2}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1097 …2}
                    "field_content_source" => null
                  ]
                  #original: array:21 [
                    "id" => 6168
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
                    "field_order" => "1"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1100 …2}
                    "field_content_type" => "free"
                    "field_content_mode" => "text, image"
                    "field_page_content_mode" => "image"
                    "field_content_text_checked" => "0"
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Автор"
                    "field_moderator" => "stas"
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                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1099 …2}
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            "text" => "<p><strong>10.</strong> Найдите ускорение, сообщаемое Солнцем:</p><p><strong>а)</strong> Меркурию;</p><p><strong>б)</strong> Земле;</p><p><strong>в)</strong> Юпитеру.</p>"
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            "task" => array:2 [
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            "text" => "<p><strong>10.</strong> Найдите ускорение, сообщаемое Солнцем:</p><p><strong>а)</strong> Меркурию;</p><p><strong>б)</strong> Земле;</p><p><strong>в)</strong> Юпитеру.</p>"
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            "text" => "<p><strong>Дано:</strong></p><p>Масса Солнца, $M_C = 1.989 \cdot 10^{30}$ кг<br>Гравитационная постоянная, $G = 6.674 \cdot 10^{-11}$ Н$\cdot$м$^2$/кг$^2$<br>Среднее расстояние от Солнца до Меркурия, $r_М = 57.9 \cdot 10^6$ км<br>Среднее расстояние от Солнца до Земли, $r_З = 149.6 \cdot 10^6$ км<br>Среднее расстояние от Солнца до Юпитера, $r_Ю = 778.5 \cdot 10^6$ км<br></p><p>Перевод в систему СИ:<br>$r_М = 57.9 \cdot 10^6 \text{ км} = 5.79 \cdot 10^{10}$ м<br>$r_З = 149.6 \cdot 10^6 \text{ км} = 1.496 \cdot 10^{11}$ м<br>$r_Ю = 778.5 \cdot 10^6 \text{ км} = 7.785 \cdot 10^{11}$ м<br></p><p><strong>Найти:</strong></p><p>$a_М$ - ускорение Меркурия<br>$a_З$ - ускорение Земли<br>$a_Ю$ - ускорение Юпитера<br></p><p><strong>Решение:</strong></p><p>Ускорение, сообщаемое планете гравитационным полем Солнца, можно найти из закона всемирного тяготения Ньютона. Сила гравитационного притяжения, действующая на планету, равна:</p><p>$F = G \frac{M_C \cdot m}{r^2}$</p><p>где $M_C$ – масса Солнца, $\text{m}$ – масса планеты, $\text{r}$ – расстояние между Солнцем и планетой.</p><p>Согласно второму закону Ньютона, эта же сила сообщает планете ускорение $\text{a}$:</p><p>$F = m \cdot a$</p><p>Приравняв правые части этих двух выражений, получаем:</p><p>$m \cdot a = G \frac{M_C \cdot m}{r^2}$</p><p>Сократив массу планеты $\text{m}$ с обеих сторон, получаем формулу для вычисления ускорения:</p><p>$a = G \frac{M_C}{r^2}$</p><p>Теперь рассчитаем ускорение для каждой планеты.</p><p><strong>а) Меркурию</strong></p><p>Подставим в формулу значения для Меркурия:</p><p>$a_М = G \frac{M_C}{r_М^2} = 6.674 \cdot 10^{-11} \frac{\text{Н} \cdot \text{м}^2}{\text{кг}^2} \cdot \frac{1.989 \cdot 10^{30} \text{ кг}}{(5.79 \cdot 10^{10} \text{ м})^2}$</p><p>$a_М \approx \frac{1.327 \cdot 10^{20}}{3.352 \cdot 10^{21}} \frac{\text{м}}{\text{с}^2} \approx 0.0396 \frac{\text{м}}{\text{с}^2}$</p><p><strong>Ответ:</strong> ускорение, сообщаемое Солнцем Меркурию, равно примерно $0.0396$ м/с$^2$.</p><p><strong>б) Земле</strong></p><p>Подставим в формулу значения для Земли:</p><p>$a_З = G \frac{M_C}{r_З^2} = 6.674 \cdot 10^{-11} \frac{\text{Н} \cdot \text{м}^2}{\text{кг}^2} \cdot \frac{1.989 \cdot 10^{30} \text{ кг}}{(1.496 \cdot 10^{11} \text{ м})^2}$</p><p>$a_З \approx \frac{1.327 \cdot 10^{20}}{2.238 \cdot 10^{22}} \frac{\text{м}}{\text{с}^2} \approx 0.00593 \frac{\text{м}}{\text{с}^2}$</p><p><strong>Ответ:</strong> ускорение, сообщаемое Солнцем Земле, равно примерно $0.00593$ м/с$^2$.</p><p><strong>в) Юпитеру</strong></p><p>Подставим в формулу значения для Юпитера:</p><p>$a_Ю = G \frac{M_C}{r_Ю^2} = 6.674 \cdot 10^{-11} \frac{\text{Н} \cdot \text{м}^2}{\text{кг}^2} \cdot \frac{1.989 \cdot 10^{30} \text{ кг}}{(7.785 \cdot 10^{11} \text{ м})^2}$</p><p>$a_Ю \approx \frac{1.327 \cdot 10^{20}}{6.061 \cdot 10^{23}} \frac{\text{м}}{\text{с}^2} \approx 0.000219 \frac{\text{м}}{\text{с}^2}$</p><p><strong>Ответ:</strong> ускорение, сообщаемое Солнцем Юпитеру, равно примерно $0.000219$ м/с$^2$.</p>"
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            "text" => "<p><strong>Дано:</strong></p><p>Масса Солнца, $M_C = 1.989 \cdot 10^{30}$ кг<br>Гравитационная постоянная, $G = 6.674 \cdot 10^{-11}$ Н$\cdot$м$^2$/кг$^2$<br>Среднее расстояние от Солнца до Меркурия, $r_М = 57.9 \cdot 10^6$ км<br>Среднее расстояние от Солнца до Земли, $r_З = 149.6 \cdot 10^6$ км<br>Среднее расстояние от Солнца до Юпитера, $r_Ю = 778.5 \cdot 10^6$ км<br></p><p>Перевод в систему СИ:<br>$r_М = 57.9 \cdot 10^6 \text{ км} = 5.79 \cdot 10^{10}$ м<br>$r_З = 149.6 \cdot 10^6 \text{ км} = 1.496 \cdot 10^{11}$ м<br>$r_Ю = 778.5 \cdot 10^6 \text{ км} = 7.785 \cdot 10^{11}$ м<br></p><p><strong>Найти:</strong></p><p>$a_М$ - ускорение Меркурия<br>$a_З$ - ускорение Земли<br>$a_Ю$ - ускорение Юпитера<br></p><p><strong>Решение:</strong></p><p>Ускорение, сообщаемое планете гравитационным полем Солнца, можно найти из закона всемирного тяготения Ньютона. Сила гравитационного притяжения, действующая на планету, равна:</p><p>$F = G \frac{M_C \cdot m}{r^2}$</p><p>где $M_C$ – масса Солнца, $\text{m}$ – масса планеты, $\text{r}$ – расстояние между Солнцем и планетой.</p><p>Согласно второму закону Ньютона, эта же сила сообщает планете ускорение $\text{a}$:</p><p>$F = m \cdot a$</p><p>Приравняв правые части этих двух выражений, получаем:</p><p>$m \cdot a = G \frac{M_C \cdot m}{r^2}$</p><p>Сократив массу планеты $\text{m}$ с обеих сторон, получаем формулу для вычисления ускорения:</p><p>$a = G \frac{M_C}{r^2}$</p><p>Теперь рассчитаем ускорение для каждой планеты.</p><p><strong>а) Меркурию</strong></p><p>Подставим в формулу значения для Меркурия:</p><p>$a_М = G \frac{M_C}{r_М^2} = 6.674 \cdot 10^{-11} \frac{\text{Н} \cdot \text{м}^2}{\text{кг}^2} \cdot \frac{1.989 \cdot 10^{30} \text{ кг}}{(5.79 \cdot 10^{10} \text{ м})^2}$</p><p>$a_М \approx \frac{1.327 \cdot 10^{20}}{3.352 \cdot 10^{21}} \frac{\text{м}}{\text{с}^2} \approx 0.0396 \frac{\text{м}}{\text{с}^2}$</p><p><strong>Ответ:</strong> ускорение, сообщаемое Солнцем Меркурию, равно примерно $0.0396$ м/с$^2$.</p><p><strong>б) Земле</strong></p><p>Подставим в формулу значения для Земли:</p><p>$a_З = G \frac{M_C}{r_З^2} = 6.674 \cdot 10^{-11} \frac{\text{Н} \cdot \text{м}^2}{\text{кг}^2} \cdot \frac{1.989 \cdot 10^{30} \text{ кг}}{(1.496 \cdot 10^{11} \text{ м})^2}$</p><p>$a_З \approx \frac{1.327 \cdot 10^{20}}{2.238 \cdot 10^{22}} \frac{\text{м}}{\text{с}^2} \approx 0.00593 \frac{\text{м}}{\text{с}^2}$</p><p><strong>Ответ:</strong> ускорение, сообщаемое Солнцем Земле, равно примерно $0.00593$ м/с$^2$.</p><p><strong>в) Юпитеру</strong></p><p>Подставим в формулу значения для Юпитера:</p><p>$a_Ю = G \frac{M_C}{r_Ю^2} = 6.674 \cdot 10^{-11} \frac{\text{Н} \cdot \text{м}^2}{\text{кг}^2} \cdot \frac{1.989 \cdot 10^{30} \text{ кг}}{(7.785 \cdot 10^{11} \text{ м})^2}$</p><p>$a_Ю \approx \frac{1.327 \cdot 10^{20}}{6.061 \cdot 10^{23}} \frac{\text{м}}{\text{с}^2} \approx 0.000219 \frac{\text{м}}{\text{с}^2}$</p><p><strong>Ответ:</strong> ускорение, сообщаемое Солнцем Юпитеру, равно примерно $0.000219$ м/с$^2$.</p>"
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№10 (с. 45)
Условие. №10 (с. 45)
скриншот условия
Физика, 9 класс Учебник, авторы: Генденштейн Лев Элевич, Булатова Альбина Александрова, Корнильев Игорь Николаевич, Кошкина Анжелика Васильевна, издательство Бином, Москва, 2016, бирюзового цвета, Часть 2, страница 45, номер 10, Условие

10. Найдите ускорение, сообщаемое Солнцем:

а) Меркурию;

б) Земле;

в) Юпитеру.

Решение. №10 (с. 45)

Дано:

Масса Солнца, $M_C = 1.989 \cdot 10^{30}$ кг
Гравитационная постоянная, $G = 6.674 \cdot 10^{-11}$ Н$\cdot$м$^2$/кг$^2$
Среднее расстояние от Солнца до Меркурия, $r_М = 57.9 \cdot 10^6$ км
Среднее расстояние от Солнца до Земли, $r_З = 149.6 \cdot 10^6$ км
Среднее расстояние от Солнца до Юпитера, $r_Ю = 778.5 \cdot 10^6$ км

Перевод в систему СИ:
$r_М = 57.9 \cdot 10^6 \text{ км} = 5.79 \cdot 10^{10}$ м
$r_З = 149.6 \cdot 10^6 \text{ км} = 1.496 \cdot 10^{11}$ м
$r_Ю = 778.5 \cdot 10^6 \text{ км} = 7.785 \cdot 10^{11}$ м

Найти:

$a_М$ - ускорение Меркурия
$a_З$ - ускорение Земли
$a_Ю$ - ускорение Юпитера

Решение:

Ускорение, сообщаемое планете гравитационным полем Солнца, можно найти из закона всемирного тяготения Ньютона. Сила гравитационного притяжения, действующая на планету, равна:

$F = G \frac{M_C \cdot m}{r^2}$

где $M_C$ – масса Солнца, $\text{m}$ – масса планеты, $\text{r}$ – расстояние между Солнцем и планетой.

Согласно второму закону Ньютона, эта же сила сообщает планете ускорение $\text{a}$:

$F = m \cdot a$

Приравняв правые части этих двух выражений, получаем:

$m \cdot a = G \frac{M_C \cdot m}{r^2}$

Сократив массу планеты $\text{m}$ с обеих сторон, получаем формулу для вычисления ускорения:

$a = G \frac{M_C}{r^2}$

Теперь рассчитаем ускорение для каждой планеты.

а) Меркурию

Подставим в формулу значения для Меркурия:

$a_М = G \frac{M_C}{r_М^2} = 6.674 \cdot 10^{-11} \frac{\text{Н} \cdot \text{м}^2}{\text{кг}^2} \cdot \frac{1.989 \cdot 10^{30} \text{ кг}}{(5.79 \cdot 10^{10} \text{ м})^2}$

$a_М \approx \frac{1.327 \cdot 10^{20}}{3.352 \cdot 10^{21}} \frac{\text{м}}{\text{с}^2} \approx 0.0396 \frac{\text{м}}{\text{с}^2}$

Ответ: ускорение, сообщаемое Солнцем Меркурию, равно примерно $0.0396$ м/с$^2$.

б) Земле

Подставим в формулу значения для Земли:

$a_З = G \frac{M_C}{r_З^2} = 6.674 \cdot 10^{-11} \frac{\text{Н} \cdot \text{м}^2}{\text{кг}^2} \cdot \frac{1.989 \cdot 10^{30} \text{ кг}}{(1.496 \cdot 10^{11} \text{ м})^2}$

$a_З \approx \frac{1.327 \cdot 10^{20}}{2.238 \cdot 10^{22}} \frac{\text{м}}{\text{с}^2} \approx 0.00593 \frac{\text{м}}{\text{с}^2}$

Ответ: ускорение, сообщаемое Солнцем Земле, равно примерно $0.00593$ м/с$^2$.

в) Юпитеру

Подставим в формулу значения для Юпитера:

$a_Ю = G \frac{M_C}{r_Ю^2} = 6.674 \cdot 10^{-11} \frac{\text{Н} \cdot \text{м}^2}{\text{кг}^2} \cdot \frac{1.989 \cdot 10^{30} \text{ кг}}{(7.785 \cdot 10^{11} \text{ м})^2}$

$a_Ю \approx \frac{1.327 \cdot 10^{20}}{6.061 \cdot 10^{23}} \frac{\text{м}}{\text{с}^2} \approx 0.000219 \frac{\text{м}}{\text{с}^2}$

Ответ: ускорение, сообщаемое Солнцем Юпитеру, равно примерно $0.000219$ м/с$^2$.

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