{"title":"月球背面运动的简单计算","authors":"V. V. Nesterenko","doi":"10.1002/asna.20230143","DOIUrl":null,"url":null,"abstract":"<p>A simple and clear method to calculate the averaged motion of the apsis line in the Moon orbit is proposed. The obtained result is <span></span><math>\n <semantics>\n <mrow>\n <mn>3</mn>\n <mo>°</mo>\n <msup>\n <mn>1</mn>\n <mo>′</mo>\n </msup>\n <mn>1</mn>\n <msup>\n <mn>2</mn>\n <mo>′′</mo>\n </msup>\n </mrow>\n <annotation>$$ {3}^{{}^{\\circ}}{1}^{\\prime }1{2}^{\\prime \\prime } $$</annotation>\n </semantics></math> for the starry period of the Moon revolution around the Earth or <span></span><math>\n <semantics>\n <mrow>\n <mn>40</mn>\n <mo>°</mo>\n <mn>2</mn>\n <msup>\n <mn>2</mn>\n <mo>′</mo>\n </msup>\n <mn>4</mn>\n <msup>\n <mn>8</mn>\n <mo>′′</mo>\n </msup>\n </mrow>\n <annotation>$$ {40}^{{}^{\\circ}}2{2}^{\\prime }4{8}^{\\prime \\prime } $$</annotation>\n </semantics></math> per year. The modern observed value of the latter quantity is <span></span><math>\n <semantics>\n <mrow>\n <mn>40</mn>\n <mo>°</mo>\n <mn>4</mn>\n <msup>\n <mn>1</mn>\n <mo>′</mo>\n </msup>\n </mrow>\n <annotation>$$ {40}^{{}^{\\circ}}4{1}^{\\prime } $$</annotation>\n </semantics></math> per year. In “Principia” Newton derived <span></span><math>\n <semantics>\n <mrow>\n <mn>1</mn>\n <mo>°</mo>\n <mn>3</mn>\n <msup>\n <mn>1</mn>\n <mo>′</mo>\n </msup>\n <mn>2</mn>\n <msup>\n <mn>8</mn>\n <mo>′′</mo>\n </msup>\n </mrow>\n <annotation>$$ {1}^{{}^{\\circ}}3{1}^{\\prime }2{8}^{\\prime \\prime } $$</annotation>\n </semantics></math> for the Moon month and <span></span><math>\n <semantics>\n <mrow>\n <mn>20</mn>\n <mo>°</mo>\n <mn>1</mn>\n <msup>\n <mn>2</mn>\n <mo>′′</mo>\n </msup>\n </mrow>\n <annotation>$$ {20}^{{}^{\\circ}}1{2}^{\\prime \\prime } $$</annotation>\n </semantics></math> per year, that is approximately two times less than the observed values. Contrary to the Newton approach, we use a simple and obvious averaging of the Sun disturbing force for the starry period of the Moon revolution around the Earth. The applicability of the obtained formulae to satellites of other planets and to the planets themselves is argued. Comparing Newton's calculation with our method, we reveal the reason, rather convincing, that brought Newton to an imprecise result.</p>","PeriodicalId":55442,"journal":{"name":"Astronomische Nachrichten","volume":"345 4","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Simple calculation of the Moon apsides motion\",\"authors\":\"V. V. Nesterenko\",\"doi\":\"10.1002/asna.20230143\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A simple and clear method to calculate the averaged motion of the apsis line in the Moon orbit is proposed. The obtained result is <span></span><math>\\n <semantics>\\n <mrow>\\n <mn>3</mn>\\n <mo>°</mo>\\n <msup>\\n <mn>1</mn>\\n <mo>′</mo>\\n </msup>\\n <mn>1</mn>\\n <msup>\\n <mn>2</mn>\\n <mo>′′</mo>\\n </msup>\\n </mrow>\\n <annotation>$$ {3}^{{}^{\\\\circ}}{1}^{\\\\prime }1{2}^{\\\\prime \\\\prime } $$</annotation>\\n </semantics></math> for the starry period of the Moon revolution around the Earth or <span></span><math>\\n <semantics>\\n <mrow>\\n <mn>40</mn>\\n <mo>°</mo>\\n <mn>2</mn>\\n <msup>\\n <mn>2</mn>\\n <mo>′</mo>\\n </msup>\\n <mn>4</mn>\\n <msup>\\n <mn>8</mn>\\n <mo>′′</mo>\\n </msup>\\n </mrow>\\n <annotation>$$ {40}^{{}^{\\\\circ}}2{2}^{\\\\prime }4{8}^{\\\\prime \\\\prime } $$</annotation>\\n </semantics></math> per year. The modern observed value of the latter quantity is <span></span><math>\\n <semantics>\\n <mrow>\\n <mn>40</mn>\\n <mo>°</mo>\\n <mn>4</mn>\\n <msup>\\n <mn>1</mn>\\n <mo>′</mo>\\n </msup>\\n </mrow>\\n <annotation>$$ {40}^{{}^{\\\\circ}}4{1}^{\\\\prime } $$</annotation>\\n </semantics></math> per year. In “Principia” Newton derived <span></span><math>\\n <semantics>\\n <mrow>\\n <mn>1</mn>\\n <mo>°</mo>\\n <mn>3</mn>\\n <msup>\\n <mn>1</mn>\\n <mo>′</mo>\\n </msup>\\n <mn>2</mn>\\n <msup>\\n <mn>8</mn>\\n <mo>′′</mo>\\n </msup>\\n </mrow>\\n <annotation>$$ {1}^{{}^{\\\\circ}}3{1}^{\\\\prime }2{8}^{\\\\prime \\\\prime } $$</annotation>\\n </semantics></math> for the Moon month and <span></span><math>\\n <semantics>\\n <mrow>\\n <mn>20</mn>\\n <mo>°</mo>\\n <mn>1</mn>\\n <msup>\\n <mn>2</mn>\\n <mo>′′</mo>\\n </msup>\\n </mrow>\\n <annotation>$$ {20}^{{}^{\\\\circ}}1{2}^{\\\\prime \\\\prime } $$</annotation>\\n </semantics></math> per year, that is approximately two times less than the observed values. Contrary to the Newton approach, we use a simple and obvious averaging of the Sun disturbing force for the starry period of the Moon revolution around the Earth. The applicability of the obtained formulae to satellites of other planets and to the planets themselves is argued. Comparing Newton's calculation with our method, we reveal the reason, rather convincing, that brought Newton to an imprecise result.</p>\",\"PeriodicalId\":55442,\"journal\":{\"name\":\"Astronomische Nachrichten\",\"volume\":\"345 4\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-02-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Astronomische Nachrichten\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/asna.20230143\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ASTRONOMY & ASTROPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Astronomische Nachrichten","FirstCategoryId":"101","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/asna.20230143","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
A simple and clear method to calculate the averaged motion of the apsis line in the Moon orbit is proposed. The obtained result is for the starry period of the Moon revolution around the Earth or per year. The modern observed value of the latter quantity is per year. In “Principia” Newton derived for the Moon month and per year, that is approximately two times less than the observed values. Contrary to the Newton approach, we use a simple and obvious averaging of the Sun disturbing force for the starry period of the Moon revolution around the Earth. The applicability of the obtained formulae to satellites of other planets and to the planets themselves is argued. Comparing Newton's calculation with our method, we reveal the reason, rather convincing, that brought Newton to an imprecise result.
期刊介绍：
Astronomische Nachrichten, founded in 1821 by H. C. Schumacher, is the oldest astronomical journal worldwide still being published. Famous astronomical discoveries and important papers on astronomy and astrophysics published in more than 300 volumes of the journal give an outstanding representation of the progress of astronomical research over the last 180 years. Today, Astronomical Notes/ Astronomische Nachrichten publishes articles in the field of observational and theoretical astrophysics and related topics in solar-system and solar physics. Additional, papers on astronomical instrumentation ground-based and space-based as well as papers about numerical astrophysical techniques and supercomputer modelling are covered. Papers can be completed by short video sequences in the electronic version. Astronomical Notes/ Astronomische Nachrichten also publishes special issues of meeting proceedings.
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