ABSTRACT
The gravitational force plays the most prominent role in astrophysics. It is responsible for holding the solar system, the galaxies, and the galaxy clusters together. The gravitational force is well described by the Newton's inverse square law. Consider two point particles of mass M and m. Here we treat heavenly bodies, such as the Sun, Earth, etc., as particles. Let https://www.w3.org/1998/Math/MathML"> r → https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003470472/1d6c823b-2cbe-41fe-9812-7c4211c6fc0a/content/math5_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> denote the position vector of m with respect to M, as shown in Figure 5.1. The force on m due to M is given by https://www.w3.org/1998/Math/MathML"> F → = − G M m r ^ r 2 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003470472/1d6c823b-2cbe-41fe-9812-7c4211c6fc0a/content/math5_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> The point masses, <italic>M</italic> and <italic>m</italic>, are located at the origin <italic>O</italic> and at the position vector <inline-formula> <alternatives> <mml:math display="inline" xmlns:mml="<a href="https://www.w3.org/1998/Math/MathML" target="_blank">https://www.w3.org/1998/Math/MathML</a>"> <mml:mrow> <mml:mover> <mml:mi>r</mml:mi> <mml:mo stretchy="false">→</mml:mo> </mml:mover> </mml:mrow> </mml:math> <inline-graphic xlink:href="<a href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003470472/1d6c823b-2cbe-41fe-9812-7c4211c6fc0a/content/math5_11.tif" target="_blank">https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003470472/1d6c823b-2cbe-41fe-9812-7c4211c6fc0a/content/math5_11.tif</a>" xmlns:xlink="<a href="https://www.w3.org/1999/xlink" target="_blank">https://www.w3.org/1999/xlink</a>"/> </alternatives> </inline-formula>, respectively. The gravitational force <inline-formula> <alternatives> <mml:math display="inline" xmlns:mml="<a href="https://www.w3.org/1998/Math/MathML" target="_blank">https://www.w3.org/1998/Math/MathML</a>"> <mml:mrow> <mml:mover> <mml:mi>F</mml:mi> <mml:mo stretchy="false">→</mml:mo> </mml:mover> </mml:mrow> </mml:math> <inline-graphic xlink:href="<a href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003470472/1d6c823b-2cbe-41fe-9812-7c4211c6fc0a/content/math5_12.tif" target="_blank">https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003470472/1d6c823b-2cbe-41fe-9812-7c4211c6fc0a/content/math5_12.tif</a>" xmlns:xlink="<a href="https://www.w3.org/1999/xlink" target="_blank">https://www.w3.org/1999/xlink</a>"/> </alternatives> </inline-formula> on <italic>m</italic> due to <italic>M</italic> points toward the origin. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003470472/1d6c823b-2cbe-41fe-9812-7c4211c6fc0a/content/fig5_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
