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| The gravitational acceleration $ a $ of object A towards object B is proportional to the mass of object B ( $ m_B $ ) divided by the square of the distance between them ( $ r_AB $ ). | The gravitational acceleration $ a $ of object A towards object B is proportional to the mass of object B ( $ m_B $ ) divided by the square of the distance between them ( $ r_{AB} $ ). |
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| $ F = { \Large { { G m_B m_A } \over { r_AB^2 } } } ~ ~ ~ \rightarrow ~ ~ ~ a_A = { \Large { F \over m_A } } = { \Large { { G m_B } \over { r_AB^2 } } } $ | $ F = { \Large { { G m_B m_A } \over { r_{AB}^2 } } } ~ ~ ~ \rightarrow ~ ~ ~ a_A = { \Large { F \over m_A } } = { \Large { { G m_B } \over { r_{AB}^2 } } } ~ ~ ~ $ and also $ a_B = { \Large { F \over m_B } } = { \Large { { G m_A } \over { r_{AB}^2 } } } $ |
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BarycenterNot
Some claim that the Earth's insolation is a function of its distance from the Sun (it is) and that this varies because the Earth orbits around the Solar System's "barycenter" (which is nonsense, and outright dishonesty if you hear it from a climate denier who claims to know physics).
The Truth
(as we understand and measure it)
The gravitational acceleration a of object A towards object B is proportional to the mass of object B ( m_B ) divided by the square of the distance between them ( r_{AB} ).
F = { \Large { { G m_B m_A } \over { r_{AB}^2 } } } ~ ~ ~ \rightarrow ~ ~ ~ a_A = { \Large { F \over m_A } } = { \Large { { G m_B } \over { r_{AB}^2 } } } ~ ~ ~ and also a_B = { \Large { F \over m_B } } = { \Large { { G m_A } \over { r_{AB}^2 } } }
There are some tiny modifications described by general relativity, but those second order effects only become important when distances are small and masses are enormous.
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