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_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 } } } ~ ~ ~ and so ~ ~ ~ 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.

To be pedantic - the forces F on object A and object B are equal (though opposite) vectors pointing at each other. The equations above would be more accurate if expressed as vectors, but less understandable for most readers. If you are interviewing for an orbit designer job at NASA, and they ask you this, ask them whether they want the relativistic equations, the vector equations, or the simpler equations above. When NASA estimates mission costs, they use vectors, and when they compute precise space probe trajectories, they use general relativity.

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