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.

When NASA delivers a lander to Mars, it must enter the Martian atmosphere with kilometer precision after a 500 million kilometer journey from Earth. They need 9 decimal place accuracy, and include gravitational effects from all the inner planets in those calculations.

However, if we merely wish to compute the distance from the Earth to the Sun to estimate solar insolation, we can pretty much ignore the other planets, because they are far away, and accelerate both the Earth and the Sun almost equally, just as the Earth pulls on both you and the vehicle you ride in almost equally.

The difference between almost and zero occurs when two objects are at slightly different distances from the object that is pulling on them. The Earth is on average about 1 astronomical unit (au) from the Sun, 150,000,000 kilometers. Earth's orbit is actually slightly elliptical; I'll touch on that later.

When NASA delivers a lander to Mars, it must enter the Martian atmosphere with kilometer precision after a 500 million kilometer journey from Earth. They need 9 decimal place accuracy, and include gravitational effects from all the inner planets in those calculations.

However, if we merely wish to compute the distance from the Earth to the Sun to estimate solar insolation, we can pretty much ignore the other planets, because they are far away, and accelerate both the Earth and the Sun almost equally, just as the Earth pulls on both you and the vehicle you ride in almost equally.

The difference between almost and zero occurs when two objects are at slightly different distances from the object that is pulling on them. The Earth is on average about 1 astronomical unit (au) from the Sun, 150,000,000 kilometers. Earth's orbit is actually slightly elliptical; I'll touch on that later.

Jupiter is the second largest mass (that we know about!) in the solar system; with a mass