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How Much Do Jupiter and Saturn Pull the Earth Away From the Sun?

-- Bruce Bryan | September 10, 2023

Question:

Is the earth being pulled away from the sun as Jupiter and Saturn near each other?

Could it increase the distance between the earth and the sun by as much as 6%?

Would that lower solar flux by the inverse square as much as 12%?

Will it occur in winter 2024 ?

-- Bruce Bryan

Answer:

To calculate the relative amount of gravitational pull that Jupiter and Saturn exert on the Earth relative to the Sun, you can use the equation for the force exerted by one body on another, which is force = (constant)*(mass of first body)*(mass of second body)/(distance between the two bodies)^2. Using this equation with masses in terns of Earth masses and Earth-Sun distances (which is called an Astronomical Unit), you can use the fact that the mass of the Sun, Jupiter, and Saturn are about 3.3×10^5, 317.8, and 95.2 times the mass of the Earth, while the distances are 1, 4.2, and 8.54 AU for the Earth to Sun, Jupiter, and Saturn distance, respectively. Using the force equation, then, you should find that the force exerted by the Sun on the Earth is about 18317 and 252809 times that exerted by Jupiter and Saturn on the Earth, respectively. This means that the gravitational force exerted by Jupiter and Saturn is about 0.005% and 0.0004%, respectively, of the gravitational force exerted by the Sun on the Earth. This extra force has no measurable effect on Earth, and the difference between when Jupiter and Saturn are in orbital alignment with Earth and when they are not produces no measurable effects.

-- Jeff Mangum

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