I have a question regarding a simple application of Newton's equation of gravity. As an exercise, I applied the equation to the EARTH - MOON - SUN system to see the relative gravitational force of the SUN and the EARTH on the MOON. I found something very interesting.(adsbygoogle = window.adsbygoogle || []).push({});

I chose the following conditions: New MOON at apogee; EARTH at aphelion. According to the Handbook of

Chemistry and Physics the data was as follows:

SUN EARTH MOON

Distance from Earth (km) 1.520 E08 --------- 4.055 E05

Mass (kg) 1.991 E30 5.979 E24 --------*

From this I found the distance from the SUN to the MOON to be 1.498 E08 by subtracting the EARTH - MOON distance from the EARTH - SUN distance.

Since I was interested only in the relative forces of the EARTH and the SUN on the MOON I could simplify the gravitational formula by eliminating the gravitational constant and the mass of the MOON. Newton's full formula is F = G x M1 X M2 / (D x D). The formula for relative force then is F = M / (D x D).

The following are the results:

SUN force on the MOON = 8.872 E13

EARTH force on the MOON = 3.636 E13

Resulting in a relative force of SUN / EARTH as 2.44.

I found that the SUN's force was almost 2-1/2 times stronger than the EARTH's. This, of course, is ... IMPOSSIBLE! If the MOON is to maintain its orbit around the EARTH, not only must the EARTH's force be consistently stronger to counteract the SUN's pull, but it must also be strong enough to act as a tether on the MOON and re-curve it toward the EARTH (away from the SUN), especially when it is at apogee. Only when the SUN's force is less than the EARTH's should the MOON begin to re-curve back toward the EARTH.

Is there something wrong with Newton's equation? Am I missing something obvious? Is there some other force that acts to compensate for the SUN's stronger gravitational attraction for the MOON?

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# Newton's Equation

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