
#1
Jun1613, 02:46 PM

P: 9

Which of them larger? The gravity of the earth to the moon or the gravity of the sun to the moon?




#2
Jun1613, 03:13 PM

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I assume you mean the force of gravity the earth exerts on the moon and the force of gravity the sun exerts on the moon. You could, of course, actually calculate both forces but it seems to me that the fact that the moon orbits the earth, not the sun, says it all.




#3
Jun1613, 03:37 PM

P: 9

of course I mean the gravitational force ,why the moon does not orbit the sun? Is it relate to the difference of amount of gravitational force of each the sun and earth to the moon or related to the different distance of the moon from sun and earth ?




#4
Jun1613, 04:35 PM

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Gravity on the moon 



#5
Jun1613, 04:44 PM

P: 549

But the Moon does orbit the Sun, in very much similar way, if a bit more wobbly, as the Earth does.




#6
Jun1613, 04:46 PM

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The other is that gravitational force not being the right metric to decide whether a body is orbiting some other body. A much better metric is energy. Energy answers the question, "is object A gravitationally bound to object B?" Force is pretty much irrelevant. 



#7
Jun1813, 04:50 AM

P: 62

See this wikipedia article on Hill Sphere.
Moon is closer to Earth therefore its gravitational influence on Moon is more than that of Sun. 



#8
Jun1813, 07:10 AM

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What do you mean by "gravitational influence"? Certainly not force. It's a simple calculation. The gravitational force exerted by the Sun on the Moon is 2.2 times that of the Earth on the Moon. Certainly not potential energy. Now that factor of 2.2 becomes a factor of 850. So what exactly did you mean by "gravitational influence"? I intentionally did not mention the Hill sphere because it's an advanced topic and because it does not answer the question at hand. The question at hand is "why can we say that the Moon is orbiting the Earth?" The Hill sphere doesn't address this question. What answers the question of "why can we say that the Moon is orbiting the Earth?" is mechanical energy. The Moon's mechanical energy with respect to the Earth is negative: The Moon is gravitationally bound to the Earth. The Hill sphere helps address the question of "is the Moon's orbit stable?" The answer is a tentative yes since the mean EarthMoon distance is about 1/4 of the Hill sphere radius and since the Moon's orbital plane is only slightly inclined with respect to the ecliptic. Suppose instead that the Moon's orbit was highly inclined, almost 90 degrees with respect to the ecliptic. We haven't change the orbital radius, so the Hill sphere approach would yield the same answer. This is the wrong answer. A highly inclined lunar orbit doesn't work. The orbit would quickly become very eccentric thanks to the Kozai mechanism, eventually resulting in the Moon crashing into the Earth in a decade or less. The Hill sphere also doesn't answer the question of why distant retrograde orbits are so peculiarly stable. It can take a long time before a DRO goes chaotic. 



#9
Jun1813, 10:53 PM

P: 62

The article I pointed to begins as "Hill sphere is the region in which it dominates the attraction of satellites. To be retained by a planet, a moon must have an orbit that lies within the planet's Hill sphere." So I thought it is good article to read. Thank you for explaining factors that determine stable orbit. 



#10
Jun1913, 09:49 AM

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If you read that wikipedia article on the Hill sphere (it's a rather lousy article IMHO), you see that they define "gravitational influence" as meaning "having the same angular velocity", which to me is rather bogus. Even then, they get the Hill sphere wrong by a factor of √3. The Hill sphere is rather arbitrarily defined as a sphere with origin at the center of the secondary body and with a radius equal to the distance to the L1 point. The wikipedia article doesn't mention that the definition is a bit arbitrary. It does mention that it helps determine if an orbit is stable. Note well: This means that whether an object is orbiting another must be defined by some other metric. Almost nothing orbits forever in the Nbody problem. Orbits are transient. Mercury most likely will be ejected from the solar system in a few billion years due to interactions with Jupiter and Venus. Does the fact that it won't be orbiting several billion years from now mean that it isn't orbiting now? Of course not. 



#11
Jun1913, 10:41 PM

P: 62

I just searched more, and guess what I found? Why does the Moon orbit the Earth rather than the Sun? 



#12
Jul1713, 11:13 PM

P: 365

Earth Gravitational Force greater:
[tex]\frac{G*M_{EARTH}}{R^2} > \frac{G*M_{SUN}}{R^2}[/tex] 


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