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 Subject: Sun's gravitational force Category: Science > Astronomy Asked by: sousme-ga List Price: \$2.00 Posted: 04 Nov 2002 18:29 PST Expires: 04 Dec 2002 18:29 PST Question ID: 98953
 ```The sun is 320,000 times as massive as the earth, but only 400 times as far from the moon as the earth is. Therefore the force of the sun's gravity on the moon should be twice as big as the earth's and the moon should go around the sun instead of around the earth. Since it doesn't, Newton's theory of gravity must be wrong!" What's the matter with this reasoning?```
 ```The attractive force of gravity is proportional to the mass of the two objects in question and to the square of distance. Mass of the earth: about 6 x 10^24 kg Earth-moon distance: about 384,000 km Mass of the sun: about 2 x 10^30 kg Sun-moon distance: about 150,000,000 km The sun's gravitational pull on the moon is proportional to 2 x 10^30 / (1.5 x 10^8)^2 = about 8.8 x 10^13 The earth's gravitational pull on the moon is proportional to 6 x 10^24 / (3.84 x 10^5) = about 4 x 10^13 Sure enough, the sun pulls on the moon harder than the earth does! Sounds crazy, doesn't it? Consider the earth by itself - it would orbit the sun pretty much like it does now. Consider the moon by itself - it would orbit the sun pretty much like it does now. We say that the moon orbits the earth because it's convenient. But it's more true to say that the moon orbits the earth and the sun. The earth and the sun orbit the center of our galaxy. The galaxy and the sun don't so much orbit as go pretty straight (there's a mind-boggling amount of mass in a galaxy - hard to change its direction!) If you trace the path the moon makes in space, it's a spiral around the sun. The earth also orbits in a spiral because of the affect the moon's gravity has on our planet. Since the earth is rather more massive than the sun, the moon moves more than the earth does in response to the gravitational attraction the two share, but both bodies orbit the sun.``` Request for Answer Clarification by sousme-ga on 06 Nov 2002 12:23 PST `How come the moon isn't pulled away from the earth then?` Clarification of Answer by haversian-ga on 07 Nov 2002 10:46 PST ```As I said, both the moon and the earth orbit the sun. Since they are at (about) the same distance and moving at (about) the same angular velocity, they have (about) the same orbit. One way to think about it is to smash the earth and the moon together into one bigger mass situated at the current center of mass of the earth-moon system. This new planet would orbit the same way the center of mass of the earth-moon system orbits currently. Now that you know how the center of mass moves, you can put the earth and moon back where they belong, revolving around that point as it in turn revolves around the sun. Just as the gravity of the sun doesn't tear the earth apart (the eastern and western hemispheres are tied together with gravity, just like the earth and moon are), it doesn't tear the earth-moon system apart. If this isn't making sense, do you want me to look for some basic orbital mechanics sites to point you to that might have helpful drawings?```
 ```Hello haversian, A useful web reference that may help you understand the issue of gravitational forces can be found at http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html#isqg It all relates to the "inverse square law". regards rcd-ga```
 ```You may be interested to know that the path of the Moon's orbit is everywhere concave toward the Sun. Sometimes when people draw it as a sinusoid (more or less) superimposed upon the nearly circular orbit of the Earth around the Sun, it is sketched as convex to the sun inside the Earth's orbit and concave toward the Sun outside. In fact, it is nowhere convex inward. So in that sense the moon does orbit the Sun with only a small perturbation by the presence of the Earth.```