Does centrifugal force hold the Moon up?

Answer 1

In the 1960s, Wernher von Braun put together a series of articles about space flight, some of which were published in Popular Science Monthly. Eventually they were collected and made into the book Space Frontier, (1st ed., Holt, Rinehart and Winston). It's a very readable book, and talks about how rockets work, and flight and safety in space. In one of the articles, von Braun explains why a satellite is able to stay up while in Earth orbit.

He begins the article by asking what would happen if we could throw an object horizontally, but at faster and faster speeds, such as in the picture shown here. "Eventually", he writes, "the curvature of the downward-bent trajectory would become equal to the curvature of the earth." This is well and good. (It's not quite right to say that the curvatures are the same, even for circular motion, but it's good enough.) The important point is that as the bullet moves faster and faster, a magical speed is reached where the curved Earth drops away from the bullet precisely as fast as the bullet falls to the ground; added to which, the direction of "down" keeps changing. As a result, the bullet never gets any closer to the ground--it's in orbit. This is actually a marvellous special feature of an inverse square force like gravity; it would not be guaranteed to happen if gravity were not inverse square. In general, orbits are ellipses, and one such is drawn on the left. A picture just like this was originally included by Sir Isaac Newton in his Principia of 1687.

After this fine start, von Braun then proceeds to muddy the water. He says that as the bullet is shot at ever faster speeds, "its trajectory will be less deflected because the centrifugal force is increased by its higher speed, and more effectively counteracts the Earth's gravitational pull." At this point physicists baulk. Centrifugal force? What has that got to do with satellite motion?

Next, von Braun draws a picture of a satellite in Earth orbit. Acting on the satellite are two forces: gravity, pulling the satellite toward Earth, and this centrifugal force, pushing the satellite away. He writes "A circular orbit occurs whenever a small mass, travelling through the gravitational field of a big one, happens to have a speed at which the centrifugal force is precisely strong enough to balance the large body's gravitational pull." And later, "If the balance between gravitational and centrifugal force is not perfect, [...] the small body will describe an elliptical path around the large one."

What would Newton say? He too would draw the forces acting on the satellite, and would then proceed to apply his "force = mass × acceleration"; but first, he'd want to choose an "inertial frame" within which to do this, since his laws only work in inertial frames. An inertial frame is one in which, if we throw a ball, it moves away from us with constant velocity (i.e. constant speed in a straight line). Since this doesn't quite happen on Earth, the frame Newton would choose would be something more all-encompassing, outside of Earth. One good approximation would be the frame of the Solar System, within which the sun is at rest and the Earth revolves fairly accurately in a circle around it, once a year. An inertial frame like this is presumably what von Braun is using, because anything noninertial won't tie in too well with his picture of Earth plus satellite.

In an inertial frame, if there really were two equal but opposite forces on the satellite as von Braun drew them, then the total force on it would be zero. So it wouldn't accelerate; it would move in a straight line with constant speed. Since the orbiting satellite doesn't move in a straight line, the picture drawn by von Braun can't be right.


Nothing holds the Moon up!

In reality, nothing holds the Moon up. As Newton's inertial frame analysis predicts, the Moon is completely under gravity's thrall; in other words, it falls, because in such a frame there's only one force on the Moon: gravity. Gravity accelerates it. That doesn't mean its speed must necessarily change, or that it must get closer to Earth (although actually both of these things do occur slightly during the month, but that's not an important point). If Newton's F=ma is solved for the general case of falling under gravity, the motions that result are lines, circles, ellipses, parabolae, and hyperbolae. In one of those great correspondences between Nature and pure mathematics, these are precisely the curves that result if we take a cone and slice it in any direction.

Even if the Moon's orbit were circular, its direction of travel would still be changing, which is one kind of acceleration. (Remember that acceleration is a change in velocity, meaning that acceleration can change an object's speed, or it can change merely the direction of motion, or both.) The Moon, and every other satellite, fall just as surely as an apple does when pulled down by gravity. Whereas the apple changes its speed but not its direction of motion, the Moon changes its direction of motion, but not its speed. The real difference between a satellite and an apple falling from a tree, is that for the fast sideways-moving satellite, the direction of "down" is always changing. But the satellite really is falling, and in fact a near-Earth satellite has almost the same acceleration that a falling apple has. If it's above us now, then in about 45 minutes, for a low satellite, it will have fallen so far down that it'll be on the other side of Earth. By then, the direction of down has reversed completely, and the satellite will again fall down for those who live on the opposite side of Earth, returning to us about 90 minutes after we first saw it. Of course, it never hits Earth because of its ever-present sideways motion. The Moon is much further away, where gravity is weaker, so it takes fully two weeks to fall to the other side of Earth..

Answer 2

If there was only the centrifugal force the moon would get out of the solar system.

Answer 3

When a body revolves in a circle, (then from the frame of reference of this body,) it experiences a force radially outward. It is the centrifugal force. Gravitational pull by the earth acts in the opposite direction and balances this centrifugal force. It prevents the moon from accelerating in the radial direction. (and from falling on earth)

Answer 4

^ What Stardust stated is actual spectacular. think of you have have been given one among those little bungee cords. in case you pull on one end, that end gets plenty nearer to you. the middle of the cord basically gets somewhat nearer to you. the different end of the cord keeps to be the place it is. yet once you have been an ant status interior the direction of the cord, you will possibly think of that the two ends of the cord had have been given extra faraway from you. you think of which you, interior the middle, are sitting nonetheless, so which you think of the two ends are moving faraway from the middle. Tides are a similar way. The moon pulls the sea on the close part in direction of it plenty. And it pulls the rocky center of the earth in direction of it somewhat. Then the sea on the a techniques part keeps to be the place it became, and what you get is two tidal bulges. it extremely is very much oversimplified, however the factor is to visualise that the moon isn't PUSHING the sea away on the a techniques part to make a bulge. it rather is actual pulling the rock surprising out from under the water to make a bulge.

Answer 5

No, centripetal force is responsible.In centripetal force, if force stops acting, body will move outside the orbit.In centrifugal it will move in.

Answer 6

Well all I know is because earth is round, by the time moon commes close to earth the surface of the earth bends, and the speed is too much for the earths gravity to pull it back. all it manages to slow it down and then the moon starts faling again. The cycle continues!

Answer 7

Wow, somebody knows how to cut and paste. (The first answer.)

The short answer is: no.