During orbit which two forces are in balance

One good approximation would be the frame of the Solar System, within which the Sun is at rest and 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, neither von Braun's picture nor his explanation can be right. 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.

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 farther away where gravity is weaker, so it takes fully two weeks to fall to the other side of Earth.

Centrifugal force was invented to allow us to do proper bookkeeping in a noninertial frame, if we insist on using such a frame to work with Newton's laws and there might be a good reason for wanting to do so.

For a simple example of a noninertial frame, consider what happens when you stand in a bus while the driver brakes. For a few moments, every passenger moves forward. The heavier ones feel a strong force that acts on their large mass, while the lighter ones feel a small force acting on their small mass.

All feel the same acceleration. This is called a fictitious force, because it's a force that we invoke to explain why we are suddenly accelerated forward. In the almost inertial frame of the outside street, this force doesn't exist. The real force there is a single simple one provided by the friction of the ground on the bus tyres, and transmitted through its brakes to its body. This force accelerates the bus backwards—or, to use the more intuitive expression, decelerates the bus.

Unless the passengers hang on, they will continue to move forwards until something inside the bus stops them. Depending on our choice of frame then, there are two forces to choose from when analysing why the passengers are impelled forward:. In the inertial street frame, there is a braking force that pushes backwards on the bus. This is a bona-fide force, in the sense that it's produced in an inertial frame. It acts on the bus only, so unless we hold on, we'll continue to move forward at constant velocity.

In the noninertial frame of the decelerating bus, the force is a mysterious force that acts on us, but not on the bus. It pushes us forwards, and has a strength that is proportional to how massive we are. These two forces have to remain in perfect balance. If anything changes the other force has to change as well. This is Newton's first law. Any object that tends to go in motion has to stay in motion as well. And so we have two motions. We have the orbit that's going all the way around. And gravity that's pulling it in.

If either of these changes the other would change as well. So lets say our big planet simply disappeared. Well that moon all of a sudden doesn't have a gravitational pull and it would just shoot off into space.

Or lets say that the moon suddenly stops. All of a sudden it's momentum around the planet or the sun would stop and that moon would shift and fall into either the planet or the sun. It fall into the larger object of mass.

Any of these values is also equal to the centrifugal force produced at the center-of-mass C by its revolution around the barycenter.

This fact is indicated in Fig. The Effect of Gravitational Force. While the effect of this centrifugal force is constant for all positions on the earth, the effect of the external gravitational force produced by another astronomical body may be different at different positions on the earth because the magnitude of the gravitational force exerted varies with the distance of the attracting body. According to Newton's Universal Law of Gravity, gravitational force varies inversely as the second power of the distance from the attracting body.

Thus, in the theory of the tides, a variable influence is introduced based upon the different distances of various positions on the earth's surface from the moon's center-of-mass. The relative gravitational attraction Fg exerted by the moon at various positions on the earth is indicated in Fig. It has been emphasized above that the centrifugal force under consideration results from the revolution of the center-of-mass of the earth around the center-of-mass of the earth-moon system, and that this centrifugal force is the same anywhere on the earth.

Since the individual centers-of-mass of the earth and moon remain in equilibrium at constant distances from the barycenter, the centrifugal force acting upon the center of the earth C as the result of their common revolutions must be equal and opposite to the gravitational force exerted by the moon on the center of the earth. This fact is indicated at point C in Fig.

The net result of this circumstance is that the tide-producing force Ft at the earth's center is zero. At point A in Fig. The smaller lunar gravitational force at C just balances the centrifugal force at C.

Since the centrifugal force at A is equal to that at C, the greater gravitational force at A must also be larger than the centrifugal force there. The net tide-producing force at A obtained by taking the difference between the gravitational and centrifugal forces is in favor of the gravitational component - or outward toward the moon.

The tide-raising force at point A is indicated in Fig. The resulting tide produced on the side of the earth toward the moon is know as the direct tide. At point B, on the opposite side of the earth from the moon and about 4, miles farther away from the moon than is point C, the moon's gravitational force is considerably less than at point C. At point C, the centrifugal force is in balance with a gravitational force which is greater than at B. The centrifugal force at B is the same as that at C.

Since gravitational force is less at B than at C, it follows that the centrifugal force exerted at B must be greater than the gravitational force exerted by the moon at B. The resultant tide-producing force at this point is, therefore, directed away from the earth's center and opposite to the position of the moon.

This force is indicated by the double-shafted arrow at point B. The tide produced in this location halfway around the earth from the sublunar point, coincidentally with the direct tide, is know as the opposite tide.

The Tractive Force.