Does Centrifugal Force Hold The Moon Up?

December 31, 2019 Patrick DelVecchio

Newton's Revolutionary Idea

Nothing Holds The Moon Up!

Do you think centrifugal force keeps satellites in orbit? If you have this mistaken belief, do not feel bad, you are in good company. None other than Werner Von Braun himself, one of the original rocket scientists, shared this view. He incorrectly explained orbits by claiming that centrifugal force cancels gravity. If this were the case, the satellite would fly off in a straight line away from Earth. As it turns out, the correct explanation is that the orbiting satellite is falling towards Earth.

“In the 1960s, Wernher von Braun put together a series of articles about space flight, some of which were published in Popular Science Monthly. … In one of the articles, von Braun explains why a satellite is able to stay up while in Earth orbit.

… 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?

… 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.” – Don Koks

If you are interested in this subject, I highly recommend reading Don Koks’ article, ”Does centrifugal force hold the Moon up?”. That fascinating article inspired this particular blog entry.

• Patrick DelVecchio

16th Century Artillerie • Wikimedia Commons

Let’s take a proper gander at Newtonian physics

Sir Isaac Newton’s great insight was that we could use projectile physics to explain the motions of orbiting bodies.

Picture from a 1550 edition of: "De sphaera mundi" (On the Sphere of the World). The most influential astronomy textbook of the 13th century. • Wikimedia Commons

Let’s Take A Look At Globular science

Line of Sight and Earth’s Curvature

The surface of Earth is supposed to curve away from the horizon so that one end of an 8000-meter straight line is 4.9 meters higher than the other. This fact would help Sir Isaac Newton explain the motions of Earth's moon, as we shall see later.

Illustration exaggerated for effect.

Earth is a globe.

Altitude is defined as the distance from Earth’s center. Up and down means away from and towards Earth’s center.*

Horizontally Launched Projectiles

“Let's return to our thought experiment from earlier in this lesson. Consider a cannonball projected horizontally by a cannon from the top of a very high cliff. In the absence of gravity, the cannonball would continue its horizontal motion at a constant velocity. This is consistent with the law of inertia. And furthermore, if merely dropped from rest in the presence of gravity, the cannonball would accelerate downward, gaining speed at a rate of 9.8 m/s every second. This is consistent with our conception of free-falling objects accelerating at a rate known as the acceleration of gravity.” • www.physicsclassroom.com

In the absence of gravity, fired cannonballs move further away from Earth’s center, gaining altitude.

“If our thought experiment continues and we project the cannonball horizontally in the presence of gravity, then the cannonball would maintain the same horizontal motion as before - a constant horizontal velocity. Furthermore, the force of gravity will act upon the cannonball to cause the same vertical motion as before - a downward acceleration. The cannonball falls the same amount of distance as it did when it was merely dropped from rest (refer to diagram below). However, the presence of gravity does not affect the horizontal motion of the projectile. The force of gravity acts downward and is unable to alter the horizontal motion. There must be a horizontal force to cause a horizontal acceleration. (And we know that there is only a vertical force acting upon projectiles.) The vertical force acts perpendicular to the horizontal motion and will not affect it since perpendicular components of motion are independent of each other. Thus, the projectile travels with a constant horizontal velocity and a downward vertical acceleration.” • www.physicsclassroom.com

Frame from the only surviving hand-colored print of Georges Méliès's 1902 film Le voyage dans la lune. • Wikimedia Commons

The Moon Is Falling

“Newton realized that the moon's circular path around the earth could be caused in this way by the same gravitational force that would hold such a cannonball in low orbit, in other words, the same force that causes bodies to fall.” • Michael Fowler, Physics Dept., U.Va.

Newton’s Thought Experiment

“The mountaintop at V is supposed to be above the earth's atmosphere, and for a suitable initial speed, the projectile orbits the earth in a circular path. In fact, the earth's curvature is such that the surface falls away below a truly flat horizontal line by about five meters in 8,000 meters (five miles). Recall that five meters is just the vertical distance an initially horizontally moving projectile will fall in the first second of motion. But this implies that if the (horizontal) muzzle velocity were 8,000 meters per second, the downward fall of the cannonball would be just matched by the earth's surface falling away, and it would never hit the ground! This is just the motion, familiar to us now, of a satellite in a low orbit, which travels at about 8,000 meters (five miles) a second, or 18,000 miles per hour. (Actually, Newton drew this mountain impossibly high, no doubt for clarity of illustration. A satellite launched horizontally from the top would be far above the usual shuttle orbit, and go considerably more slowly than 18,000 miles per hour.)” • Michael Fowler, Physics Dept., U.Va.