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4.2 Centripetal Force and Planetary Orbits

4.2.1 Centripetal Force (and the Centrifugal Pseudo-Force)

Have you ever wondered why planets follow nearly circular rather than straight paths? Or why the planets continuously orbit the Sun rather than just falling into or flying away from it? Well, in short, the answer is centripetal (and centrifugal) force—a force that is derived from Newton’s laws of motion.

Centripetal force acts in a direction perpendicular to an object’s linear velocity and, as a result, it accelerates said object by changing its travel direction (rather than its travel speed; remember velocity has a magnitude and direction!). Assuming the object’s speed doesn’t change from some other external force, the centripetal force will continuously cause the object to change its direction by some amount, leading that object down a curved rather than straight path. You might hear centripetal force referred to as a center-seeking or center-pulling force.

It’s important to note that centripetal force is not its own, separate kind of force. Other forces in physics, like gravity, friction, and tension, actually provide the centripetal force needed to maintain curved or circular motion. For example, gravity provides the centripetal force for orbiting planetary bodies. If gravity didn’t act as a centripetal force in the cosmos, planetary orbits would not exist!  Let’s learn more about centripetal force and the physics behind planetary orbits below. (Note: Some of the content that you read and watch in this section will be repetitive, but that is intentional. Hearing and reading concepts explained in many different ways is the key to learning after all!)

Watch the below two videos by Khan Academy AND read this online article: Lucas, Jim. “What are centrifugal and centripetal forces?.” Live Science, 4 Sept 2024.

 

4.2.2 Motions of Satellites and Spacecraft

Newton’s universal law of gravitation and Kepler’s laws describe the motions of Earth satellites and interplanetary spacecraft as well as the planets. Sputnik, the first artificial Earth satellite, was launched by what was then called the Soviet Union on October 4, 1957. Since that time, thousands of satellites have been placed into orbit around Earth, and spacecraft have also orbited the Moon, Venus, Mars, Jupiter, Saturn, and a number of asteroids and comets.

Once an artificial satellite is in orbit, its behavior is no different from that of a natural satellite, such as our Moon. If the satellite is high enough to be free of atmospheric friction, it will remain in orbit forever. However, although there is no difficulty in maintaining a satellite once it is in orbit, a great deal of energy is required to lift the spacecraft off Earth and accelerate it to orbital speed.

To illustrate how a satellite is launched, imagine a gun firing a bullet horizontally from the top of a high mountain, as in Figure 4.6, which has been adapted from a similar diagram by Newton. Imagine, further, that the friction of the air could be removed and that nothing gets in the bullet’s way. Then the only force that acts on the bullet after it leaves the muzzle is the gravitational force between the bullet and Earth.

Figure 4.6: (a) For paths a and b, the velocity is not enough to prevent gravity from pulling the bullet back to Earth; in case c, the velocity allows the bullet to fall completely around Earth. (b) This diagram by Newton in his De Mundi Systemate, 1731 edition, illustrates the same concept shown in (a). [Figure 3.11 Firing a Bullet into Orbit (2022), Andrew Fraknoi/David Morrison,/Sidney Wolff, CC BY 4.0]

If the bullet is fired with a velocity we can call va, the gravitational force acting upon it pulls it downward toward Earth, where it strikes the ground at point a. However, if it is given a higher muzzle velocity, vb, its higher speed carries it farther before it hits the ground at point b.

If our bullet is given a high enough muzzle velocity, vc, the curved surface of Earth causes the ground to remain the same distance from the bullet so that the bullet falls around Earth in a complete circle. The speed needed to do this—called the circular satellite velocity—is about 8 kilometers per second, or about 17,500 miles per hour in more familiar units.

For Further Exploration

Use the Newton’s Mountain simulator to see for yourself the effects of increasing an object’s speed. You can raise the speed until you find the speed that is just fast enough for an object to orbit the Earth, the circular satellite velocity, and also the speed at which an object leaves the Earth forever, or the escape speed.

Each year, more than 50 new satellites are launched into orbit by such nations as Russia, the United States, China, Japan, India, and Israel, as well as by the European Space Agency (ESA), a consortium of European nations. Today, these satellites are used for weather tracking, ecology, global positioning systems, communications, and military purposes, to name a few uses. Most satellites are launched into low Earth orbit, since this requires the minimum launch energy. At the orbital speed of 8 kilometers per second, they circle the planet in about 90 minutes. Some of the very low Earth orbits are not indefinitely stable because, as Earth’s atmosphere swells from time to time, a frictional drag is generated by the atmosphere on these satellites, eventually leading to a loss of energy and “decay” of the orbit.

Watch either one or both of the below videos that summarize why satellites orbit Earth rather than fall to its surface.

4.2.3 Orbital Motion: Putting the Math Together

At this point, we’ve learned about Newton’s laws of motion, Newton’s law of universal gravitation, Kepler’s three laws of planetary motion, and centripetal force, all of which help describe and predict the orbital motion of the planets throughout the cosmos. Watch the below video, which discusses planetary orbits in the context of many of these mathematical principles, for a big picture review.

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Introduction to Planetary Geology Copyright © by Dara Laczniak is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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