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How to Use Newton's Law of Universal Gravitation to Predict Orbital Period and Speed

Newton's Law of Universal Gravitation Orbit
Credit: Public Domain

By Andrew Bennett

Most of us are familiar with gravity as the force the pulls things down toward the ground, but it turns out to be much broader than that. All objects exert gravitational forces on each other. We notice the one from the Earth so much more than from any other object because it is so big and close. We also don't notice the effect of ourselves exerting a gravitational force on the Earth. This is because such a small force doesn't do anything noticeable to something the size of the Earth.

What Is Newton's Law of Universal Gravitation?

Newton's Law of Universal Gravitation says that for any pair of objects, the size of the gravitational forces they exert on each other depends on their masses and the distance between them.

In this video, you will learn about the basic idea of gravitational attraction. Then, you will learn how the Newton's Law of Universal Gravitation equation works. Finally, you will learn how to solve an example problem.

Note: Be sure to watch to the end of the video to discover a neat effect that we see for an object near the Earth's surface!

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Combining Circular Motion, Newton's Laws, and Universal Gravitation

We often find situations in the world that are "crossovers" between several different areas of physics, or of science in general. This is a nice reminder that those divisions are just to help us keep things straight in our heads; there are no real divisions in the phenomena themselves. Orbital motion is one of these cases. It combines what we've done with Newton's laws and circular motion with our understanding of universal gravitation.

In the second video, we start with the premise that one (smaller) object is orbiting another (larger) object and that the orbital path is circular. There are many examples of this, such as human-made satellites and spacecraft, as well as near examples of this, such as the motion of the Earth around the sun or the moon around the Earth. Although these are actually elliptical orbits, they are very nearly circular, so we can still make some good predictions using these methods.

Photo Credit: YouTube Screenshot (https://www.youtube.com/watch?v=B-YZqmdG8AQ)

What Are Orbital Period and Speed?

The orbital period is how long it takes an object to complete one orbit around another object. The orbital speed is how quickly an object moves around the center of its orbital path.

Video: Orbital Period and Speed Equations

In the next video, we combine what we know about forces, circular kinematics, and gravitation to develop equations that predict both the orbital period and speed necessary to maintain an orbit. We also compare our results to the findings described in Kepler's laws based on the observation of our planets. The fact that the predictions made by the equations match the observations was an important way of validating both sets of models.

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Gravitate to My YouTube Channel

For more videos on physics topics ranging from gravity to momentum, check out my YouTube channel. If you want to receive alerts when I publish to this blog, please sign up for email notifications.

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