Video: Motions of Planets, Moons, and Satellites

In this lesson, we will learn how to describe the velocities and accelerations of planets, moons, and man-made satellites that are moving along circular orbits.

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Video Transcript

In this video, we’re talking about the motion of planets, moons, and satellites. All of these objects move in what are called orbits. An orbit is a cyclical path typically around some other larger body. For example, the Earth orbits around the larger body of the Sun. And there’s a smaller moon that orbits around the Earth as well as all the satellites that orbit around Earth too. The motion of these bodies through space all comes down to the influence of one specific force, the force of gravity.

Now, gravity is an interesting force because any object that has any mass at all will tend to exert this force on other objects with mass. Say, for example, we put another object here. When we do, this object will be affected by a gravitational pole created by this first object. If we drew in that force as a vector, it would look like this. It would point from the second object towards the center of the first one. And by the way, this attractive force works the same in both directions. Just as the larger body exerts a force on the smaller one, the smaller body exerts a force on a larger one which has the same magnitude. But when it comes to motion, this smaller body will tend to move more because it has less mass.

Now, as the force of gravity has been investigated over time, it’s been discovered that distance has something to do with this force. If we were to take a third mass which had the same exact mass as this second one we placed here and position it farther away from our original object. Then this mass would still experience a gravitational force from the larger mass on the far right. But it would be smaller. It would be weaker. And if we put an identical mass still farther away from our original object, the force on that mass from the object would be weaker still. So far then, there are three things we can say about this force of gravity.

First off, any pair of objects, so long as those objects have mass, experiences a gravitational force. This means that two pencils sitting on our desktop, two cars driving down the road, or a planet orbiting a star, all have a gravitational force in between them. A second thing we can say about this force is that the force of gravity always attracts, and it never repels. Notice the direction of the arrows of the force acting on these three identical bodies from the larger one. The force of gravity always pulls other objects in, and it never pushes them away. And thirdly, we can say that the closer two objects are, the stronger the force of gravity between them. Another way of saying this is the farther apart objects are, the weaker the forces. And again we saw this with our three identical objects placed different distances away from our original mass. As the objects got farther away, the force on them got weaker and weaker.

Keeping all this in mind, let’s say that we’re now in outer space. And in this space, thanks to a formation process that’s been going on for many years, we have a star. Now, things would be pretty uninteresting if this was the only thing that existed in the whole universe. Because remember, for the force of gravity to have an effect, we need to have at least two objects. Well, look at this. Here comes a second object moving along past our first one. Now that we have two objects to consider, we know that the force of gravity will be acting on them. If we were to sketch in a line that goes from the center of our one object to the center of our other object, then along this line there will be a force acting on the moving object and an equal but opposite force acting on our star.

Now, depending on how strong this force is and how fast our object in motion moves, a few different things can happen. One possible outcome is that even though there’s this attractive force which tends to pull this body in motion towards the star. It could be that this object is moving so fast that it escapes the pole of the star. In that case, the objects trajectory might look like this. Yes, it is being pulled towards the star, as we can see from the path slightly bending. But that pole isn’t strong enough to bring this moving object in a regular, steady orbit around the star.

But let’s say that instead of the object moving very fast compared to the force acting on it, it’s moving very slow. In that case, the force of gravity will be the dominating influence on this object’s motion. The fact that it was already moving in a certain direction won’t have a strong effect. If that’s true, then the path of this moving object might look like this. Following a curved line path that we see here, it’s drawn into the star and eventually crashes into its surface. We can see that this path also doesn’t lead to a steady regular orbit around the star. But if the initial conditions are just right, if the velocity of this planet points in a certain direction, and if the planet speed has a particular relationship to the force of gravity acting on it. When all these factors balance out just right, this moving object is able to start moving around the star in a regular path, an orbit.

Any time we see an object in orbit, we’re witnessing a delicate balance between attractional forces of gravity and object motion. And, in general, there are two types of orbits that an object can have. If we clear a little bit of screen space, we can see what these types are. The first kind of way that a smaller body could orbit a larger one is by moving in a circular path, a circular orbit, around it. This is how we often see orbits drawn in sketches. But, actually, it’s the exception rather than the rule when it comes to orbital pairs. It’s much more common for objects to move in what are called elliptical orbits. An ellipse looks like a circle that’s been squished or flattened. And ellipses themselves can have different shapes. Some are more like a circle, and some are less.

Now, when an object is moving in a perfectly circular orbit around some other object. Then there’s a particular relationship between the gravitational force acting on the moving object and its velocity. For a circular orbit, an object’s velocity is always perpendicular to the gravitational force acting on it. This isn’t always true, though, for objects that have an elliptical orbit. In those cases, there’s usually not a 90-degree angle between the object’s velocity and the force acting on it. Speaking of object velocity, let’s consider this elliptical orbit in green. We saw from our three observations about gravity that the closer two objects are together, the stronger the force is between them.

This means that, for our object that’s in an elliptical orbit around the star, when the object is here in its orbit, the force of gravity acting on it is stronger than when it’s here. That’s because the distance between the star and the object in this case is smaller than the distance between the star and the object here. All of this has an influence on the object’s velocity. When the object is closer into the star, not only is the gravitational force on it stronger, but its velocity is greater as well. This object in elliptical orbit then will be moving fastest when it’s closest to the star it orbits. And it will be moving slowest when it’s farthest away.

We can take this idea and apply it to our own solar system. In this system, we have a star, our sun, being orbited by eight planets. And these planets have varying distances from the sun. Some are closer; some are farther away. What we’ve seen here in this example is that the closer an orbital object is to the object it orbits, the faster it’s moving. And this principle holds true for the planets in our solar system. The fastest moving planets are the ones closest to the sun. With mercury, the closest planet of all, being the fastest moving of all. And then, on the other end of things way out here we have Neptune, the slowest moving planet.

Talking about faster or slower moving objects in orbit brings up a term called orbital period. An object’s orbital period is the amount of time it takes to go through one complete revolution of its orbit. So, for example, if we track the Earth through one complete revolution of its motion, we know that this takes about 365 days. That’s its orbital period. Now, let’s think for a moment on a bit of a smaller scale about objects that orbit Earth. So here’s our Earth. And besides the moon, we know that there are also man-made objects which orbit our planet. Along with satellites used for communication of various kinds, we’ve also constructed a satellite called the International Space Station. The orbital period for the International Space Station is only about 90 minutes. In other words, it goes through one complete revolution of its orbit every hour and a half.

But imagine we wanted to make a satellite which stayed over the exact same location on Earth’s surface as the Earth rotated. In other words, as the Earth turns on its axis, we would want a satellite to stay over one particular spot, say this one right here, even as that goes on. In that case, we would send up a satellite to be at that location, and its orbital period would need to be the same amount of time that it takes the Earth to spin on its access. We know it takes 24 hours for that to happen. So that would be this satellite’s orbital period. Satellites like this that stay over the same location on Earth’s surface at all times have a special name. They’re called geostationary satellites. From the name, we can tell that these satellites stay still. They’re stationary over the Earth. In order for this to be true for a satellite to stay over the same spot of the Earth at all times, it needs to be in orbit above the Earth’s equator.

Knowing all this about orbiting objects, planets, moons, and satellites, let’s get a bit of practice using an example.

The diagram shows two different possible orbits of an object around a star. Which of the following correctly describes the shape of orbit a)? A) Elliptical, B) Circular, C) Helical, D) Spiral, E) Highly elliptical.

All right, taking a look at our diagram, we see these two orbits marked a) and b). And this question focuses on orbit a). We want to know which of these five paths correctly describes this particular orbit. Now, the first thing we can do is recall that whenever one object is in orbit around another one, there are two possible paths that that orbiting object can follow. Orbital paths are either circular or they’re elliptical. These are the two allowed shapes we could say for orbital motion. That eliminates two of our possible answer choices, option C and D. Helical and spiral are not allowed orbital paths.

At this point, we can recall the difference between these two allowed orbits of circles and ellipses. We all know what a circle looks like. And an ellipse looks like a circle that’s been squished or compressed. So if this was a circular orbital path, an elliptical path would look something like this. Now, we can see that our three remaining answer choices are elliptical, circular, and something called highly elliptical. For an orbit to be highly elliptical, we could think of that as a very compressed circular orbit. The squishing, we could say, has gone even farther to create something that looks like this. This would be an example of a highly elliptical orbit. So which of these three — elliptical, circular, or highly elliptical — is the orbit marked out in a)?

We can see that this orbit does not look like a compressed circle, but rather it just looks like a circle itself. It’s definitely not highly elliptical then. We’ll cross off option E. And we also don’t think it’s elliptical. The shape of orbit a) is circular. Now, let’s consider the same question, but about orbit b).

Our next question asks, which of the following correctly describes the shape of orbit b)? A) Circular, B) Spherical, C) Highly elliptical, D) Spiral, E) Helical.

Just like before, we can cancel out any answer options which are neither circular nor elliptical. As we’ve seen, those were the only two possible paths that an orbiting body can have. So this means that option B, spherical, option D, spiral, and option E, helical, are off the table. So then, orbit b) is either circular or it’s highly elliptical. If we revisit our sketch of a circular orbit, an elliptical orbit, and a highly elliptical orbit marked out in yellow, we can clearly see that orbit 𝑏 is not circular. This eliminates option A. And as we consider highly elliptical as a description of this shape, we see that there’s a match. This orbit has a very compressed or squished look compared to a circular orbit. And, therefore, it is highly elliptical. This is the correct description of the shape of orbit b).

Let’s take a moment now to summarize what we’ve learned about the motion of planets, moons, and satellites. First off, we saw that all orbiting objects, planets, moons, and satellites move in orbits due to the force of gravity. We saw that gravity, first, exists between all objects that have mass. Second, it always attracts and never repels. And, third, that it gets stronger the closer two objects are together. We learned further that when an object is in orbit, it follows either a circular or an elliptical path. And, lastly, satellites that stay over the same spot on Earth are called geostationary. This means that they have an orbital period of 24 hours.

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