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Circular Velocity & Escape Velocity

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  • 0:01 Circular Velocity
  • 2:24 Geosynchronous Satellite
  • 3:00 Escape Velocity, Open…
  • 5:10 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov
This lesson will describe the concepts of circular velocity, escape velocity, open orbits, closed orbits, and geosynchronous satellites. It will provide the equations necessary for you to be able to calculate out circular and escape velocity as well.

Circular Velocity

Have you ever wondered how fast a satellite up in space has to be traveling to stay in circular orbit around the Earth?

The velocity an object needs to have in order to orbit another larger object in a circle is called circular velocity. An object traveling at circular velocity obviously travels in a circle, but one traveling just under or just over this velocity travels in an elliptical orbit. While our solar system bodies (namely the planets and their natural satellites) travel in very slightly elliptical orbits, we'll just say they're circular for simplicity's sake for this lesson.

Circular Velocity Formula
circular velocity formula

That being said, there's actually quite a simple formula for circular velocity on screen where it is equal to the square root of G, the gravitational constant of 6.67 X 10 ^-11 m^3/s^2kg, multiplied by M, the mass of the larger (central) object in kilograms, and divided by the radius, R, of the orbit in meters.

I used the word 'satellite' before, but that word doesn't necessarily refer to a man-made satellite. The Moon is Earth's natural satellite as well. Let's figure out the Moon's velocity then.

Earth has a mass of 5.98 X 10^24 kg, and the moon is in orbit around Earth 3.84 X 10^8 m from Earth's center. Just plug away to get an answer of 1,020 m/s, or about 2,278 mph.

Note how the equation shows you that circular velocity is inversely proportional to the square root of the radius. This means a smaller orbit will result in a faster speed because the force of gravity on the smaller object will be stronger.

To demonstrate this, you can tie a rope to a marble and spin it in a circle. The marble is like a small object in orbit around your hand, the bigger object. Start twirling the marble in front of you in a circle. Then, stick your finger out so that the string begins to loop around your finger. As it loops around your finger, the string gets shorter (R gets smaller), and the marble spins faster and faster until it hits your finger and stops.

Geosynchronous Satellite

While the Moon is a satellite of Earth, it isn't a geosynchronous satellite of Earth. A geosynchronous satellite is simply a satellite that remains above the same spot on Earth's surface. It does so by orbiting around the Earth in an eastward direction, completing its orbit every 24 hours. This happens at about 42,000 kilometers from the Earth's center. If the satellite was much closer to Earth's center, right above Earth's atmosphere, it could have an orbital period of only 90 minutes as it travels at 7,790 m/s, way faster than the moon.

Escape Velocity, Open & Closed Orbits

Circular orbits, and technically the slightly elliptical orbits of our solar system's planets and satellites, are all a type of closed orbit. This is a circular or elliptical orbit that returns to the same place in its orbit over and over.

If you spin that marble in a circle above your head and keep your hand steady, the marble will return to the same point in space over and over again as it circles around. It does so because it's in a closed orbit. It has nowhere to go but stay in that circle, which is, by definition, a closed shape.

In a circular orbit, the speed of an object is the same throughout its orbit. In elliptical orbits, the smaller object's speed is faster as it nears the larger object.

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