# Question Video: Relating a Satellite’s Height above Earth to Orbital Period Physics • 9th Grade

The table shows the height at which three satellites orbit Earth. Each satellite follows a circular orbit. Which satellite takes the longest time to orbit Earth? Which satellite takes the shortest time to orbit Earth? Eutelsat 113 West A is a geostationary satellite. How long does it take to orbit Earth?

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### Video Transcript

The table shows the height at which three satellites orbit Earth. Each satellite follows a circular orbit. Which satellite takes the longest time to orbit Earth? Which satellite takes the shortest time to orbit Earth? Eutelsat 113 West A is a geostationary satellite. How long does it take to orbit Earth?

To answer these questions, we’ll need to refer to the table, which includes information about how high above Earth’s surface each satellite orbits. According to the table, Terra orbits at a height of 709 kilometers above Earth’s surface. ICESat-2 orbits at 496 kilometers above Earth’s surface. And Eutelsat 113 West A orbits at 35800 kilometers above Earth’s surface. Let’s begin with the first part of the question and determine which satellite takes the longest time to orbit Earth. What we’re comparing then is each satellite’s orbital period, which is the amount of time it takes for it to complete one full orbit around Earth. Let’s recall the factors that determine a satellite’s orbital period.

For the special case of circular orbit, like we have here, a satellite’s orbital period depends on the mass of the large body that it’s orbiting and how far away the satellite is. In this question, all of the satellites are orbiting the same thing, Earth. So we can compare their orbital periods just by comparing their distances from Earth. When a satellite is farther away from Earth, it moves slower than it would if it were closer to Earth and it has to travel a longer path in order to complete an orbit. Because of this, a satellite that’s farther away has a longer orbital period.

Now we’re being asked which satellite has the longest period. So we can just think about which satellite is farthest from Earth. Looking at the table, it’s clear that Eutelsat 113 West A is the farthest from Earth. In fact, it’s about 50 times farther from the surface than Terra and over 70 times farther from the surface than ICESat-2. Therefore, we know that Eutelsat 113 West A takes by far the longest time to orbit Earth.

Moving on, let’s think about which satellite takes the shortest time to orbit Earth. We’ve already established that the farther away a satellite is, the longer its orbital period. So it makes sense that a satellite closer to Earth has a shorter orbital period because it moves faster and doesn’t have to travel as far to complete an orbit. Here, we wanna know which satellite has the shortest orbital period. So we just have to identify which satellite is closest to Earth. Again, referring to the table, we can see that out of these three satellites, ICESat-2 is closest to Earth. Therefore, we know ICESat-2 takes the shortest time to orbit Earth.

In the last part of this question, we’re told that Eutelsat 113 West A is in a geostationary orbit. We wanna know how long it takes to orbit Earth or what its orbital period is. First, we can think about what it means for a satellite to be geostationary. The title tells on itself; it’s still with respect to Earth. This effect is achieved by orbiting above the equator in the same direction that Earth spins on its axis, west to east.

And in order to be stationary with respect to Earth’s surface, the satellite has to complete one full orbit in the same amount of time it takes Earth to complete one full rotation. One full rotation of the Earth, or one day, takes 24 hours. This is the orbital period required for a satellite to be in geostationary orbit. Therefore, we know that it takes 24 hours for Eutelsat 113 West A to orbit Earth.