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Okay, let's review. We've seen how the Sun's position, satellites, and geometry help us survey the Earth.

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But what if we wanted to survey Mars?

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Well, we don't live on Mars, so how do scientists and NASA survey the Red Planet?

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I thought you'd never ask. Let's visit NASA's Jet Propulsion Laboratory in Pasadena, California, and find out.

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What is the Mars Global Surveyor and where is it?

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How does the Mars Global Surveyor use geometry to survey the Martian landscape?

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The Mars Global Surveyor is a spacecraft that is in orbit around Mars.

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Its purpose is to take pictures of Mars, to measure the temperature of the surface and the atmosphere of Mars,

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and to bounce laser signals off the surface of Mars to precisely determine the shape of Mars.

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You might think of Mars as simply being a sphere by looking at pictures of it, but to scientists it has lots of bumps and ridges.

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For example, the poles of Mars are so cold that the atmosphere actually condenses out to form dry ice at the poles.

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And as much as 25% of the atmosphere condenses out into the dry ice at the poles, so there's quite a large change in the atmosphere.

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Also, Mars is known for having a large bulge on the side of it, the largest volcano in the solar system, known as Olympus Mons.

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And so one of the functions of the Mars Global Surveyor was to measure the shape of Mars to carefully determine how big is this bulge.

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It has a huge effect on the orbits of spacecraft. It is such a large bulge on the side.

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The way that we use geometry to convert the laser pulses into the shape of Mars, what we have to do is carefully time how long it takes for the pulses to reach Mars and bounce back to the spacecraft.

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And then we combine that with the shape of the orbit, which we determine by looking at how the radio signal changes as the spacecraft goes around Mars.

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What is aerobraking? How does geometry influence aerobraking?

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Aerobraking is when we use drag from the atmosphere to gradually shrink the orbit down.

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So what we have to do is use the drag from the atmosphere to gradually slow the orbit down so that it would shrink from this highly elliptical 45-hour orbit down to a very circular two-hour orbit around Mars.

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This is geometry in action.