https://youtu.be/wy8gi1JqeF4
PHYS 1101: Lecture Fourteen, Part Eight
The last example I want to do is a satellite. It’s a classic case of simple uniform circular motion. It’s on a very different scale. We’re not use to thinking of it this way, but the physics is exactly the same. It behaves and follows the same laws of physics just as the puck does on a rope going around in a circle, you on a roller coaster hitting a corner, a box in a trunk as the car rounds the corner. It’s all the same physics governing the motion. But of course some details are going to be different.
Here’s what we’ll do. Our problem is, there is a satellite that is placed in orbit above Mars. Mars has a radius of 3,397 kilometers and a mass of 6.4 times ten to the 23rd kilograms. The mission of the satellite is to observe the Martian climate from an altitude of 488 kilometers. We’ve got to figure out the orbital period of the satellite.
The object undergoing uniform circular motion is definitely the satellite. Let me draw my satellite. I have no idea what satellites look like, but I’m going to do that. This object is going around Mars following a circular path. They’re not telling me which snap shot to consider here so it’s up to me.
I’m going to put the object here at the top for the snapshot that I care about. Right away on this I’m going to sketch that any object with circular motion is not in equilibrium. I have to have acceleration toward the center. I’m looking for a net force that has to point toward the center of that orbit.
What forces do I have? There is nothing touching the satellite. It’s out in space around Mars, no contact forces. But there definitely is a long range gravitational force on this satellite that’s due to the large mass of Mars itself.
Let me sketch that force in. The only force I have is a long range gravitational force. This is the gravitational pull from Mars. How big is it? Is the size “M” times “G” like we do on the surface of the Earth? No. Not “M” times “G.”
Once we’re away from the surface of a planet or even in this case we’re not on the planet Earth, we can’t use the typical force due to gravity anymore. We have to go and understand the general equation, the general physics behind gravitational forces. Let’s do that first because we have to figure out the magnitude of this force. What determines it?