A satellite orbits a planet of unknown mass in a circle of...

A satellite orbits a planet of unknown mass in a circle of radius 2.0 x 10^7 m. The magnitude of the gravitational force on the satellite from the planet is F = 120 N A). What would be the magnitude of the gravitational forces exerted on the sattelite by the planet if the radius of the orbit were increased to 3.0 x 10^7 m ? B). if the satellite circles the planet once every 2.0 h in the largest orbit, what is the mass of the planet?

Transcript

00:01 In this video, i'm going to be looking at orbital motion and the gravitational force law.

00:06 Okay, so what we have is a satellite orbiting a planet.

00:10 We don't know the mass of the planet, but we can still define the variable mass of planet.

00:16 Okay, so we have the satellite mass as well.

00:19 So we have mass of planet, mass of satellite.

00:22 We're told that this satellite orbits the planet with a radius r sub -s of 2 .0 times.

00:30 10 to the 7 meters.

00:34 Okay.

00:35 We're told that the gravitational force between the planet and the satellite at this radius is f sub g equals 120 new new neutens.

00:49 And what we want to do is find the new gravitational force between these two.

00:55 So i'll call that f sub g new equals what? if we change the radius from its initial value of 2 .0 times 10 to 7 meters to, i'll call that r -sub -satellite new equals 3 .0 times 10 to the 7 meters.

01:21 So how do we solve this? we're going to need to use that universal gravitational law.

01:27 So that says f sub g equals mass 1 times mass 2 times g, the gravitational constant, divided by the distance between the two objects squared.

01:42 Okay, so for my first situation, we have mass of the planet times mass of the satellite times that g, okay, divided by r sub s squared.

01:57 Okay, and we're given the value of that.

02:00 That's 120 newtons.

02:04 Okay, let's do the same thing for when we increase that radius.

02:08 So i'll call that f sub -g -n.

02:14 Okay, and that's going to equal mass of the planet times mass of the satellite times g.

02:23 Okay, divided by r -s -sub -n squared.

02:28 Okay, and we do not know what that equals yet.

02:31 That's what we're solving for.

02:33 Okay, so how do we solve this? what i'm going to do is divide f sub g by f sub g n.

02:41 Okay.

02:43 So we have f sub g divided by f sub g.

02:50 Okay, so that's going to be mass of the planet, mass of the satellite, gravitational constant divided by r sub s squared.

03:04 Okay, divided by mass of planet, mass of satellite, g, divided by rsn squared.

03:19 Okay, and we'll see that every term is gone except for those radiuses squared.

03:27 So this just gives me r -s -n squared over r -s -s -squared...

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