00:01
Although satellites orbit parent bodies in ellipses, we're going to simplify the situation with gravity and put a satellite in a circular orbit.
00:15
So what we know is that there is a force holding the mass around the planet in a circular orbit.
00:25
And we'll call that a centripetal force.
00:28
It is also equal to newton's force of gravity, which comes about as g, the product of the two masses, divided by the separation between the centers of the two masses squared.
00:47
Now we also know from circular motion that the centripetal force must be equal to mass times centripetal acceleration.
00:58
According to newton's second law.
01:07
So that centripetal force is equal to the mass of the orbiting satellite times centripetal acceleration, which we know to be v squared, the tangential speed of the satellite over the distance to the center of the planet.
01:31
Now we can just simply put in the gravitational force, and we see that we can find the velocity of the satellite.
01:41
The mass does not matter, and one factor of r will cancel, giving us v is equal to square root of gm over r.
01:57
We can also use this if we needed to calculate the kinetic energy of that satellite, one half mv squared and the square root will go away and give us something that looks like an energy.
02:28
A reminder that the potential energy, gravitational potential energy, is negative because of the attraction.
02:37
And it's just minus gm, m over r.
02:41
So we see that there is a nice relationship between the kinetic energy and the gravitational potential and the total energy, which is just the sum of those two, is then minus half the potential energy.
03:02
This is a very solid result coming about due to the inverse square nature of the force...