00:01
Hi there, so for this problem, we are told that a satellite in a circular orbit that is 500 miles is above the surface of the earth.
00:18
So the question is, what is the period of the orbit? so we need to determine that period.
00:23
Now, first of all, we consider that the radius of the earth is equal to 4 ,000 miles.
00:37
The gravitational constant, we're also given that value.
00:41
The mass of the earth, let's label this as capital m, is 5 .98 times 10 to the 24.
00:52
And we know that the number of meters in a mile is, so we know that 1 ,6009 meters equals to 1 mile.
01:12
So with that said, the first, well, for this to obtain the period, we're going to use kepler's law that states that a period of an orbit is four times pi to the square times the separation distance to the three.
01:35
And this divided by the gravitational constant times the mass of the object, in this case, the mass of the earth.
01:43
Now this value r is equal to the 4 ,000 miles of the radius of the earth plus the 500 miles that we are given.
01:54
So this will give us 5 ,000 and 4 ,500 miles.
02:05
So now we need to convert this from miles to meters.
02:11
And for that we multiply this by a factor of conversion that we are given for this, then this in meters is equal to 7.
02:37
Okay, that will be 7 .2 ,4005 times 10 to 6 meters...