00:02
We know that for the circular orbit of the space vehicle about the moon, the force acting on the space vehicle, f is equal to m v squared over r, where little m is the mass of the space vehicle, v is a speed of its orbit, and r is the radius of its orbit about the moon.
00:23
But the law of gravitation tells us that this is equal to g, and the mass of the moon and the mass of the sun.
00:33
Space vehicle divided by the square of the distance between them, the square of the orbit, r squared.
00:40
So if we equate these two, we can see that we can formulate an expression v squared, where v is the speed of the orbit.
00:49
And v squared is equal to gm over r.
00:55
So we can use this equation, and we can find the circular orbit a.
01:01
So the initial circular orbit squared is equal to and we'll just subtrude our values in here so that's 66 .73 times 10 to the minus 12 meter cubed kg per square second so we'll just suppress the units now times 73 .49 times 10 to the 21 and that's kg so again that's si unit that's the mass of the moon over the radius of the orbit for a is 2 ,200 times 10 to the 3 meters and hence if we take the square root of that we get the circular speed or the speed of the circular orbit of the satellite orbit a is 1 ,493 meters per second now we can do the same for the circular orbit b so so bb squared is equal to, again, we'll substitute our values in here...