00:01
The gravitational acceleration on the moon's surface is about one -sixth that on the earth's surface, and the radius of the moon is about one -quarter that of the earth.
00:11
The problem wants us to find the mass of the moon in terms of the mass of the earth.
00:15
So let's go ahead and write out newton's gravitational force law.
00:22
F -big -g equals g -m -1, m -2 over r squared.
00:27
And let's go ahead and use this equation on a test mass on the test -mass on the earth -b -g equals g -m -1 -2 over r -squared.
00:31
The moon first.
00:33
So let's give this test mass a mass of m and that'll have an acceleration of m -a, i'm sorry, am, and the right side will be g.
00:45
M -1 will be the mass of the test mass, and m -2 is the mass of the moon, divided by the radius of the moon because the object is on the surface of the moon.
00:57
And what we want to find is this m here so m will be equal to we can cancel out the test mass so that m m is equal to a m r m squared multiplied by 1 over g so now we can plug in the relationships over here on the left into this equation so that we get 1 6th a xe times one -fourth r e squared the whole thing squared over g that is a g let me turn that into a better -looking g and we want to find m m in terms of the earth's mass so now let's go ahead and apply newton's gravitational force law on a test mass on the earth so f big g equals big g m1 and m2 over r squared...