Expert: Courtney Seligman - 11/22/2010

Question
Dear expert,

thank your previous answer.


If a tiny ball is stuck thanks to a glue on the border of a spinning disk, the quicker the disk spins, the greater is the centrigufal force F (=ball mass.(v˛/radius plate) exerting on the ball,

but from a precise speed, the glue won't be strongh enough to fix firmly the ball, and the latter's movement relative to the disk would be affected.

That's when F centrifugal > F glue


So i tried to apply the same calculation to Earth motion on Moon:

we know Earth exerts 1.98E20 N on the Moon
and the centrifugal force on Moon due to Earth's revolution velocity:

Fc= Moon's mass*(Earth velocity˛/Earth orbital radius)
Fc=4.35E20 N

But that's greater than Earth's force on Moon,
so if the calculation are correct, the Moon should have been greatly afected.


But indeed, the experience shows us that's not the case, so could you tell me where my caculation and reasoning were wrong?

                                        


                                           Sincerely

Answer
I haven't seen the forces involved expressed as actual forces, but as accelerations (that way, you don't need to know the mass of the satellite, which is often unknown or uncertain):

gravitational acceleration g = GM/r-squared
vs
orbital acceleration a = v-squared/r

where r would be the average lunar distance of 388 thousand kilometers, v the average lunar velocity of 1023 meters per second, M the Earth's mass of 5.97 x 10^24 kilograms, and G the gravitational acceleration of 6.674^-11 (kg/m/s units).

A quick calculation yields:

g = .00270 m/s-squared
and
a = .00272 m/s-squared

Since the individual numbers involve some round-off error, I'd say the two values are the same (as they must be); so there is something wrong with one of your values. To check which, the values can be multiplied by the lunar mass (7.35^22). That gives results around 2^20, so your initial statement about the force exerted on the Moon appears to be correct, but the subsequent calculation of the force required to keep the Moon in its orbit is off by a factor of two. Since you don't show your work, I don't know how you made the error, but that's where it lies.