Centripetal vs Centrifugal force

Hi. So basically I was confused between these 2 forces. Although I understand the difference.
But we know that for an object orbiting the Earth, the centripetal force is provided by the gravitational force.
That is mg = mv²/r ( or GMm/r² = mv²/r)
So technically it should mean that if the gravitational force is 50N, then centripetal force should also be 50N? Or no?
But if we simply apply the formula of centripetal force for Earth by putting radius and stuff, we get a really small value? So how come they are equalled?
Is it something to do with Centrifugal force or what?

Reply 1

lordaxil

You are forgetting about the reaction force for an object in contact with the Earth's surface.

The formulae for weight and centripetal force are only exactly equal when there are no other forces acting (e.g. the object is in free-fall, like a satelite in orbit, for instance). It turns out that when you put numbers in, the weight of a 5 kg object is far in excess of the centripetal force needed to keep it moving on the Earth's surface at the equator without flying into space. Otherwise, if you walked off a cliff, you would just float there in midair, like Wile E Coyote (I do not advise trying this).

The difference betwee reaction force and weight is not normally noticeable because scales and pan balances are calibrated to the local gravitational field. However, at maximum extent (about 0.3% of the object's weight) it is big enough to be important if you are selling things like precious metals. I heard a story about merchants being able to make a profit just by moving gold from equator closer to the poles, but not sure that is really true.