In the above expression is G the same for all planets, or is this value only for earth?
I think it's universal. For example, this could be used to calculate the gravitational force between Mars and Earth and isn't really much use for objects that fit on the Earth as their masses aren't large enough.
I think it's universal. For example, this could be used to calculate the gravitational force between Mars and Earth and isn't really much use for objects that fit on the Earth as their masses aren't large enough.