Difference between force equations?

[Sammy1024]

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I think there's 2 force equations:

F = GMm/r^2 and
F = GMe/Re where e stands for Earth.

I was wondering when do you know which one to use?

I was doing this problem:
Suppose you are standing on the surface of the Earth with a baseball of mass m. How fast would you have to throw the baseball horizontally, so that it never landed on the Earth?

And the answer was:

and they had used the top equation and simplified it, but how do you know which one to use? Thank you! :]

 

[syoung]

Well... it basically comes from combining F = GMm/r^2 and F = mv^2/r

 

[Sammy1024]

So I can use the first equation 100% of the time, and if it happens to reduce to the second equation then I use the second equation? Like the first equation is the official equation and the second equation is a result depending on the question?

 

[syoung]

Yep. Consider what variables you are given.

 

[Sammy1024]

Thanks! :]