Formula for gravity/circular motion in terms of V? (i think )

[tman12345]

If F=mg, and Fc=Fg, Fc=mv2/r (thats v squared; my apologies, i have no idea how to use the superscript button), and Fg=Gm(1)m(2)/r2 (squared), where m(2) is the mass of, say, the earth, and m(1) is the mass of the object orbiting the earth. By substituting these equations together, we get

mv2/r=Gm(1)m(2)/r2,

and we can cancel out the r on the left, and the m (which is mass). but I have a problem; which mass is canceled out on the right side? is it the mass of the object or mass of the earth?


thanks

 

[Doc Al]

Which do you think? Which mass is executing circular motion as it orbits the other? Which mass are you finding the centripetal force on?

 

[tman12345]

I think i am supposed to be finding it with respect to the earth, so I believe then the mass of the Earth is what is left

 

[Doc Al]

I think i am supposed to be finding it with respect to the earth, so I believe then the mass of the Earth is what is left

Right.

Force on orbiting object due to gravity: $$F = GM_{earth}M_{object}/R^2$$

Applying Newton's 2nd law to orbiting object: $$F = M_{object}V_{object}^2/R$$

Combined:

$$M_{object}V_{object}^2/R = GM_{earth}M_{object}/R^2$$

$$V_{object}^2/R = GM_{earth}/R^2$$

 

[natives]

Cancel out mass of object in revolution,thats the mass acted upon by the centripetal force.

 

[tman12345]

thanks a lot! that really helped.
next time ill try to not leave my physics book at school over the weekend