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

Right.

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

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

Combined:

[tex]M_{object}V_{object}^2/R = GM_{earth}M_{object}/R^2[/tex]

[tex]V_{object}^2/R = GM_{earth}/R^2[/tex]

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