# Math Help - physics -gravity

1. ## physics -gravity

Io is the largest of Jupier's moons with a mass 1/4000 of the mass of Jupiter.
The distance between the two bodies is 4.22x10^8m. Find the distance from Jupiter at which the resultant gravitational field is from the two bodies is zero.
Do i use Fc=Fg?
and find out the mass of Jupiter and the moon.
then use F=-Gm1m2/r^2 to work out the force on Jupiter,put the force back into mrw^2 with Io's mass and work out the radius? or am i completely work?
thanks.

2. Originally Posted by MK47
Io is the largest of Jupier's moons with a mass 1/4000 of the mass of Jupiter.
The distance between the two bodies is 4.22x10^8m. Find the distance from Jupiter at which the resultant gravitational field is from the two bodies is zero.
Do i use Fc=Fg?
and find out the mass of Jupiter and the moon.
then use F=-Gm1m2/r^2 to work out the force on Jupiter,put the force back into mrw^2 with Io's mass and work out the radius? or am i completely work?
thanks.
let $M$ = mass of Io

$4000M$ = mass of Jupiter

let $R$ = distance between Io and Jupiter

let $x$ = distance from Jupiter where $a = 0$

$\displaystyle \frac{GM}{(R-x)^2} = \frac{G(4000M)}{x^2}$

solve for $x$ in terms of $R$ ... then sub in your given value for $R$