# physics -gravity

• Oct 30th 2010, 06:33 AM
MK47
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? (Headbang)
thanks.
• Oct 30th 2010, 07:00 AM
skeeter
Quote:

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? (Headbang)
thanks.

let $\displaystyle M$ = mass of Io

$\displaystyle 4000M$ = mass of Jupiter

let $\displaystyle R$ = distance between Io and Jupiter

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

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

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