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## Homework Statement

How far from Earth must a space prove be along a line toward the Sun, so that that the Sun's gravitational pull on the probe balances the Earth's pull

## Homework Equations

F=Gm1m2/d^2

## The Attempt at a Solution

d1=distance from probe to Earth

distance from sun to earth = 1.50x10^11 m

distance from the sun to probe = 1.5x10^11 m - d1

mass of earth = 5.98x10^24 kg = m2

mass of sun = 1.99x10^30 kg = m3

m1 = mass of probe

I set the force on the probe from earth equal to the force on the probe from the sun to get:

(Gm2m1)/d1^2 = (Gm1m3)/(d1^2-(3.0x10^11)d1+2.25x10^22)

When I solve for d1, I do not get the answer which is 2.6x10^5 Km. It could easily be a math error, but the fact that I have to use such tedious calculations makes me wonder if I am doing the problem correctly, especially as the mass of sun, mass of earth, distance from sun to earth are not given.

(Gm2m1