Question

can you walk me through this problem

At what distance from the Earth will a spacecraft on the way to the Moon esperience zero net force due to these two bodies because the EArth and Mon pull with equal and opposite forces?

mass of earth = m1 = 5.98 E 24 kg
mass of moon = m2 = 7.36 E 22 kg
radius moon to earth = 3.84 E 8 m = r1 + r2
r1 = radius satalite to earth
r2 = radius satalite to moon

Answer 1

You haven't done what I suggested.
Pick an object, massm, and find the force of gravity on it from the Earth, let the distance be x. Then the same object, the force of gravity on it from the Moon, distance 3.84E8-x, then set the two forces equal, and solve for x.

Answer 2

m3 = mass of satalite

(G m3 m2)/x^2 = (G m3 m1)/(3.84 E 8 m - x)^2

I can cancel out the m3 and the G right?

Answer 3

ok so I got down to this

x = sqrt( ((m1 + m2)(3.84 E 8))/m2 )

which gave me the wrong answer