# Gravitation Problem (stuck on Algebra )

1. Mar 30, 2004

### NanoTech

Gravitation Problem (stuck on Algebra!!)

We just started Gravitation in my Physics class. Here is the problem:
How far from Earth must a space probe be along a line toward the Sun so that the Sun's gravitational pull on the probe balances Earth's pull?

Sorry I'm really bad with the Latex programming and it will take forever to do so here are my calculations. The first part is naming the variables.
Me = Mass of Earth
Ms = Mass of Sun
m = mass of space probe
r1 = dist. from center of Earth to probe
r2 = dist. from center of the Sun to probe

$$\frac {GMem}{r1^2}$$ = $$\frac {GMsm}{r2^2}$$

First I substituted r2 = d-r1 , where d is the distance from center of earth to sun.

$$\frac {Me}{r1^2}$$ = $$\frac {Ms}{(d-r1)^2}$$

Ok, here's the Algebra part that I can't figure out...

Sorry , I have no idea how to write this in Latex!!!

r1 = d squareroot of Me / squareroot of Ms + Me

I don't know how to get to that, what is the Algebra. Or a simple analogy for me to understand it? Thanks. ~David Wilkerson

Last edited: Mar 30, 2004
2. Mar 30, 2004

### Chen

You almost finished it yourself...

$$G\frac{M_em}{r_1^2} = G\frac{M_sm}{r_2^2}$$
Becomes:
$$\frac{M_e}{r_1^2} = \frac{M_s}{r_2^2}$$

The other equation is:
$$d = r_1 + r_2$$
As you said. Two equations, two unknowns, you can solve it.

$$\frac{M_e}{r_1^2} = \frac{M_s}{(d - r_1)^2}$$