Where does gravitation of earth and sun cancel

[robvba]

Homework Statement

For a spacecraft going from the Earth toward the Sun, at what distance from the Earth will the gravitational forces due to the Sun and the Earth cancel?
Earth's mass: Me
the Sun's mass: Ms
Earth-Sun distance: r

Homework Equations

F=Gm1m2/r^2

The Attempt at a Solution

a bit brain dead. please help

 

[LowlyPion]

Homework Statement

For a spacecraft going from the Earth toward the Sun, at what distance from the Earth will the gravitational forces due to the Sun and the Earth cancel?
Earth's mass: Me
the Sun's mass: Ms
Earth-Sun distance: r

Homework Equations

F=Gm1m2/r^2

The Attempt at a Solution

a bit brain dead. please help

It says where forces cancel. Hmmm... Cancel equal cancel equal which to choose.

 

[robvba]

I figure that F has to equal 0 and that one equation has to equal another.

 

[Rake-MC]

Perhaps try this,

$$\frac{GM_e}{r^2} = \frac{GM_s}{(r_e - r)^2}$$

Can you explain to me why this is the case?

 

[robvba]

Perhaps try this,

$$\frac{GM_e}{r^2} = \frac{GM_s}{(r_e - r)^2}$$

Can you explain to me why this is the case?

gravity experienced due to Earth on the sun = gravity experienced due to sun on the earth...?

 

[Rake-MC]

No, this equation is slightly different.

It's from $$a = \frac{GM}{r^2}$$

So you can see it only takes into account 1 mass. It's saying that at distance 'r', this is the acceleration caused by mass M. Regardless of the mass of the object it's acting on.

 

[HallsofIvy]

Perhaps try this,

$$\frac{GM_e}{r^2} = \frac{GM_s}{(r_e - r)^2}$$

Can you explain to me why this is the case?

It's impossible to "explain" without knowing what the variables mean! I can guess that "r_e" is either the radius of the Earth distance from the Earth to the space ship, but neither of those makes this formula true. Once denominator should be the distance from the Earth to the space ship, squared, and one should be the distance from the sun to the space ship, squared. Is r the distance from the Earth to the sun and r_e the distance from the sun to the earth? Robva initially designated r as the distance from the sun to the earth. If you meant r_e as the distance from the Earth to the space ship, then the denominator on the left has to be r_e².

 

[Rake-MC]

Sorry yes I should have explained. I think G and the two masses speak for themselves. r is the distance you are solving for (where gravitational force of both masses are equal). r_e is the mean distance from the centre of the Earth to the centre of the sun.

But by re-reading his variables I realize I got r and r_e backwards.

[tex]
\frac{GM_e}{r_e^2} = \frac{GM_s}{(r - r_e)^2}
[tex]

So I re-wrote it with his variables. r being the distance from Earth to sun. r_e being distance we're solving for.

Apologies.

EDIT: I've solved the equation and it works.