How to get the distance from the Sun when the net gravitational force exerted by the

[Littlemin5]

Homework Statement

Find the point between Earth and the Sun at which an object an be placed so that the net gravitatinal force exerted by Earth an the sun on this object is zero.

Me=5.98 x 10^24kg
Ms=2 x 10^30kg
Distance from sun to earth= 1.5 x10^11m

Homework Equations

F=Gm1m2/r^2 --> not sure if this is right?

The Attempt at a Solution

So I tried to manipulate the situation and thought I could do:
When x equals the distance from the sun.

(G(Ms)) / x^2 = (G(Me))/ (d-x)^2

When I plugged in the numbers though I got 1.49x10^11m as my answer. I don't feel like this is right because it's pretty much the full distance between them. Is this not the way to do it, and if not how do I go about doig this problem?

 

[cepheid]

Newton's law of gravitation is certainly right ;-)

Your method looks fine to me. Think about it intuitively. The sun is ridiculously huge, right? In fact, the sun is SO much more massive than anything else in the solar system, that it plays a dominant role over all of the gravitational interactions that occur. In this case, that means that your object has to be MOST of the way along the distance from the sun to the Earth before Earth's gravity starts to dominate. I mean, I think you can see from your numbers exactly how this result came about. The sun is more massive by six orders of magnitude (a factor of a million!)

Keep in mind also that the distance of the object from the Earth (1.5 - 1.49 hundred billion) is nothing to sneeze at (in human terms).

0.01 x 10^11 m = 10^9 m = 10^6 km

So out of the 150 million kilometres distance from here to the sun, the object has to travel a million kilometres away from Earth before the sun's gravity begins to dominate. That may only be a fraction of the distance to the sun, but it's still a million kilometres.

 

[Littlemin5]

When you explain it like that then my answer makes more sense. Thanks so much though for clearing that all up!