Ok, this extra credit assignment is driving crazy. I keep trying to put it away and work on something important, but it can't get it out of my mind.(adsbygoogle = window.adsbygoogle || []).push({});

The full question is:

On the agonic line between Earth and Mars lies the agravic point with respect to the gravitational fields of the two planets. Determine the location of that point as a function of the locations of both Earth and Mars.

I assume they are talking about the point between the planets where the force of gravity of the earth equals the force of gravity of mars.

I've tried a few different things to get a formula that would tell me how far from earth the point would be if the distance between them was known. It keeps leading me to a quadratic with no real solution if the distance between them is large.

Even if I can figure out what I'm doing wrong there, I'm not totally sure it's what the question is asking. What do they mean by "as a function of the locations of both planets"? Shouldn't I be free to set up my own coordinate system with Earth at the origin?

Here's what I have so far:

G = gravitational constant

Me = mass of Earth

Mm = mass of Mars

x = distance between the center of the Earth and the agonic point (I think this should end up being the dependant variable)

d = distance between the Earth and Mars (I think this should be the independent variable)

Since I want to find the point where the gravitational field of the Earth is equal to the gravitational field of Mars, I set them equal to each other.

[tex]\frac{G*Me}{x^2}=\frac{G*Mm}{(d-x)^2}[/tex]

The G's cancel, after a little algebra, I end up with:

[tex]d^2-2dx+(x^2-\frac{Mm}{Me}x^2)[/tex]

If I try to solve this for x I end up with a negative under the square root sign if d is large.

Can someone help me out with this? Am I even getting close?

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# Homework Help: Agravic point between planets

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