Setting up binary star (light density based on distance) problem

[oogabuga]

For my vector calc class we were given an assingment to do some stuff with a binary star system. You might note the lack of vectors and the lack of calc; this is because I am just having an issue with the setup. I am sure I can get the rest without assistance.

We are given the two stars of equal light intensity. One at the origin and the other at (0,0,14).

The light intensity 'L' at a point 'P' is given with L=(1/(D1^2))+(1/(D2)^2), where D1 and D2 are the distances from the two stars.

So what is a formula for L in rectangular coordinates (x,y,z)?

I tried playing around with with the equation for an ellipsoid for a while but that seemed fruitless. Also a sphere (with rad = sqrut(D1^2+D2^2), but gave up on that.

Any pointers? If you are feeling ambitious I will also need to find this is spherical coordinates, but I have yet to play with that myself...

 

[zachzach]

Well what is $$D1$$ and $$D2$$ in rectangular coordinates? Draw a graph and put the two stars on it. Then put a random point on the graph at $$(x_0, y_0,z_0)$$. To find $$D_1$$ draw a vector from the origin (where star 1 is) to the point. What is the magnitude of this vector? To find $$D_2$$ draw a vector from $$(0,0,14)$$ (star 2) to $$(x_0,y_0,z_0)$$. What is the magnitude of this vector?