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