Mathematica: How to use a single equation with multiple parameters to calculate any parameter

Question

Hi,

Currently I use a single equation with different combination of known/unknown parameters. As I don't have any fancy calculator it would be much easier to define the equation in Mathematica and passing known parameters to calculate unknown values.

I would be very thankful if anyone of you could give an example solution (if possible using given equation).

Let's say we have an equation of satellite speed at given point in the elliptical orbit:

v = sqrt(u(2/r - 1/a))

where

v = speed u = constant 3.986 * 10^14 m^3/s^2 r = radius (distance from the center of the Earth) a = semi major axis of the ellipse

This equation can be used to calculate the speed or for example we know what is the speed needed for a manoeuvre to move the cargo to other orbit and have to model the orbit (a) at given radius (r)

Thanks!

Answer 1

You can define equations in Mathematica using the ":=" operator. To define the example equation:

v[u_, r_, a_] := Sqrt[u*(2/r-1/a)]

I'm not sure how to generalize it to solve for any unknown...If I figure it out I'll get back to you.

You may want to try something like:

Solve[v[1, r, 7]==15, r]

that will solve for r assuming you know v, u, and a... you can then change each of the paramaters for the unknown...