Calculating the mass of a central object by observations of an orbiting satellite (assumes orbital plane is very close to ecliptic)

RLM 27 Nov 2006

0. Define a few useful constants

1. Enter observed x positions (pixel units) and times (fractional hours)

Number of observations

Observed data with error estimate (s).

1. Time units are fractional hours

2. Displacement (x) in pixel units

Sinusoidal model

2. Enter best-fit model parameters guesses, adjust for rough fit on plot

Guesses for semi-major axis (pixels), adjust for rough fit in plot below

3. Use solve block to find least-sqares best fit for R, P, f

Now use MathCAD'ssolve block, minerr function to get best least-squares fit

Find model parameters which minimize sum of squared differences between model and data

4. Convert fitted parameters to physical units, use Kepler '3rd law to solve for central mass

Convert solution to real units

Fractional error:

known answer