ESA, the European Space Agency, has made space more accessible to some new users as can be seen from the Vega VV02 launch Tuesday morning. Riding up with the Proba-V was Vietnam's VNREDSat 1A and Estonia's ESTCube-1 student satellite. Tracking satellites visually can be difficult because they have to be in sunlight to be seen and then daytime is too bright and at night this just leaves times just before sunrise and after sunset when they are not in the Earth's shadow. ESTCube-1 sends out coded messages on two amateur radio frequencies. This suggests the possibility that one can use the Doppler Effect to acquire some information about the satellite's location. Consider what happens when the satellite makes a close approach to a known position, x0, of the Earth's surface.
To use this information we need to relate the shape of the frequency curve to range and velocity of the object. One can derive the following set of formulas where omega is the angular frequency and c the velocity of the transmitted wave.
One gets the formula used to plot the frequency curve which contains two unknown parameters, the minimum distance, xm here, and the velocity. The velocity can be found from the minimum and maximum ratios of the transmitted frequency and the observed frequency. The close approach distance can then be estimated by fitting it to the frequency observations. So it's not too difficult to estimate the range and velocity at the time of close approach. One may want to keep tabs on ESTCube-1 since it will be testing an e-sail tether in an attempt to make controlled changes to its orbital parameters.