Calculating orbital parameters for given requirements

Question

I'm trying to determine what's the best way to calculate the required orbit for a LEO remote sensing satellite. I understand there exists the trade-off between sensor coverage and sensor accuracy, but I'm just trying to find something quantitative to start with.

Say I have some generic requirements;

• I want the satellite to have maximum coverage over a country's landmass (e.g. all of India is scanned)
• The revisit rate is to be maximised

Assuming I have an arbitrary swathe width of 500Km, how do I calculate the orbital altitude and inclination such that I can maximise a country's coverage and do it as fast as possible?

Thanks for any guidance!

Answer 1

Obviously this is an optimization problem and should be solved as such if you are looking for actual solutions but as a back of the envelope calculation I suggest tuning the inclination of the orbit to get a change in Right Ascension ($\Delta \Omega$) which results in the ground track shifting +- 500km eastwards over successive orbits.

The formula for $\Delta \Omega$ due to the earth oblateness ($J_2$) goes as follows:

$$\dot{\Omega} = -[\frac{3}{2}\frac{\sqrt{\mu}J_2 R^2}{(1-e^2)^2a^{\frac{7}{2}}}]\cos{i}$$

Assuming you have a circular orbit with a fixed semi-major axis (You have your swath width as a fixed input, which I assume comes from some FOV and an altitude), you can determine the inclination from this formula by taking into account earth rotation and then finding out how much the RAAN should change over one orbit to result in a 500km shift in ground track.

Obviously you will need a certain minimum inclination to be able to fully image the entire landmass of India.

This is far from an optimal solution, for which you would have to perform an optimization including coverage analysis in your cost function.