Orbital uncertainty

The amount of sunlight that a satellite receives during an orbit is critical to planning operations. In a prior post I examined the changing orientation of the orbital plane with respect to the Sun which is described by the beta angle. In another post I detailed the large uncertainty in tracking CubeSats that are simultaneously deployed. This uncertainty causes difficulty in calculating the beta angle from the early orbital elements and introduces error in predicting the number of hours of sunlight per day. It takes about 40 days for a group of CubeSats to spread apart enough that they can be individually tracked to generate orbital elements that have decent long term accuracy for predicting the beta angle.

One way to generate an early estimate of the beta angle and the amount of sunlight is to use the orbital elements for the International Space Station (ISS) from which the satellites were deployed. All of the CubeSats should have similar orbits that are very close to the ISS. There are some errors in using this method but it can be useful for a short while if care is taken in interpreting the results. This method has the advantage that calculations can be done before deployment.

Percent sunlight for ISS and EQUiSat
Percent sunlight for ISS and EQUiSat.

The above plot shows the percent sunlight that the ISS receives per orbit. The orbital elements from January to early July were used to project these values for the rest of the year. The calculations for the Brown Space Engineering EQUiSat satellite launched in July 2018. The values are based on the orbital elements from September – after the 40 day instability of the early published elements. The two curves are very similar with a slight offset in the timing and amplitude of the peaks. That offset is mostly negligible with an important exception.

Percent sunlight error
The difference between the ISS estimate of sunlight and EQUiSat.

The above plot shows the difference between a good calculation for EQUiSat and the ISS estimate. The error is mostly less than 2.2% of an orbit which corresponds to a 1/2 hour error in exposure to sunlight per day. Near the time of a beta angle maximum the errors grow to 10% which is 2 1/2 hours per day. The errors are symmetrically plus and minus so the total amount of sunlight per month is similar for both. It is just the timing of the maximum that is shifted a few days. The exact amount of sunlight on a particular day could be off within a range of 5 hours per day. But these results are good enough to plan expectations for solar power and temperature during a particular week. This could be used for the first month or so until better methods become possible.

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