Problem 45800. SatCom #6: Inclination of a Sun-Synchronous Orbit

Satellite and Space Engineering - Problem #5
This is part of a series of problems looking at topics in satellite and space communications and systems engineering.
A particularly interesting (and useful) orbit is the 'Sun-Synchronous Orbit.' This orbit has the special feature that the plane of the orbit precesses (rotates) in inertial space at exactly the same rate as the earth rotates around the sun. Therefore, the orbit plane always maintains a fixed angle with respect to the sun, which means that the satellite always passes over the same point on the ground at the same local mean solar time. Now, satellite orbits, in the absence of external forces, will not precess, but will remain on a plane fixed with respect to inertial space. However, the unequal forces on the satellite caused by the equatorial bulge of the Earth tends to make inclined orbits precess, and by tuning the orbit inclination and altitude (actually the semi-major axis and eccentricity of the orbit ellipse), the orbit can be made to precess at just the right angular rate to maintain a fixed direction towards the sun. (See: <https://en.wikipedia.org/wiki/Sun-synchronous_orbit> for more information about such orbits.)
You are given the satellite orbit's apogee and perigee altitudes (in km). Calculate the inclination needed to achieve a sun-synchronous orbit.
You should take the radius of the Earth to be 6371km.
Hint : If you are not sure about how to derive the semi-major axis and eccentricity of the orbit given its apogee altitude, perigee altitude and the Earth's radius, you probably ought to try Problem 45797. SatCom #5: Determine Elliptical Orbit Parameters first ( <https://www.mathworks.com/matlabcentral/cody/problems/45797-satcom-5-determine-elliptical-orbit-parameters> ).
Example: The CLOUDSAT satellite has an apogee of 710 km and a perigee of 709 km. It's orbit inclination is approximately 98.2 degrees.
Some future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!
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Last Solution submitted on Mar 18, 2025

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