I have come across a problem that has had me stumped for a while now.

A spacecraft is in a Sun-synchronous Earth orbit with a =1.40 R⊕ and e = 0.2. The argument of periapsis is ω = 0◦ , and the Right Ascension of the Ascending Node, Ω, is equal to the Sun’s Right Ascension plus 12 hours. Calculate the length of time per orbit for which the spacecraft is in Earth’s shadow, assuming that the Earth is at an equinox.

I'm not fully sure how to interpret this, as everywhere I read, Sun-synchronous orbits are always sunlit?

Any help or a point in the right direction would be much appreciated.

  • $\begingroup$ How sun-synchronous orbits really work is not a trivial thing to understand, or even explain, especially because of the substantial inclination of the Earth's axis relative to its orbit around the Sun. But I'm sure that nowhere reasonable have you read that "...Sun-synchronous orbits are always sunlit" though they are possible. If you can find a link, or cite a paragraph with block-quotes describing what it is that you've read, maybe we can figure out the disconnect there. A high orbit that follows the terminator (dusk/dawn) can in principle remain in Sunlight essentially all of the time. $\endgroup$ – uhoh Jan 7 '18 at 2:47
  • $\begingroup$ There may be a very rare eclipse of the Sun by the Moon, but those can be predicted and the orbit planned to avoid them. Take a look here for more info... en.wikipedia.org/wiki/Sun-synchronous_orbit#Technical_details Also check out this video youtu.be/4K5FyNbV0nA It is possible that this simulator (where you can enter your data) can "shed some light" on the problem, but I am not sure how to "turn on" the Sun and visualize daylight with it yet. orbitalmechanics.info $\endgroup$ – uhoh Jan 7 '18 at 2:51
  • $\begingroup$ Also, Quora; quora.com/What-is-a-Sun-synchronous-orbit and also quora.com/… where a beta-angle of about 90 degrees would put the orbit near the terminator and therefore more likely to remain in sunlight. Also this; wmo.int/pages/prog/sat/globalplanning_en.php $\endgroup$ – uhoh Jan 7 '18 at 2:58

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