Is there a low Earth orbit with a 24-hour day night cycle?

Question

Are there any possible low-Earth orbits that use precession to match Earth's day/night cycle? So like SSO, but specifically aimed to achieve a 24hr day/night in LEO.

If so, what would its parameters be?

Answer 1

There are not! To obtain a 24 hr day/night period, you have to pass through the Earth's shadow every 24 hours. This means you're orbiting once every 24 hours (as no orbits precess rapidly enough to precess into & out of Earth's shadow this quickly). A 24 hour orbit is a geosynchronous one, and those are out at approximately 35,500 km. Orbits at this altitude precess very slowly, and will certainly not precess at a rate of 360°/yr. This means they'll quickly no longer enter Earth's shadow and no longer have a 24/hr period.

What there are: geosynchronous orbits which are right on the ecliptic. Even these I suspect will often miss Earth's shadow depending on the time of year.

Regardless, any geosynchronous orbit will only ever be in shadow for a brief amount of time--much less than a terrestrial night. In fact, it's a rule of thumb that the higher you go the [relatively] less time you spend in Earth's shadow: the shadow not only gets narrower, your orbit gets bigger. Thus, the proportion of time you spend in shadow to the proportion of the time you don't is always much higher than it would be on the ground.