What ratio of time is the ISS in sunlight?

[md65536]

All the sources I see, repeat that the ISS spends on average about 45 minutes of a 90 minute orbit in darkness. I can't fathom why and I can't find any more accurate numbers.

Only at equinox, would half of every orbit be above night on Earth. In summer and winter the orbits can vary over the day, as some orbits are in longer days and some in longer nights. However I'd like to ignore that variation and consider only the average times.

First, the ISS is raised above the surface of the Earth, so it is in the sun more than the surface is. The higher a satellite is, the less it will be in the Earth's shadow. For example, the moon is in sunlight about 100% of the time.

Second, the ISS orbit is tilted off the ecliptic. If a satellite is in a polar orbit (or better, orbiting over the edge of the polar circles in an optimal way), it can spend 100% of the time in sunlight for part of the year.

Combined, using one very rough measure using a satellite tracking website, the ISS can spend about 5.25 minutes in the sun while the point on Earth below it is in darkness, on every sunset and sunrise. I think this measure must vary? But if this were the correct average measure, in a 93-minute orbit the ISS would spend 57 minutes in daylight and 36 minutes in darkness, or 61% of the time in light.

This seems like an important difference from "about 50%" that I see quoted everywhere. Am I getting something wrong? Is there a more accurate calculation available? To me it seems like the 50% estimate is more misleading than a useful simplification. Why wouldn't they use a more accurate number, even if it's too complicated to explain?

Edited November 1, 2023 by md65536

[swansont]

38 minutes ago, md65536 said:

First, the ISS is raised above the surface of the Earth, so it is in the sun more than the surface is. The higher a satellite is, the less it will be in the Earth's shadow. For example, the moon is in sunlight about 100% of the time.

The ISS is only about 400 km above the earth, which has a radius of about 6400 km.

 

[md65536]

2 hours ago, swansont said:

The ISS is only about 400 km above the earth, which has a radius of about 6400 km.

 

Right, which means that it's in the sun more than someone on the ground is. How much more is what I'm wondering.

 

At 400km high, the ISS can be seen from 2300km away. That's more than a timezone at the equator, and more than 2 at the highest latitude the ISS passes over (51.6 degrees). So for example, the sun may have set for you an hour or two ago while the ISS above you is still lit by the sun. Or to think of it another way, if you were on the ground and had 12 hours of daylight, someone in a 400km-tall tower would get in the ballpark of 2 to 4 more hours of sunlight that day, which means 4 to 8 more hours of light than dark (very rough estimate). That's 58% to 67% of the time in sunlight, rather than 50%. I'm leaving out some important details, but how different is the correct answer from this estimate?