24+ hours of sunlight for the ISS

[AstroBrant]

I came across this:

I never considered that this might happen, so I thought, "Cool!"

Then I had to go and ruin it by trying to figure out how it happened. The video description stated that this occurred when the ISS was orbiting mostly over the terminator. So I concluded that it must be at one of the equinoxes. But with an orbit inclined to 51 degrees and a polar tilt of 23.5 degrees, the maximum latitude achievable would be 74.5 degrees. I wouldn't have thought the altitude would have been high enough to see over the pole.

I tried to picture the orbit of the ISS along with the orbit of the earth around the sun, its polar axis, and the terminator. It was becoming a bit much for my old brain, but I think I got it. Then I wondered if the station's orbit around the earth has any sidereal precession. If so, it seems that would make this kind of occurrence pretty rare.

Looking forward to your thoughts and information.

[smartcooky]

I came across this:

I never considered that this might happen, so I thought, "Cool!"

Then I had to go and ruin it by trying to figure out how it happened. The video description stated that this occurred when the ISS was orbiting mostly over the terminator. So I concluded that it must be at one of the equinoxes. But with an orbit inclined to 51 degrees and a polar tilt of 23.5 degrees, the maximum latitude achievable would be 74.5 degrees. I wouldn't have thought the altitude would have been high enough to see over the pole.

I tried to picture the orbit of the ISS along with the orbit of the earth around the sun, its polar axis, and the terminator. It was becoming a bit much for my old brain, but I think I got it. Then I wondered if the station's orbit around the earth has any sidereal precession. If so, it seems that would make this kind of occurrence pretty rare.

Looking forward to your thoughts and information.

Well, I'm no orbital mechanics  expert, but since the earth's terminator speed is approximately 1600 kph in a westerly direction, then I imagine any orbit with an inclination such that the spacecraft's westward vector is also around 1600 kph should keep it chasing the terminator and not catching up, so a period of even longer than 24 hours in sunshine (or darkness) might be possible.

If I've overlooked something I'm sure there people where who will correct me.

ETA: It just occurred to me that this might fall down near the middle of summer/winter, when one pole is in 24hr darkness and the other in 24hr daylight. This would mean the range of possible orbital inclinations would be greater around mid June than around mid-December.

[AstroBrant]

ETA: It just occurred to me that this might fall down near the middle of summer/winter, when one pole is in 24hr darkness and the other in 24hr daylight.

Well, a big duh for me. In my post I meant to say solstices, not equinoxes. At least I got it right when I posted my comment on YouTube.

[ka9q]

Yes, this happens on occasion in high inclination orbits. The angle "beta" between the sun and the orbit plane varies as the earth orbits the sun and the orbit plane precesses in inertial space. At beta angles approaching 90 degrees the spacecraft can be in continuous sunlight. The spacecraft designer has to anticipate this and avoid any thermal problems.

Precession happens because the earth is not a perfect sphere, but an oblate spheroid due to its rotation. For orbital inclinations less than 90 degrees (e.g., the ISS), every time the spacecraft crosses the equator (northward or southward) the earth's equatorial bulge tugs it a little west of its original orbit track. The net effect is to cause the orbit plane to slowly precess westward at a rate that depends on the inclination and the orbital period. (The lower the inclination and the shorter the period, the faster the precession.)

The "sun synchronous" orbit widely used for polar weather and other earth-observing satellites makes effective use of this property to keep the beta angle as constant as possible. Since the earth orbits the sun in an eastward direction, you want the orbit plane to precess eastward at the same rate. This requires a retrograde orbit, i.e., an inclination greater than 90 degrees. For each inclination (or each period) there's a corresponding period (or inclination) that produces an eastward precession of about 360/365 degrees per day. The beta angle still won't be constant because of the tilt of the earth's axis but the local time under the spacecraft will remain approximately the same (e.g., 3AM/3PM, 9AM/9PM, etc). A 6AM/6PM sun-synch orbit is often in continuous sunlight.

Since you can't safely launch to the northwest or southwest from the east coast of Florida, NASA and the Air Force launches to these orbits from Vandenberg Air Force Base northwest of Los Angeles. They launch to the southwest, which takes them over open water all the way to Antarctica, flying down past San Diego (where I live) as they do so. When the sky is clear and the lighting is right, they can be very impressive sights. A Delta II typically stages just as it's passing by.

[AstroBrant]

The angle "beta" between the sun and the orbit plane varies as the earth orbits the sun and the orbit plane precesses in inertial space. At beta angles approaching 90 degrees the spacecraft can be in continuous sunlight.

I looked up beta angle on wiki and linked to this about the ISS.
http://spaceflight.nasa.gov/station/flash/start.swf
The animation on beta angle was what I needed to understand this. As I suspected, it's not that this is difficult to comprehend. It's just difficult to communicate verbally.

Not only does the orbital plane precess in an east-west direction, but it appears to change north-south angle to the sun vector significantly as well. The combination of those two appear to be what determines the beta angle. That east-west precession is far faster than I would have thought. It appears to precess a full 360 degrees in a month or two.

As I suspected, the times when the ISS would see 24 continuous hours of sun exposure would have to be near the solstices.

Precession happens because the earth is not a perfect sphere, but an oblate spheroid due to its rotation. For orbital inclinations less than 90 degrees (e.g., the ISS), every time the spacecraft crosses the equator (northward or southward) the earth's equatorial bulge tugs it a little west of its original orbit track. The net effect is to cause the orbit plane to slowly precess westward at a rate that depends on the inclination and the orbital period.

The animation does confirm this westward precession, (opposite the rotation of the earth.) I guess I had an intuitive sense that it would precess with the rotation, but on thinking about it, I guess there was no reason to think that.

Thank you for your explanation.

[ka9q]

Not only does the orbital plane precess in an east-west direction, but it appears to change north-south angle to the sun vector significantly as well.

The orbital plane precesses only in right ascension; inclination remains constant. The north-south effect is due to the earth's axial tilt and orbit around the sun.

The combination of those two appear to be what determines the beta angle. That east-west precession is far faster than I would have thought. It appears to precess a full 360 degrees in a month or two.

Yeah, it's fast because of the relatively low inclination (compared with a polar orbiter) and the short orbital period. This gives the earth's equatorial bulge more opportunities to tug on the spacecraft.

As I suspected, the times when the ISS would see 24 continuous hours of sun exposure would have to be near the solstices.

Yes, because of the inclination. If it were in a polar orbit, then the very high β (and continuous sunlight) periods would occur during the equinoxes. And if it were in an equatorial orbit, then the nodes would be undefined and β would never exceed 23.5°.

The animation does confirm this westward precession, (opposite the rotation of the earth.) I guess I had an intuitive sense that it would precess with the rotation, but on thinking about it, I guess there was no reason to think that.

Right. To first order, the earth is symmetric around its rotation axis so its rotation would have no effect. It's not perfectly symmetric with longitude but you tend to see these second-order effects only on orbits whose periods are close integral fractions of a sidereal day. This includes not only geostationary satellites but also GPS satellites in 12-sidereal-hour orbits.

This Wikipedia article has a pretty good explanation:

http://en.wikipedia.org/wiki/Nodal_precession

Note: the formulas ought to use Ω' for the precession rate because Ω is the standard symbol for RAAN (Right Ascension of the Ascending Node) while ω is conventionally used for a different orbital parameter, the argument of perigee.