# Space Station Solstice

By Phil Plait | July 25, 2012 7:00 am

This is pretty neat: on June 6, a couple of weeks before the summer solstice, astronauts on the International Space Station pointed a camera to the north and took pictures as they orbited the Earth. Taken over the course of about an hour – 2/3 of a full orbit – this was made into a video where you can see the Sun setting and rising again. What’s cool, though, is the Sun never completely sets. It dips toward the edge of the Earth, then pulls away again:

I love how the Sun shines through the gaps in the solar array.

The geometry of this is fun! Normally, as it orbits the Earth, the ISS passes behind the Earth relative to the Sun, going into the Earth’s shadow. The Earth itself blocks the Sun, so it’s nighttime for the astronauts. Mind you, their orbit is roughly 90 minutes, so this happens on average 18 times per day and lasts for about 45 minutes.

But the ISS orbits the Earth at an angle: the orbit is tilted relative to the Equator by a little over 50°. During the northern hemisphere summer, the Earth’s north pole itself is tilted toward the Sun by about 24°. Combined, this means that for a time around the solstice the ISS can stay in daylight for an entire orbit. The Sun gets very nearly blocked by the Earth, but not quite. I drew a diagram that might help:

The circle represents the Earth. The Sun is off to the left, so the left side of the Earth is lit and the right side is dark. The north pole of the Earth is tipped toward the Sun as shown, and you can see the Equator marked as well. The "terminator" is the day/night line.

I added the rough angle of the ISS orbit – this was done by eye, but shows you how this works. As you can see, the orbit is tilted only a bit from the terminator. Because the ISS is 400 km (240 miles) above the surface, the orbit "pokes over" the edge of the Earth in the diagram (which I exaggerated a bit for clarity). Because of this, the ISS can see the Sun even when it’s over the night side of the Earth: it’s up high enough that the Earth doesn’t block the Sun.

And that’s what the video shows. At the top of its orbit (as shown in the diagram) the Sun gets very close to but not completely blocked by the limb of the Earth’s horizon, and the ISS sees daylight for a full orbit!

Pretty nifty. And look: your tenth grade geometry teacher may have overstated it a bit when she said some day your life may depend on this stuff… but it does make life a lot cooler when you do understand it.

Tip o’ the spacesuit visor to the ESA G+ page.

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CATEGORIZED UNDER: Astronomy, Cool stuff, NASA, Space

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1. Carlos

This was a happy coincidence for this year’s solstice, but does not necessarily happen on each and every solstices. This time the period of continuous sunshine was from 6 Jun 2012 00:35 to 10 Jun 2012 17:27 (UTC). You will note that it does NOT overlap the exact solstice, which the diagram would lead you to believe.

Phil’s diagram leaves another key ingredient out (he was understandably simplifying things a bit!). The orbital plane of the space Station (and any other satellite) rotates about the earth’s axis (precession of the ascending node due to Earth’s oblateness). In order to for the sun to never set on the ISS, the orbit plane needs to be roughly pointing straight on at the sun. Had the orbit plane been rotated around 90 degrees you would not have seen this effect. ISS orbital’s plane rotates relative to the starts at approximately 4.6 degrees per day. Which is why by the time 21 Jun (the solstice) rolled along this effect was no longer visible. The orbit had rotated almost 100 degrees and now was edge on to the sun, insuring the Station would go behind the earth’s shadow.

The key parameter of interest here is the angle of the orbital plane to the sun line – also known as the Beta angle. When the orbital plane is at right angles to the sun line the Beta angle is 90 degrees. When the orbit is edge on to the sun the Beta angle is 0 degrees. At the Station’s altitude, you get continuous sunlight when the Beta angle grows beyond 70 or so degrees. As Phil’s diagram shows, the Beta angle for Station can at most be around 74 degrees (50 inclination + 24 earth tilt). If you plot the Beta angle through the year it is a sinusoid curve with a high frequency and low frequency component. The primary oscillation of +- 50 degrees (i.e. from the inclination) cycles roughly every 2 months due to the precession of the ascending node. The low frequency oscillation of +-24 degrees (i.e. from the earth’s tilt) cycles every 12 months.

When the variations in the two contributions to Beta angle properly align you get Beta angles greater than 70 degrees or so resulting in continuous daylight for some period of time. I did some quick simulations and we’ve had continuous sunshine near the last 3 solstices. It may be possible that the fast component of the Beta angle change is fast enough to ensure there is always a period of continuous sunshine near the solstice, but I have not had the time to double check. And of course this will be different for different satellites at different inclinations or altitudes.

2. Jake

I’m sure this is out there, but you probably know the answer quicker. Is the orbital alignment consistant? Is the south end of the orbit always facing the sun, and the north end away? Or does the orbit “precess” around the earth?

3. Pete Jackson

Watching the slow approach and departure of the Sun from the Earth’s limb gave me an idea. Would the ISS not be a good platform to observe for small bodies orbiting the Sun within the orbit of Mercury, as well as objects approaching the Earth from the sunward direction (otherwise very hard to detect). It would seem relatively easy to mount, with a mount that compensates for the ISS’ orbital motion, a fast large-aperture camera, and fire away towards the directions near the Sun when it is below, but close, to the Earth’s limb. I would anticipate very short exposures that are later stacked.

4. Good point, Carlos (#1) – I didn’t know the orbital plane precessed that much!

5. I like how you at times can see Crescent Earth beneath you — terminator is visibly curved.

6. Grizzly

Okay, another stupid question here. But given the orbital mechanics, if a period of constant daylight is possible, the opposite must also occur. Are there extended periods of “night” and how often do they occur?

7. Carlos

@Grizzly (#6) – No there is no period of constant night. The satellite is always going around the earth, and sooner or later it must come back “in front” of the earth on the sunlit side. Imagine the earth with its shadow (umbra) cone projecting behind it, away from the sun. The shadow moves up and down 24 degrees with the season due to the tilt of the earth’s axis. Now take a hula hoop wich represents the orbit. You can rotate it up and down (inclination) and around the earth’s axis (right ascension of the ascending node, RAAN, if you must know). Under some rotations the entire hoop is outside of the umbra cone – much like the diagram Phil drew. However, it is impossible for the entire hoop to be INSIDE of the umbra cone, which is what is required for a period of constant night. According to my handy SMAD book (Space Mission Analysis and Design) the longest eclipse (night) period for a satellite at space station altitude is a little over 36 minutes. This is regardless of inclination or RAAN. This happens when the orbit (hula hoop) crosses right through the middle of the umbra cone.

8. Nathan

Back when I started following the Shuttle I would frequently hear about how certain time periods were blacked out for launch window “due to high beta angle.”

This situation where the orbital plane of the ISS results in nearly continuous daylight was difficult for me to visual first. Phil’s diagram is nice but I also found an ISS flash app on NASAs site that gives a nice animated visual guide.

As a bonus it explains the flight orientations of the ISS during these periods too (XVV, XPH, and YVV). YVV is the orientation/attitude flown during high beta angle and is informally known as Barbecue.

http://spaceflight.nasa.gov/station/flash/start.swf

That provides such a beautiful example of Rayleigh scattering as well.

10. realta fuar

Thanks Carlos! As usual, some of the B.A.’s readers know more about a subject than the B.A. Aren’t “educational” blogs generally supposed to work in the other direction? . This is presumably good for the B.A.; for his readers, I’m not so sure as most people don’t read the comments for any blog.

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