How does time work in outer space?

Time should work the same in space as it does on Earth. She saw 32 sunsets in eleven 24 hour "days" because the space station is traveling fast enough to make three trips around the Earth in one 24 hour day (do the math).

---------------------edit------------------

Yes, the International Space Station is moving (at 17208.8 mph), or else it would fall to the Earth. Click on the second link to see where the space station is now relative to the ground beneath it and relative to the day/night side of the Earth.

------edit-----

What they mean by time being "constant" is that time always passes by at the same rate (in other words, a person on the Moon would age at the same rate as a person on the Earth). So, to answer your question, we would still age, since time is a constant on Earth too. Being a "constant" does not mean that it stopped.

Randy G, with his edits has a great answer. But I thought I would point out, so you don't get confused in the future that time is not totally constant. Because of gravity you age slightly slower on the surface of the Earth (time is slowed down by gravity). So in space, and to a lesser degree on the moon you time would go by slightly more quickly, although you wouldn't notice, especially not in an orbit close to Earth like that in the space station where the difference is miniscule. The actual sunsets she witnessed are due to the space station moving around the Earth faster than it rotates as Randy explained. (You can see the ISS move slowly overhead sometimes at night) But this has nothing to do with time being relative (ie not constant).

In space missions, we count time as "Mission Elapsed Time", usually beginning at liftoff and counting in seconds. You can use that to convert to any time system you like.

One thing we do when planning a mission is to look at when things are going to happen. Orbital mechanics dictate a lot of the schedule and the relative positions of the space craft, sun, moon, earth, satellites and the like often dictate exactly when something has to happen. This isn't always in the middle of a "day", so we may start shifting sleep schedules for the crew a few days in advance of the launch so that we don't wind up having them do some tricky work in the middle of their personal "night".

How many days had passed when she arrived back on the surface? If she had been traveling around the earth at twice the speed of light for 11 days, how many days would have passed when she landed?

She observed events, not time.

Time only exists, relative to earth's rotation and orbit, anywhere because humans count it and, as long as everyone counts the same, it is the same no matter where anyone is at or how fast they are going.

Time works pretty much the same in orbit as it does on the surface of the planet. But, being in orbit, she was traveling around the earth once every 90 minutes so she saw quite a few more 'sunsets' (and 'sunrises') than people on the surface who take 24 hours to make one revolution.

Doug

The use of sunrise and sunset to mark time is irrelevant, as are the standard time zones. there were small changes to how time is perceived in space, in lower gravity, time appears to move faster, however; she did not really experience any radical time shifts. Now if she were to approach a black hole, or travel at a speed near the speed of light, the lady could have experienced a radical relativistic time shift.

Each planet rotates at a different rate. So, a Martian day is a different length than a day on Venus, etc. But in space, I imagine you would just measure time using a clock based on the length of a day from your home planet, which in our case is Earth!

no, time moves in a constant line the reason that girl was seeing all kinds of thing is because she was orbiting the earth at about 20,000 miles an hour.

Yes.

You get sucked into a worm hole where you have to live with the cast of "The Black Hole" for 20 days per earth day you're in space!

Bring plenty of twizlers!

unless you're travelling at the speed of light, time is constant