It might seem like a trivial process to communicate with astronauts on the International Space Station, but there is a small problem. Suppose you have a radio transmitter and receiver in Houston, Texas. You could use this to send a signal to the ISS and everything would be great. Except for when it isn't great. The problem is that the ISS only takes about 90 minutes to orbit the Earth. This results in the ISS being on the other side of the Earth for a good part of this 90 minute orbit.
Have you ever tried to use your cell phone deep in a mine? No? Well, if you did, you would find that it wouldn't really work. 100 meters of dirt and rock can effectively prevent radio communications between your phone and the cell tower. Just imagine what would happen when you try to send a signal through the whole Earth. Right, nothing happens because it won't make it through.
This is where the Tracking and Data Relay Satellite System (TDRSS) becomes useful. These are essentially several satellites in geostationary orbit. Since these relay satellites are in a geostationary orbit, ground stations know exactly where to point to communicate with them. Then the relay satellite communicates with space craft in orbit.
What is a Geostationary Orbit?
The International Space Station orbits at an altitude of around 370 km above the surface of the Earth. At this location, it takes just over 90 minutes to circle the Earth. But what happens as you increase in orbital altitude? For any object in orbit, there is essentially just one force to consider - the gravitational force. It is pulling straight towards the Earth with a magnitude:
I am calling m1 the mass of the object and ME the mass of the Earth (in case it wasn't clear). For an object in a perfectly circular orbit, this force is related to the acceleration needed to move in a circle. I can write this acceleration as:
Here, T is the orbital period. Since this is the only force, I can make the following relationship between force and acceleration to get an expression for the orbital radius as a function of the orbital period.
If you put in values for the mass of the Earth and a period of 1 day (in seconds), you will get somewhere around 4 x 107 meters for an orbital radius. This is pretty high compared to the orbital radius of the ISS as you can see in my illustration at the top.
Oh, just an extra thing for clarification. Geosynchronous means that the orbital period is one day. This could work for a satellite orbit that goes over the North and South poles. Since the Earth rotates about a different axis than this orbit, this geosynchronous satellite would appear in the same position in the sky just once a day. In a geostationary orbit, the satellite has an orbital period of one day and also orbits above the equator. This makes the orbital axis for both the Earth and the satellite in the same direction. A geostationary orbiting object will appear to stay in the same location in the sky.
Communications Lag
Lag is really what I wanted to talk about - not sure why I took a detour into orbital motion. I guess I just can't help myself sometimes. However, the point is that if you use the satellite as a relay, it can be pretty far away. This large distance can lead to lag. By lag, I mean a delay in communications. Person one says something and it take a noticeable time for the next person to reply.
What kind of lag could you expect talking to the ISS? Let say that a communications signal goes all the way out to the relay and back. Since this signal is some type of light (like radio waves), it would travel at the speed of light (2.99 x 108 m/s). Of course the actual distance depends on the location of the ground-based person and the space based person. However, I will just go with an estimated distance of twice the TDRSS altitude at 3.6 x 107 m which is 7.2 x 107 meters. This would give a signal travel time of 0.24 seconds. Of course, this is just an estimate for the minimum lag. It could be larger based on the location of the "talkers". I am a little surprised it is this low though.
To me, it seems like there is some lag in the communications with the ISS. Maybe it isn't really there or maybe it is a software induced lag. Just as a completely random test, I looked at this video recording of a NASA-Google+ hangout including actual live astronauts on the ISS.
When someone asks a question, there is a natural pause. At the beginning of the hangout, the NASA person asks a ground-based astronaut a question. Just by pausing the video, I get a 2 second pause between the end of the "ask" and the beginning of the "answer". I had intended on using some more technologically advanced techniques for measuring this delay, but it was getting out of control in terms of complexity.
Looking at the same type of time difference when the moderator talks to the ISS astronauts, I get about a 4 second delay. Ok, I get it. Every person is different. Some people just take a longer pause before answering a question. However, it does seem like there is a noticeable delay more than the expected 0.24 seconds.
Well, what about a duet with the ISS? That is just what astronaut Chris Hadfield and the Barenaked Ladies did recently. Here is there song: I.S.S. (Is Somebody Singing).
A very nice duet. But is this actually possible? Well, I don't think it's fake. But could you really just have a duet like this? Let's look at the best case scenario. Suppose the ISS passes right overhead (I suspect the ground based location was in Canada - so I doubt it went overhead) - but let's just say it did. At it's closest approach, the ISS would be 350 km from the ground-based signers. This would give a delay of just 0.001 seconds. That's fine - but this assumes direct communication from the Barenaked Ladies to the ISS. Could they do this for 4 and a half minutes? During this time, the ISS would travel 4.5/92 or 5% the way around the Earth. Not too far. However, in terms of distance this is 34 kilometers.
How about a picture? If the ISS is in a circular orbit, then in 4.5 min it would have an angular displacement of 17.6°. This should be a scale image of the ISS at both the beginning and end of the Barenaked Ladies song.
Although everything might look great - in this case the ISS starts just 10° above the horizon. That might make it difficult to have straight line communications with. I guess it's possible though.
Ok, so what if this duet used a satellite relay instead? If this produced a 1 second communications delay, could they still do the duet? I'm not really a musician, but it seems like this would be a big problem. If Chris Hadfield started 1 second early, then he could be right in sync (but not 'N Sync - that's a different band) with the Barenaked Ladies. That might be difficult to keep up for the whole duet. Another possible solution would be to pre-record the Barenaked Ladies' part of the song so that Hadfield could use that to follow along. It doesn't look like Hadfield has an earpiece - that seems odd. I am going to guess that either the BNL or Hadfield was actually using a recording instead of a real live duet. Oh, but calm down. I'm not saying that BNL nor Hadfield are not super awesome. The duet rocks, I love it.
Duet From the Moon
If an ISS-Earth duet is feasible, what about an Earth-moon duet? Yes, the first step would be to actually get a human being on the moon. But let's say we have that. How much of a time lag would there be for direct communication with the moon? I will use an Earth-moon distance of 375,000 km (the moon is not in a perfectly circular orbit around the Earth). In this case, I can use the speed of light to find the time to get a signal from the Earth to the moon:
This much of a delay would definitely be a problem. Even for the Barenaked Ladies. Maybe Aerosmith could do a duet at this distance - but no one else.
