Space Travel is Relatively Complicated

The principle of relativity comes up regularly in the context of space travel, and this week’s launch of NASA’s “Curiosity” rover mission was no exception.  The BBC has a pretty nice article about it, but as happens so often in press articles, it stumbles in a big way at one point.  Quoting from the article: “By the time the encapsulated rover was ejected on a path to the Red Planet, it was moving at 10 km/s (6 miles per second.)”  Oh my heavens.  10 kilometers per second.  That sounds very fast; highway speeds are 100 kilometers per hour.  Unfortunately, the statement is completely meaningless.

In fact, right now, as you sit in your chair, reading this nice little article, you are moving at 30 kilometers per second.  In a sense, anyway.  Yet nobody is about to issue you a traffic ticket, or give you an award for traveling faster than a speeding bullet (less than a kilometer per second.)

Do you know that Einstein did not invent the principle of relativity?  Click here to read on…

7 responses to “Space Travel is Relatively Complicated

  1. I am a bit confused. Isn’t 1 kilometer a physical distance? If I am in interstellar space (somewhere in the Sagittarius arm) and I move from point A to point B (a distance of 10 kilometers) in one second, then my speed is 10 kps. If I am moving from A to B to C to D to …… each point being ten kilometers from the other and I cover each interval in one second , then, like the Mars spacecraft I could be traveling at 10 kps. I know that I am gravitationally bound to the galaxy and thus moving 10 kps + N kps along with the rest of the stars and dust and dark matter (if it moves). But, unless we are traveling at relativist speeds where the Lorenz-Fitzgerald length contractions come into play, to say that a spacecraft moving through space at 10 kps is meaningless doesn’t make much sense. Speed limit signs don’t say MAXIMUM SPEED 12758065 MPH (taking into account the orbital velocity of the earth at solar apogee, the speed of the solar system as it revolves around the galaxy, the speed of the galaxy in the local cluster, and the increasing acceleration of space-time.) You don’t get a ticket for going 127580073 in a 12758055 MPH zone.

    • “I am a bit confused. Isn’t 1 kilometer a physical distance? If I am in interstellar space (somewhere in the Sagittarius arm) and I move from point A to point B (a distance of 10 kilometers) in one second, then my speed is 10 kps. ”

      Yes, 1 kilometer is a physical distance. You can measure it with a long ruler. So let’s put a 10 kilometer ruler between points A and B. And then if you move from point A to point B in one second, your speed is 10 kps relative to points A, B and the ruler.

      But I claim that you made a mistake: you thought points A and B were stationary, but they are not. They are moving relative to me at 5 kps, and I’m stationary. So you are actually moving at 15 kps — relative to me.

      On what grounds are you correct about your speed, and on what grounds am I incorrect?

      There is no experiment you can do to prove that A and B are stationary and I am not. Oh sure, you can prove that A and B are stationary relative to the stars, if you want. But you can’t prove the stars are stationary either. And they’re not stationary relative to the Andromeda galaxy, for instance.

  2. OK, but when we send a spacecraft from earth far into space (like Voyager) how do we measure its speed at time t(x)?

    I am a classical philologist and senior scientist at an AI company, not a physicist, but I have to warn you, I’ve read enough Scientific Americans and enough Brian Greene to make me really, really smart about cosmology, relativity, and string theory! 🙂

    • The point of relativity isn’t that speed is meaningless; it is just that speed doesn’t mean anything until you say what it is relative to. We are perfectly free (and it makes sense to do so) to measure locations and speeds of interplanetary rockets relative to the sun’s center. The planets have their orbits; the rocket has its trajectory; and the aim is to make the rocket arrive where the planet is at the time that you want. We can do that calculation using a sun-centered description of locations and speeds.

      Once you get close to a planet, though, it may no longer be convenient to use the sun anymore. For instance, as you are dropping the Mars rover into Martian orbit (before you lower it to the planet’s surface), measuring locations and speeds relative to Mars’ center will make more sense.

      It is not difficult to shift from a sun-centered description of locations and speeds to a Mars-centered description. But you must specify which one you are using! otherwise you will make a serious mistake.

  3. “Yes, 1 kilometer is a physical distance. You can measure it with a long ruler. So let’s put a 10 kilometer ruler between points A and B. And then if you move from point A to point B in one second, your speed is 10 kps relative to points A, B and the ruler.”

    Matt, you have here confirmed my position that the speed of the neutrino (relative to the surface of the Earth) is the fixed distance between CERN and Gran Sasso divided by the measured time with no Sagnac adjustment.

    • I was making a statement that is only precise in the Galilean limit. Once Einstein’s modifications of Galilean relativity have to be accounted for, as is the case when we have velocities not at a few kps but at 300,000 kps, we have to be more careful with our clocks.

  4. The (Sagnac) correction for the GPS clocks has already been accounted for in the clock synchronization procedure adopted by the CCIR.