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68 CHAPTER TWO

FIGURE 2-31 Einstein

roughly 8,800 meters per second, and given the speed of light at roughly 300,000,000
meters per second, we get a time dialation for an orbiting spacecraft of

2
1>sqrt 11 18800>300,000,0002 2
1>sqrt 11 0.000000000862
1.0000000004

So, consider the Soviet cosmonaut who spent 458 days in space (the record) (for a
total of 458 24 60 60 39,571,000 seconds). Ignoring all the other motions of
the spacecraft other than the orbital speed, the cosmonaut’s time dialated 39,571,000
1.0000000004 39,571,000.017 seconds.
Thus, after over a year in orbit, a time change of 17 milliseconds has occurred for
the cosmonaut. That’s not very much, but at an orbital speed of 8,800 meters per sec-
ond, the cosmonaut would be off by 150 meters (8800 0.017). That’s not very far in
terms of the earth’s expanse, but a big error while you’re trying to dock! Orbital plan-
ners do take relativistic effects into account in planning orbits and interplanetary
missions.