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Double Stars |
If light behaved like a classical ballistic particle emitted from its source
with a muzzle velocity of c relative to the source, then the light rays emitted
from two sources traveling with different velocities would not travel at the
same speeds. Light emitted forward from a fast moving source would travel
faster than the light emitted forward from a slow moving source (just like a
bullet shot forward from a fast moving jet aircraft travels faster than one
shot from a similar gun at rest).
More specifically, consider a double star system with the more massive star sitting at rest emitting a light ray to the right. That light ray would travel to the right with a speed of c = 299,792,458 m/s = 299,792 km/s. If the second, less massive star circling the first happens to be traveling to the right with a typical star speed of v = 25 km/s while emitting a second light ray to the right with a classical muzzle velocity of c, the second ray would have a speed of c + v or 299,817 km/s. Therefore, the light from the second (right-moving) star would outrun the light form the first (stationary) star by 25 km/s. Conversely, when the circling star travels to the left, the light emitted to the right will have a speed of c - v = 299,767 km/s.
Now ask yourself what would happen as the star circles from left to right. The light from the left-moving star would be emitted first but travel slower to the right than that from the right-moving star. Clearly, it is only a matter of time before the faster moving light ray overtakes the slower moving light ray. Indeed, if it takes 6 months for the star to reverse itself, the position of the first light ray would be x1 = (c-v)t1 while the position of the second light ray would be x2 = (c+v)t2, with a time difference of t1- t2 = 0.5 y. Setting x1 = x2 allows us to calculate the time t2 required for the second ray to overtake the first. The result is t2 = (c-v)( 0.5 y)/2v = 3000 y. Therefore, an observer located 3000 ly from the double star would see the orbiting star located on both sides of its orbit at the same time. He would see three stars instead of two, the central star plus the orbiting star at two locations.
This phenomena does not happen. Double stars are always seen as doubles, not triples or more (as could be the case if the distance were greater than 3000 ly).
Although we have taken a simple, crude example to illustrate the point, there are thousands upon thousands of double star systems that have been studied experimentally which demonstrate conclusively that the speed of light is indeed independent of the source.
Q1. Double Star Motion.
In the above example of a double star system where it takes 3000 y for the
light from one side of the orbit to overtake that from the other side of the
orbit, which of the following statements would be true when viewed from a
distance of 3000 ly? (A) The orbiting star would appear to
speed up and slow down in its orbit, (B) The orbiting
star would disappear from time to time, (C) The
orbiting star would always appear to be doubled, (D)
More than one of these are true, (E) None of these are
true.
P1. Twin Stars.
Two stars of identical mass orbit each other in circular orbits about their
common center of mass with a period of 1 month (1/12 year). The distance
between the two stars is 15 million kilometers. (a) What is the orbital speed
of each star? (b) If light traveled like a classical ballistic particle with
muzzle velocity c, how long would it take light from one star to overtake that
from the other? (c) How far away would an observer need to be located in order
to witness this phenomena? (d) Describe the appearance of the star system to
that observer at that time. How many stars would there appear to be and where
would they appear to be located? (e) If the speed of light is independent of
the source and the system were viewed as in part d, how many stars would there
appear to be and where would they appear to be located?
P2. Two stars of identical mass
orbit each other in circular orbits about their common center of mass at a
speed of 30 km/s at a distance of 1000 light-years from the earth. Assume that
both stars go nova at the very instant that one star is traveling toward the
earth and the other is traveling away from the earth. Also assume that light
travels like a classical ballistic particle with a muzzle velocity c = 299,792
km/s relative to the source. What will be the time difference between the
arrival of the light from the two novae as observed from the earth? (Express
answer in years as #.#)
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