Physics 341: Homework Questions Due October 22nd

A pair of stars A and B revolve around each other in circular orbits with period T. Assume the Earth lies in the orbital plane at a distance x from the pair. (i.e. the orbit is seen edge-on). Make the hypothesis that light travels with the speed c RELATIVE TO THE SOURCE OF EMISSION. (i.e. this is what you would assume with Galilean Relativity).

a) Show that if this were the case, each star as seen from the Earth would appear to traverse the semi-circle on the far side of its orbit MORE rapidly than it traverses the near semi-circle.

b) Show if 4*v*x/T = c**2-v**2 where v is the speed of star A in its orbit, then A would be seen simultaneously at both ends of the diameter of its orbit! See if you can pick reasonable values of v, T and x for which this condition holds.

No such effect has ever been seen...

Starship Enterprise is overtaken by the new model, Starship Enterprise-prime, with E' passing E at a relative speed v=c/2. The captain of E salutes the captain of E' by blinking the bow and stern lights of E, simultaneously from the point of view of E. As measured by E, the distance between the lights is 100 m.

a) By how much do the times of emission of the signals from the lights differ, according to E'?

b) Explain from simple considerations why this is qualitatively so.

c) Identify the origins of the two factors that combine to produce the result.

A meter stick is at rest in the inertial frame O' with one end at the origin, and makes an angle of 60 degrees with the x' axis. Observer O' sees observer O pass him by, moving in the positive x' direction with velocity 0.8c.

a) If O fixes her x axis parallel to the x' axis, what angle does the meter stick make with the x axis, according to her measurements.

b) What is the length of the meter stick as measured by O?

It takes about 100,000 years to travel (at approximately the speed of light) from the most distant star in our galaxy to the Earth. But in principle, it is possible for a child born on a space ship as it leaves the Earth to arrive at the star before dying of old age.

a) Why?

b) Estimate the speed necessary to bring this about.