An astronomer on Earth observes a meteoroid in the southern skyapproaching the E

Question

An astronomer on Earth observes a meteoroid in the southern skyapproaching the Earth at a speed of 0.780c. At the time of its discovery themeteroid is 24.5 lightyears from theEarth. (a) Calculate the time interval required forthe meteroid to reach the Earth as measured by Earthboundastronomer.
1 yr
(b) Calculate this time interval as measured by a tourist on themeteroid.
2 yr
(c) Calculate the distance to the Earth as measured by atourist.
3 ly
(a) Calculate the time interval required forthe meteroid to reach the Earth as measured by Earthboundastronomer.
1 yr
(b) Calculate this time interval as measured by a tourist on themeteroid.
2 yr
(c) Calculate the distance to the Earth as measured by atourist.
3 ly

Explanation / Answer

gamma factor = = 1/(1-v^2/c^2) =1/(1-.78^2) = 1.6 it is easier to do the problems in reverse order. part (c): the distance to earth is contracted to (24.5 ly)/ = 15.3 ly part (b): flight time measured by tourist = (15.3)(c)/(.78c) = 19.7years part (a): flight time measured by earthbound astronomer =(24.5)(c)/(.78c) = 31.4 years

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