Marks: 2
The time taken by the space craft moving at a speed equal to half the velocity of light to go from star A to star B is 2 years as calculated at the Earth station. Which of the following is correct for the time measured by the astronaut in the space craft to reach the star B?
Choose one answer.
a. 1 year
b. less than 2 years
c. 2 years
d. more than 2 years
b. less than 2 years
Review the relativistic
"twin paradox"
The elapsed time for the high speed spacecraft (as measured by its own clock) is always less.
To answer this question, we need to understand time dilation, an effect predicted by Einstein's theory of special relativity. According to the theory, time runs slower for objects in motion relative to an observer.
In this case, the space craft is moving at a speed equal to half the velocity of light. Since the speed of light is about 300,000 kilometers per second, half of that is 150,000 kilometers per second. We are given that the time taken for the space craft to go from star A to star B, as calculated at the Earth station, is 2 years.
To determine the time measured by the astronaut in the space craft, we can use the formula for time dilation:
t' = t / √(1 - v^2/c^2)
Where:
t' is the time measured by the astronaut in the space craft,
t is the time measured at the Earth station,
v is the velocity of the space craft, and
c is the speed of light.
In this case, t = 2 years, v = 0.5c, and c = 300,000 km/s. Plugging these values into the formula, we can calculate t'.
t' = 2 / √(1 - (0.5c)^2/c^2)
= 2 / √(1 - 0.25)
= 2 / √0.75
= 2 / 0.866
≈ 2.31 years
Therefore, the correct answer is d. more than 2 years. The astronaut in the space craft would perceive the journey to take more than 2 years, around 2.31 years.