A spaceship from another galaxy passes over the solar system directly above a radial line from the sun to the Earth.(We measure that distance to be 1.5 *10¹¹ m. )On Earth,the spaceship is observed to be traveling at a speed of 0.80 c,for which $\gamma$= 5/3.As measured on Earth it takes the spaceship 625 seconds to travel from the sun to Earth.When a scientist in the spaceship measures the Earth-sun distance and the time it takes her to travel that distance,she finds the results are respectively A)9.0 *10¹⁰ m;375 s. B)9.0 *10¹⁰m;625 s. C)1.5 * 10¹¹ m;625 s. D)2.5 * 10¹¹ m;625 s. E)2.5 *10¹¹ m;1042 s.

Question

Quizplus · Accepted Answer

From Earth's perspective:

Let the distance between the sun and the spaceship be x.
We know that distance between Earth and spaceship is 1.5x.

Using time dilation formula, we have:
t = t0 / sqrt(1 - v^2 / c^2)
where t0 is the time measured in the spaceship's frame of reference, v is the velocity of the spaceship, and c is the speed of light.

Plugging in values, we have:
625 = t0 / sqrt(1 - (0.80c)^2 / c^2)
t0 = 375 seconds

From spaceship's perspective:

The spaceship is at rest in its own frame of reference, so the distance and time measured by the scientist in the spaceship are the same as the ones measured by Earth observers before the spaceship started moving. Therefore, the distance is x = 9.0 x 10^10 m and the time is 375 seconds.

Thus, the answer is A.

A Spaceship from Another Galaxy Passes Over the Solar System γ\gammaγ

A Spaceship from Another Galaxy Passes Over the Solar System $\gamma$