Question

A spaceship enters the solar system moving toward the Sun at a constant speed relative to the Sun. By its own clock, the time elapsed between the time it crosses the orbit of Jupiter and the time it crosses the orbit of Mars is 50.0 minutes. How fast is the spaceship traveling towards the Sun? The radius of the orbit of Jupiter is 778 × 109 m, and that of the orbit of Mars is 228 × 109 m.

0.319c
0.438c
0.982c
0.522c
0.671c

Answer 1

The spaceship is traveling towards the Sun with velocity 0.319c.

Step-by-step explanation:

One of the most significant works in the history of physics is Albert Einstein's 1905 theory of special relativity. The theory of special relativity explains how speed affects space, time, and mass. Small amounts of mass (m) can be interchangeable with large amounts of energy (E), as defined by the classic equation E = mc², according to the theory, which offers a means for the speed of light to define the link between energy and matter.

Given parameters:

The radius of the orbit of Jupiter is 43.2 light-minutes.

that of the orbit of Mars is 12.6 light-minutes.

Hence, actual distance between them l₀= 43.2 - 12.6 light-minute = 30.6 light-minute.

Let the velocity of the spaceship is v.

Time taken to travel this actual distance = l₀ √(1+v²/c²)/v

According to the question

l₀ √(1+v²/c²)/v = 35.0

√(c²+v²) = 35.0 v

c² = 1224 v²

v = 0.319c