Question

Light takes 4 hours to cover the distance from Sun to Neptune. If you travel in a spaceship at a speed 0.99c (where c is the speed of light in vacuum), the time (in minutes) required to cover the same distance measured with a clock on the spaceship will

Answer 1

Answer:

It will show 33.86 minutes.

Explanation:

Here, what we take into concern is Time dilation.

It is a consequence of Einstein's general theory of relativity.

According to this, one experiences lesser time if he/she moves at a relative speed with something.

Now, as per your question, the formula for velocity time dilation goes like-

\frac{T'}{T}=\sqrt{1-\frac{v^2}{c^2}}

T

T

′

=

1−

c

2

v

2

where,

T' is the time in frame of moving body,

T is time in frame of relative rest,

v is velocity of the moving body, and

c is the speed of light.

Now, if we solve this for v = 0.99c, we get

T' = 0.1411 T

that is,

T' ≈ 33.86 minutes ≈ 33 minutes 51 seconds