Question

How much younger an Astronaut will appear to Earth Observer if he returns after one year having moved with 0.5c velocity

a) 2 months
b) 1month 18 days
c) 3 months 18 days
d) 2 months 18 days

URGENT

Answer 1

Answer:

The astronaut, upon returning after a year, would have turned 1.6 months younger.

Explanation:

As we have learned, an astronaut is a person who flies outside the Earth at a high speed in a spaceshuttle, and gets back after his research.

Due to the speed that the astronaut travels, it is possible for the astronaut to undergo aging retardation, i.e., get younger with time, since he travels at a speed faster than the Earth's rotational and revolutionary speed. In this process, they end up losing time, but not in a normal measurable way.

Here, we know that the relative velocity of the astronaut with respect to the spaceshuttle is symmetrical, since the difference keeps increasing.

The Lorentz factor, thus, comes into play.
We are given that the velocity is 0.5c, and the respective Lorentz factor would be $\frac{1}{\sqrt (1-0.5^2)}$, which can be written as $\frac{2}{\sqrt3}$.
This, in simple terms, means that the astronaut went through $\frac{\sqrt 3}{2}$ years when everyone else on Earth went through an entire year.

Thus, the astronaut lost around 1.6 months.

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Answer 2

Answer:

The correct answer of this question is  turned 1.6 months younger after returning after a year.

Explanation:

Given - Astronaut will appear to Earth Observer if he returns after one year having moved with $0.5$ c velocity.

To Find - Choose the correct option.

An astronaut is a person who uses a space shuttle to travel quickly outside the Earth and returns after conducting research.

Since the astronaut travels at a pace faster than the Earth's rotational and revolutionary speed, it is possible for the astronaut to experience ageing retardation, or to age more slowly over time. They ultimately waste time in this process, but not in a way that can be measured.

Since the gap keeps growing, we can conclude that the astronaut's relative velocity with respect to the space shuttle is symmetrical in this instance.

Thus, the Lorentz factor is involved.

The relevant Lorentz factor and the velocity, which is $0.5$c.

Here, we understand that the relative speed of the respective Lorentz factor would be $\frac{1}{\sqrt{1- 0.5^{2} } }$ , which can be written as  $\frac{2}{\sqrt{3} }$

So, the astronaut would have turned 1.6 months younger after returning after a year.

#SPJ3