Question

A space probe is sent to the vicinity of the star Capella, which is 42.2 light-years from the earth. (A light-year is the distance light travels in a year.) The probe travels with a speed of 0.9930c. An astronaut recruit on board is 19 years old when the probe leaves the earth. What is her biological age when the probe reaches Capella?

Answer 1

Her current biological age = 24.02 years

Step-by-step explanation:

From time dilation equation, we know that;

t = t_o * [√(1-(v²/c²))]•L_o

Where;

t = dilated time

t_o = stationary time

v = the speed of the moving object

c = the speed of light in a vacuum

First, let's convert the rest time (t_o) from light years to years.

Thus;

t_o = [c/0.993c] * [42.2]

c will cancel out and we now have;

t_o = 42.5 years

Since t = t_o * [√(1-(v²/c²))]

Thus; t = 42.5 * [√(1-(0.993²c²/c²))]

t = 42.5/[√(1 - (0.993²))]

t = 42.5 * 0.1181

t = 5.02 years

Since the astronaut was 19 years old when the probe left the earth, thus;

Her current biological age now the probe has reached Capella, will be;

19 + 5.02 = 24.02 years