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?

Her current biological age = 24.02 years

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