• wilson_chem90
In summary, a 30-year-old female astronaut leaves her newborn child on Earth and goes on a round-trip voyage to a star 40 light-years away in a spaceship traveling at 0.90 c. The trip will take 88 years for the astronaut and 80 years for the light to make the round trip. Upon her return, the astronaut will be 68 years old and her son will be 88 years old.
wilson_chem90

## Homework Statement

A 30 year old femal astronaut leaves her newborn child on Earth and goes on a round-trip voyage at a star that is 40 light-years away in a spaceship traveling at 0.90 c. What will be the ages of the astronaut and her son when she returns?

## Homework Equations

t = to / {1 - v^2/c^2} ( { } = Square Root)

## The Attempt at a Solution

Since its 40 light years away traveling at .90 c. That means it'll take 48 years for the whole trip. ( 0.20 x 40 light years + 40 = 48 years)

to = t {1 - v^2/c^2}
= 48 years { 1 - (0.90c)^2/c^2}
= 48 years(0.43589)
= 20.923 years

Therefore, the mother will have aged approx. 21 years, making her 51 years old when she returns and her son will have aged 48 years, making him 48 years old when his mother returns.

I'm not entirely sure if this is correct. Hopefully it is...

Your reasoning is incorrect. If the star is 40 l.y. away, this means that it takes light 80 years to make the round trip. Surely it can't take the astronaut less than that, baby or no baby. Begin by calculating (correctly) how many years baby thinks mama is gone. Find gamma and then find mama's age.

OHHHH the calculation is 80 l-y + (0.2)(40 l-y) = so its 88 years. I hope...

to = t {1 - v^2/c^2}
= 88 years { 1 - (0.90c)^2/c^2}
= 88 years(0.43589)
= 38.36 years

Therefore, the mother will have aged approx. 38 years, making her 68 years old when she returns and her son will have aged 88 years, making him 88 years old when his mother returns.

thats one old baby!

## 1. What is time dilation?

Time dilation is a phenomenon in which time appears to pass slower for an object or person who is moving at a high speed compared to someone who is stationary. This is a key concept in Einstein's theory of relativity.

## 2. How does time dilation occur?

Time dilation occurs due to the effects of gravity and motion on the fabric of space-time. As an object moves faster, it experiences a change in the rate at which time passes for it, leading to a time dilation effect.

## 3. What is the Twin Paradox?

The Twin Paradox is a thought experiment that illustrates the effects of time dilation. It involves one twin traveling at a high speed, while the other stays on Earth. When the traveling twin returns, they have aged less than the twin who stayed on Earth, despite both experiencing time at a constant rate.

## 4. Can time dilation be observed in everyday life?

Yes, time dilation has been observed in several experiments, including the famous Hafele-Keating experiment in 1971. GPS satellites also take into account the effects of time dilation due to their high speeds and altitude.

## 5. Is time travel possible with time dilation?

While time dilation does allow for differences in the passage of time between two objects, it does not necessarily lead to time travel. Time travel as depicted in science fiction would require the manipulation of space-time in ways that are currently not possible.

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