# Time Dialation-Theory of Relativity

• AlmonzoWilder
In summary, a 30 year-old astronaut leaves her newborn child on Earth and goes on a round-trip voyage to a star that is 40 light-years away traveling in a spaceship that is traveling at 0.90 c. The time for the astronaut to reach the star as viewed by an observer (her child) can be calculated as 88 years. When she returns, the astronaut's age will be 45.756 years and her child's age will be 88 years. This is due to the fact that time is relative and depends on the observer's frame of reference.
AlmonzoWilder

## Homework Statement

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

## Homework Equations

$$\Delta t_o = \Delta t \sqrt{1-v^2/c^2}$$

## The Attempt at a Solution

Since spaceship is traveling at 0.90c, the trip will take 10% longer to reach star each way, therefore time to reach star as viewed by an observer(child) can be calculated as such:
t=40yrs+(0.20)x(40yrs)
t=88yrs

And then time for the astronaut can be calculated from that value for observed time:
$$\Delta t_o = \Delta t \sqrt{1-v^2/c^2}$$
$$\Delta t_o =88yrs \Delta t \sqrt{1-(0.9c)^2/c^2}$$
$$\Delta$$to=8.756yrs

So age of astronaut is $$\Delta$$to + her original age, making her 45.756, and her child 88.

That's as far as I've gotten, I can't figure out what is done wrong, the numbers are right but if the astronaut perceives time on Earth as moving slower than that in the spaceship and yet she returns home to find her child almost twice as old as her, there has to be something wrong.

Last edited:
Sorry about the long spaces in between the equations, I'm not quite sure what I did wrong.

Okay, looking over my equation on paper, I found a small error when I calculated the age of the astronaut, she would be 38.358 =37yrs, making her 75.4 yrs old, however this still does not solve my problem, any thoughts?

In the equations, you are mixing up tex and php. The tex language, for example, uses x^y for a superscript... not the php "sup" tags that you get with the superscript button.

Here is a rewrite of your original post using the correct syntax for tex. If you click on an equation, you will see how it is written.

## Homework Statement

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

## Homework Equations

$$\Delta t_o = \Delta t \sqrt{1-v^2/c^2}$$

## The Attempt at a Solution

Since spaceship is traveling at 0.90c, the trip will take 10% longer to reach star each way, therefore time to reach star as viewed by an observer(child) can be calculated as such:
t=40yrs+(0.20)x(40yrs)
t=88yrs

And then time for the astronaut can be calculated from that value for observed time:

$$\Delta t_o = \Delta t \sqrt{1-v^2/c^2}$$

$$\Delta t_o = 88 \text{yrs} \times \sqrt{1-(.90c)^2/c^2}$$

$$\Delta t_o = 8.756 \text{yrs}$$

So age of astronaut is Δto + her original age, making her 45.756, and her child 88.

Now you have a problem there. Travelling 40 light years at 0.9c takes 40/0.9 = 44.444 years, not 44.

The factor you multiply by is
$$\sqrt{1-0.9^2} = \sqrt{1 - 0.81} = \sqrt{0.19} = 0.436$$​
You originally had this wrong, but this factor looks correct now. But you should divide by 0.9, not multiply by 1.1, to get the time elapsed back on Earth.

Cheers -- sylas

PS. (Note that you can edit your post. Getting rid of those long limes would make the thread fit on the page better.)

Last edited:
Thanks, that looks better now, not perfect but better. :)
I get what you did, but I still do not understand why the child would be so much older than the mother when she returns...

AlmonzoWilder said:
Thanks, that looks better now, not perfect but better. :)
I get what you did, but I still do not understand why the child would be so much older than the mother when she returns...

Why not?

Of course, I know why not. You are used to time being something that passes at the same rate everywhere. It's what we are all used to. If we habitually traveled at close to the speed of light, this would not be hard to understand, because we would all be used to it. But because we move at velocities so much less than light speed, the relative nature of time seems strange... seems hard to understand.

But that's the way it is, all the same. The amount of time that passes between two events is not an absolute, but depends on how you move between those two events.

Cheers -- sylas

## What is time dilation?

Time dilation is a phenomenon described by Einstein's theory of relativity in which time appears to pass slower for an object or person that is moving at high speeds or is in a strong gravitational field.

## How does time dilation occur?

Time dilation occurs because of the relationship between space and time. According to the theory of relativity, time and space are interwoven and can be affected by things like velocity and gravity. As an object's velocity increases or as it enters a strong gravitational field, time appears to slow down for that object.

## What evidence supports the theory of time dilation?

Several experiments have been conducted that support the theory of time dilation. One of the most well-known is the Hafele-Keating experiment in which atomic clocks were flown around the world and were found to be slightly out of sync with stationary clocks. The results of this experiment confirmed the predictions of time dilation.

## Why is time dilation important?

Time dilation is important because it has major implications for our understanding of the universe. It has been confirmed by numerous experiments and is a fundamental aspect of Einstein's theory of relativity. Time dilation also plays a crucial role in the functioning of GPS satellites and is essential for their accuracy.

## Can time dilation be observed in everyday life?

Yes, time dilation can be observed in everyday life, but the effects are so small that they are not noticeable to humans. However, high-speed particles and objects like satellites experience time dilation, and it is essential to take this into account when making calculations and predictions in fields like physics and astronomy.

• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
9
Views
2K
• Introductory Physics Homework Help
Replies
38
Views
3K
• Special and General Relativity
Replies
13
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
1K