Solve Twin Paradox Problem: Mary's Journey

In summary, the International Space Federation constructs a new spaceship that can travel at a speed of 0.910c. Mary, the astronaut, boards the spaceship to travel to Barnard's star, which is the second nearest star to our solar system after Alpha Centauri and is 5.98 ly away. After reaching Barnard's star, the spaceship travels slowly around the star system for 6 years doing research before returning back to Earth. Her twin, Frank, who is on Earth during this time, is older by 6 years when she returns.
  • #1
freefallin38
20
0
[SOLVED] Twin Paradox problem

Here is a problem about twin paradox that I can't quite figure out. I got part a, but I can't get part b. I think that the 6 years spent doing research is kinda throwing me off. Help!

The International Space Federation constructs a new spaceship that can travel at a speed of 0.910c. Mary, the astronaut, boards the spaceship to travel to Barnard's star, which is the second nearest star to our solar system after Alpha Centauri and is 5.98 ly away. After reaching Barnard's star, the spaceship travels slowly around the star system for 6 years doing research before returning back to Earth.
(a) How much time does the journey take?
11.44913698 years
(b) How much older is her twin Frank when she returns?
? years
 
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  • #2
freefallin38 said:
Here is a problem about twin paradox that I can't quite figure out. I got part a, but I can't get part b. I think that the 6 years spent doing research is kinda throwing me off. Help!

The International Space Federation constructs a new spaceship that can travel at a speed of 0.910c. Mary, the astronaut, boards the spaceship to travel to Barnard's star, which is the second nearest star to our solar system after Alpha Centauri and is 5.98 ly away. After reaching Barnard's star, the spaceship travels slowly around the star system for 6 years doing research before returning back to Earth.
(a) How much time does the journey take?
11.44913698 years
(b) How much older is her twin Frank when she returns?
? years

Question a is ambiguous since it does not specify in what frame...but I guess it means in the spaceship's frame.

Since the spaceship travels slowly around the star system, the six years of research lasts that amount of time in both frames (basically the two frames are at rest relative to one another during that period). So find the time taken for the ship to get to the star as measured in Earth's frame, double that and add six years.
 
  • #3
Yep, I tried doing that, using the formula T=2L/v, added 6 to that, and got 19.1429, but the answer still wasn't right. Do you think I'm doing something wrong?
 
  • #4
T=2L/v is the time the ship is in flight as experienced on earth. That's not the time experienced on the ship. Don't forget the time dilation factor.
 
  • #5
freefallin38 said:
Yep, I tried doing that, using the formula T=2L/v, added 6 to that, and got 19.1429, but the answer still wasn't right. Do you think I'm doing something wrong?
Looks like the right calculation to me. (You are calculating the time according to the Earth.) What did you put for the final answer to part b?

Note: The question is a bit ambiguous. I assume they are asking: How much older is Frank than his sister.
 
Last edited:
  • #6
do you mean gamma= 1/sqrt(1-v^2/c^2)? because part 2 asks for the twin who stayed on Earth's age, and my book said that the formula for that time, as measured on earth, is T=2L/v. So i figured just do that +6. I used T=2L/(gamma*v) +6 for part a's answer.

The answer I put for part b was T=2*5.98/.91+6= 19.1429, but the homework program says it's wrong.
 
  • #7
freefallin38 said:
The answer I put for part b was T=2*5.98/.91+6= 19.1429, but the homework program says it's wrong.
Read the note that I added to my last post.
 
  • #8
Doc Al said:
Read the note that I added to my last post.

gotcha! thank you!:smile:
 

1. What is the Twin Paradox Problem?

The Twin Paradox Problem is a thought experiment in the theory of relativity that examines the concept of time dilation. It involves two twins, one who stays on Earth and one who travels through space at high speeds, and how their experiences of time differ.

2. How does the Twin Paradox Problem relate to Mary's Journey?

Mary's Journey is a specific example of the Twin Paradox Problem, where one twin, Mary, stays on Earth while the other twin, John, travels through space and returns to Earth. It is often used to explain the concept of time dilation in a more relatable way.

3. What causes the time dilation in the Twin Paradox Problem?

The time dilation in the Twin Paradox Problem is caused by the different speeds at which the twins are traveling. According to the theory of relativity, time moves slower for objects in motion than for objects at rest.

4. How can the Twin Paradox Problem be solved?

The Twin Paradox Problem can be solved using the principles of special relativity, which involves understanding the concept of time dilation and the effects of relative velocities. The solution can be calculated using mathematical equations and can be observed in experiments with high-speed particles.

5. What is the significance of the Twin Paradox Problem in the field of physics?

The Twin Paradox Problem is significant because it challenges our traditional understanding of time and space. It also highlights the fundamental principles of special relativity and has been used to test and confirm the theory in various experiments. It has also led to the development of technologies such as GPS, which rely on the principles of relativity to function accurately.

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