posted by .

Twins who are 19.0 years of age leave the earth and travel to a distant planet 12.0 light-years away. Assume that the planet and earth are at rest with respect to each other. The twins depart at the same time on different spaceships. One twin travels at a speed of 0.854c, and the other twin travels at 0.513c.

(a) According to the theory of special relativity, what is the difference between their ages when they meet again at the earliest possible time?

The answer is 4.3 years, but I'm not sure how they arrived at that...

Lo = 12 light years (ly)
β1 =0.854,
β2 = 0.513
Twin1: L1 =Lo•sqrt(1- (β1)^2) = 12• Lo•sqrt(1- (0.854)^2) = 6.24 ly,
Twin2: L2 =Lo•sqrt(1- (β2)^2) = 12• Lo•sqrt(1- (0.513.)^2) = 10.3 ly.
The time to reach the planet:
Twin1: t1 = L1/v1 = 6.24 ly/0.854c = 7.307 years,
Twin2: t2 = L2/v2 = 10.3 ly/0.513c = 20.08 years.
The age of each twin when each arrives at the planet
Twin1: 19 + 7.307 =26.307 years,
Twin2: 19 + 20.08 =39.08 years.
Twin1 has to wait for twin 2 to arrive. As seen from Earth
Δt1 = (12 ly)/0.854 c = 14.05 years,
Δt2 = (12 ly)/0.513 c = 23.39 years.
Twin1 must wait another 23.39 – 14.05 = 9.34 years for Twin2 to arrive.
When Twin2 arrives, twin A has an age of
24.8 + 9.34 =34.14 years.
The difference between their ages when they meet is
39.08 -34.14 = 4.94 years.
(The answer 4.3 years may be obtained if you take β1 =0.900, β2 = 0.500)

Lo= 12 ly
[twin a] La= Lo*sqrt(1-v^2/c^2)= 5.23 ly
[twin b] Lb= Lo*sqrt(1-v^2/c^2)= 10.39 ly

the time to reach the planet:
[twin a] ta=La/va= 5.23ly/0.9c= 5.81 yr.
[twin b] tb=Lb/vb= 10.39ly/0.5c= 20.78 y

The age of each twin when each arrives at the planet:
[twin a] 19 y + 5.81 y= 24.81 y
[twin b] 19 y + 20.78 y= 39.78 y

Twin1 has to wait for twin 2 to arrive. As seen from Earth
Δt1 = (12 ly)/0.9c = 13.3 years,
Δt2 = (12 ly)/0.5c = 24 years.

Twin1 must wait another 24– 13.3 = 10.7 years for Twin2 to arrive.

When Twin2 arrives, twin A has an age of
24.81 + 10.7 =35.51 years.

The difference between their ages when they meet is
39.78 -35.51 = 4.27 years or 4.3 years

## Similar Questions

1. ### physics help 3!! **

Based on the following data about planet X (which orbits around the Sun): Planet X's distance from Sun = 3.6*1012 m Planet X's radius = 2*106 m Planet X's mass = 8.2*1022 kg a.) Find gx, the size of the acceleration due to gravity …
2. ### physics

On a distant planet, golf is just as popular as it is on earth. A golfer tees off and drives the ball 4.9 times as far as he would have on earth, given the same velocities on both planets. The ball is launched at a speed of 54 m/s …
3. ### physics

Consider a situation where immediately after birth, twins are separated. One continues to live on earth, while the other is whisked away in a space ship at 90% of the speed of light. After 65 years they are reunited. Will they look …
4. ### Physics

Hi,I need help with question 1) There were twins on our planet earth. They were physicst. One of them were sent to space at his 20 year. When he comes back after 20 years of stay in the space he was 40 years but his brother who stayed …
5. ### Physics

Suppose a planet is discovered orbiting a distant star with 13 times the mass of the Earth and 1/13 its radius. How does the escape speed on this planet compare with that of the Earth?
6. ### physics

Imagine a planet that orbited the sun at a distance three times that of Earth. What would the period of that planet be in Earth years?
7. ### Physics Question

Twins who are 19.0 years of age leave the earth and travel to a distant planet 12.0 light-years away. Assume that the planet and earth are at rest with respect to each other. The twins depart at the same time on different spaceships. …
8. ### Physics

On a distant planet, golf is just as popular as it is on earth. A golfer tees off and drives the ball 4.1 times as far as he would have on earth, given the same initial velocities on both planets. The ball is launched at a speed of …
9. ### Physics

At planet X, there is another planet called Y about 34 million light years away. The radius of planet X is 1 * 10^9 m. How far away from the center of the planet X is the planet Y in meters?
10. ### Mathematics

A mother is 33 years older than her twin children. In 3 years her age will be twice the combined ages of the twins. How old are the twins now?

More Similar Questions