* Sophie and Frieda are twins. They plan a trip to planet X which is 54 light years from Earth. They both leave Earth on their 30th birthday, but on different spacecraft. Sophie takes a spacecraft that travels at .99c, and Frieda takes a spacecraft that travels at .95c. As soon as Frieda arrives she is met at the terminal by Sophie (who was waiting there for her since she had arrived!). What are each of their biological ages (to the nearest 0.1 year) at this meeting? Earth and planet X are in the same (stationary) frame of reference here. A light year is 9.47x1015 m (but using meters will be awkward here)
* Sophie and Frieda are twins. They plan a trip to planet X which is 54 light years from Earth. They both leave Earth on their 30th birthday, but on different spacecraft. Sophie takes a spacecraft that travels at .99c, and Frieda takes a spacecraft that travels at .95c. As soon as Frieda arrives she is met at the terminal by Sophie (who was waiting there for her since she had arrived!). What are each of their biological ages (to the nearest 0.1 year) at this meeting? Earth and planet X are in the same (stationary) frame of reference here. A light year is 9.47x1015 m (but using meters will be awkward here)
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Transcribed Image Text:* Sophie and Frieda are twins. They plan a trip to planet X which is 54 light years from Earth. They
both leave Earth on their 30th birthday, but on different spacecraft. Sophie takes a spacecraft that travels
at .99c, and Frieda takes a spacecraft that travels at .95c. As soon as Frieda arrives she is met at the
terminal by Sophie (who was waiting there for her since she had arrived!). What are each of their
biological ages (to the nearest 0.1 year) at this meeting? Earth and planet X are in the same (stationary)
frame of reference here. A light year is 9.47x1015 m (but using meters will be awkward here)
Expert Solution
Step 1
Given:
The planet X is 54 light-years from the Earth.
The speed of Sophie's spacecraft is .
The speed of Frieda's spacecraft is .
The age at which they leave for their journey is 30.
Introduction:
The twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more.
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