Question

1. Planet J is 20 lightyears from Earth. Fred, who is 20 years old, boards his Spaceship from Earth and zips to planet J at 0.800c. Fred leaves behind his twin brother Tom. Upon reaching Planet J, Fred makes a "U-turn" and zips back to Earth. Ignore acceleration effect. (a) What are the biological ages of Tom and Fred by the time Fred reaches Planet J? (b) What are the biological ages of Tom and Fred by the time Fred returns to Earth?

Answer 1

(a) here squareroot 1 - v^2/c^2 = squareroot 1 - (0.8 c)^2/c^2 = 0.6 From Fred of reference, Actual distance covered L = L_0 squareroot 1 - v^2/c^2 = 20 light years times 0.6 times 12 light years time taken by fixed reference = L/v = 15 years In the reference of tom Actual distance travelled is L_0 = 20 light years time taken by Fred in the reference frame of L_0/V = 25 years Hence Biological age of Tom = 20 + 25 = 45 years Biological age of Fred = 20 + 15 = 35 years] returns to J planet (b) similarly Biological age of Tom = 20 + 25 + 25 = 70 years Biological age of Fred = 20 + 15 + 15 = 50 years] returns to Earth