Question
A spacecraft travels past Earth and Mars in a straight line at a speed v = 0.8c at an instant when Earth and Mars are 2.4 × 1011 m apart; the distance being measured in the fixed frame of reference in which Earth and Mars are at rest. How far apart are Earth and Mars in the frame of the spacecraft? In the frame of the spacecraft, how much time elapses between the spacecraft crossing Earth and the spacecraft reaching Mars?
Answer :
Word Count : 246
This problem involves length contraction and time dilation in special relativity. ### Given: - Speed of the spacecraft: \( v = 0.8c \) - Proper distance between Earth and Mars (rest frame): \( L_0 = 2.4 \times 10^{11} \) m - Speed of light: \( c \) ### Step _______ _________ _______ _____ ______ ___ ______ ___ ______ ____ ______ _____.
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This problem involves length contraction and time dilation in special relativity. ### Given: - Speed of the spacecraft: \( v = 0.8c \) - Proper distance between Earth and Mars (rest frame): \( L_0 = 2.4 \times 10^{11} \) m - Speed of light: \( c \) ### Step _______ _________ _______ _____ ______ ___ ______ ___ ______ ____ ______ _____.
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