Question

A certain star is 11.3 light-years away. a) How long would it take a spacecraft traveling 0.930 c to reach the star from Earth, as measured by observers on Earth? b) How long would it take a spacecraft traveling 0.930c to reach that star from Earth, as measured by observers on the spacecraft? c) What is the distance traveled according to observers on the spacecraft? d) What will the spacecraft occupants compute their speed to be from the results of parts B and C?

Answer 1

a)

D = distance = 11.3 ly = 11.3 x 9.46 x 10¹⁵ m

v = speed of spacecraft = 0.930 c = 0.930 x 3 x 10⁸ m/s

time as observed by observer on earth is given as

T_o = D/v

T_o = (11.3 x 9.46 x 10¹⁵)/(0.930 x 3 x 10⁸)

T_o = 3.83 x 10⁸ sec

b)

T = time observed by observed on the spacecraft

using the equation

T = T_o sqrt(1 - (v/c)²)

T = (3.83 x 10⁸) sqrt(1 - (0.93)²)

T = 1.41 x 10⁸ sec

c)

L_o = D = 11.3 x 9.46 x 10¹⁵ m

length measured is given as

L = L_o sqrt(1 - (v/c)²)

L = (11.3 x 9.46 x 10¹⁵) sqrt(1 - (0.93)²)

L = 3.93 x 10¹⁶ m