Astronaut Hans leaves Earth in a spaceship traveling at a speed of 0.280c relative to the observer Brian at rest on Earth. Hans is holding a pencil at an angle of 30° with the direction of travel, as
Seen by Hans. What angle does the pencil make with the direction of travel, as seen by Brian on
Earth?
A) $29 ^ { \circ }$
B) $33 ^ { \circ }$
C) $90 ^ { \circ }$
D) $30 ^ { \circ }$
E) $31 ^ { \circ }$

Question

Astronaut Hans leaves Earth in a spaceship traveling at a speed of 0.280c relative to the observer Brian at rest on Earth. Hans is holding a pencil at an angle of 30° with the direction of travel, as
Seen by Hans. What angle does the pencil make with the direction of travel, as seen by Brian on
Earth? 
A) $29 ^ { \circ }$
B) $33 ^ { \circ }$
C) $90 ^ { \circ }$
D) $30 ^ { \circ }$
E) $31 ^ { \circ }$

Quizplus · Accepted Answer

The angle observed by Brian on Earth is affected by the relativistic phenomenon known as the Terrell rotation, which involves Lorentz contraction. However, to solve this problem, we use the relativistic velocity transformation formula for perpendicular directions, which does not contract. The angle seen by Brian can be calculated using the formula for relativistic aberration. The correct answer involves understanding that the angle will appear different due to relativistic effects, specifically the transformation of velocities and directions at relativistic speeds. The calculation would show that the angle changes from the perspective of Brian, leading to the correct answer being an angle slightly different from the one observed by Hans, which is $31 ^ { \circ }$.

Astronaut Hans Leaves Earth in a Spaceship Traveling at a Speed