# Length Contraction Understanding Problem

Suppose a ball moving with 0.9c in the x-axis on a frame S' with axes parallel to frame S on which an observer sees the ball. Due to length contraction it appears as a vertical ellipsoid, when it moves in the vertical direction then as a horizontal ellipsoid, and when it moves at an angle 45$^\circ$ to both axes how does the ball now appears? I have two thoughts:

• Spherical because we can get two equal components of speed in the two axes which give equal contraction
• Diagonal Ellipsoid using the previous logic.

We are free to arrange our axes as we want, so no matter what direction the ball is going I can rotate my axes so my $x$ axis lies along the direction of motion of the ball. If you look at the diagram above and imagine rotating your axes 45º anticlockwise then the ball will be moving along the new $x$ axis and therefore will be shortened along the new $x$ axis.