Classify the space-time interval between each pair of events as timelike, spacelike, or lightlike:

(a) A sunspot erupts on the surface of the Sun and is seen on Earth \(500 \mathrm{~s}\) later.

(b) A supernova explodes and is noticed \(8.00 \times 10^{20} \mathrm{~m}\) away after \(8.45 \times 10^{4} \mathrm{y}\) by an observer at rest relative to the supernova.

(c) You receive light in the Earth reference frame emitted by a satellite \(60,000 \mathrm{~km}\) away at \(t=0\), and \(233 \mathrm{~ms}\) later receive light emitted by a spaceship \(180,000 \mathrm{~km}\) away in the same direction as the satellite.

(d) At \(t=0\), a pilot traveling at \(0.75 c_{0}\) relative to a star system receives signals from two planets A and B in that system. She then passes planet \(A\) (event 1) at \(t=450 \mathrm{~s}\) and \(90 \mathrm{~s}\) after that passes planet B (event 2 ).