A few examples of what you can ask Wolfram|Alpha about:
Celestial Mechanics
compute the orbital period of a massive body orbiting another
interactively compute the orbital speed of a body
visualize relation between eccentric and true anomaly
compute locations of Lagrange points
investigate the relationship between orbital distance and phase
compute the luminosity of a star of specified mass
compute luminosity from apparent magnitude and distance
compute cosmological properties of the universe
compute cosmological properties, given a redshift
Black Holes
compute properties of a black hole
compute properties of a rotating black hole
Asteroid Impacts
calculate the outcome of an asteroid impact
Cosmic Rays
find out how many cosmic rays reach Earth