The figure on the right shows a portion of the ring and moon system of Saturn. The inner edge of the Cassini division is defined by a 2:1 resonance with Mimas; that is, a particle at that distance orbits twice for every one orbit made by Mimas, and as a result, it feels an unbalanced gravitational tug outward. If Mimas has an orbital semimajor axis of 185,539 km, what is the semimajor axis of the inner edge of the Cassini division in km?

On August 27, 2003, the planet Mars was at a distance of 0.373 AU from Earth. The diameter of Mars is 6788 km. Calculate the angular diameter of Mars, as seen from Earth on August 27, 2003. Give your answer in arcminutes.

Imagine a trans-Neptunian object with roughly the same mass as Earth but located 50 AU from the sun. a) based on the solar nebula theory, what do you think this object would be made of and why? b) on the basis of speculation, assume a reasonable density for this object and calculate its diameter in units of Earth radii.

If you were to record the spectrum of Saturn as well as the A ring, you would find light from one edge of the rings redshift and light from the other edge blueshift. If you observed a spectral line at a wavelength of 525 nm, what difference in wavelength (in nm) should you expect between the opposite edge of the rings? (Hint: The radius of the edge of the A ring is 136,500 km. Use the formula for orbital velocity and the formula for the Doppler shift.)  _______ nm