How to calculate the angular diameter of Saturn when it lies 9.1 AU from Earth.?
The angular diameter = 2*tan(Saturn’s radius / Distance to Saturn). This is because you can make a right triangle with the base of the triangle from the earth to Saturn and the height of the triangle as Saturn’s radius. But that angle will only be half of the angular diameter, hence the multiplication by two. You’ll obviously want to convert 9.1 AU to kilometers first before you put that in. To find Titan’s orbital period, you can derive the distance from Titan to Saturn using a similar method. You will also need the mass of Saturn. Then use the formula Period = 2*pi* (a^3/gm)^1/2 where a = the semi-major axis of Titan (i.e. what you calculated in the first sentence of this paragraph), g = gravitational constant, and m = mass of Saturn.
