Can somebody provide an algorithm for calculating a planet's or asteroid's visual magnitude?

I am looking for an algorithm that will allow me to calculate the absolute and apparent magnitudes of a planet or asteroid given the brightness of the parent star, the size of the body, the albedo of the body, the distance of the body from the star, and the distance of the observer from the body (and any other variables that I've forgotten to mention). I'm fairly comfortable in math but I'm by no means an expert, so I would appreciate an explanation on how to use the algorithm. Any and all detail is appreciated. This is for my own edification. Thanks in advance.