I'm either missing something or failing at some basic math here, but is it possible to calculate the map resolution (map units/pixel) based on altitude (from sea level)? I have center coordinates and projection.
Map resolution is in no way related to the altitude,
ESRI defines resolution as
The detail with which a map depicts the location and shape of geographic features. The larger the map scale, the higher the possible resolution. As scale decreases, resolution diminishes and feature boundaries must be smoothed, simplified, or not shown at all; for example, small areas may have to be represented as points.
My two cents from the conversation following the previous answer: from what @Thiatt explains, he wants to define resolution as the apparent size of a pixel, viewed from an altitude A (which is actually a good definition). So, this is a simple trigonometry problem.
First, you have to set an "angular swath" (or "field of view", I don't know the english correct term) α, which would be the maximum view angle (from the nadir). Let's say α = 45°, but you can adjust it depending on the resolution you want.
Now, I will assume that the max horizontal and vertical extent of your map, from the center, is N = 500 px (i.e. your map size is 1000 x 1000 px).
Then, if R is the resolution (in m/px), you have the following relationship:
With α = 45° and N = 500 px, you get R = 0.2 m/px at the altitude A = 100 m, and R = 2 m/px for A = 1000 m. If R is too low for your application, increase α in the formula.
Hope this will help.