Has anyone else noticed this?

[PlutonianEmpire]

One thing I noticed, from working with moons of planets, is that there seems to be a correlation between planetary density, and the apparent angular diameter of said planet as seen from a particular moon that has a particular orbit period.

To test this, I used the AstroSynthesis 2 trial, and the Semi-Major Axis calculator on orbitsimulator.com. I created four planets, each with its own moon, where all moons had an orbit period of exactly three days. For simplicity's sake, the first two planets' radii are 10,000 km, and the last two being 100,000 km, separated into two categories. Each moon had a radius of 1 meter, to eliminate the variations in the camera's distance from the parent planet due to moving the camera around the moon with the mouse. AstroSynthesis measures planetary densities in increments of Earth's density, so a density of 1 would be the exact same density as Earth's density. Masses are measured the same way, 1 = the mass of Earth.

Planet 1a:
Radius: 10,000 km
Density: 1.0
Mass: 3.854055

Moon 1a:
SMA: 137760.3345 km
Orbit Period: 3 days.
Angular diameter of parent planet: 8° 19' 31.8"



Planet 1b:
Radius: 10,000 km
Density: 0.1
Mass: 0.3854055

Moon 1b:
SMA: 63942.6830 km
Orbit Period: 3 days
Angular Diameter of parent planet: 17° 59' 41.4"



Planet 2a:
Radius: 100,000 km
Density 1.0
Mass: 3854.054544

Moon 2a:
SMA: 1377603.2907
Orbit period: 3 days
Angular diameter of parent planet: 8° 19' 31.8"



Planet 2b:
Radius: 100,000 km
Density 0.1
Mass: 385.4054544

Moon 2b:
SMA: 639426.8051
Orbit Period: 3 days
Angular diameter of parent planet: 17° 59' 41.5"



Has anyone noticed this before?

[Hungry4info]

This is fairly easy to understand when you consider the situation like this:
Hold the mass constant. Changing the density then means you're changing the radius. If the mass is constant, then the moon's orbital period stays constant for a given semi-major axis. From that moon, since the body's radius is changing, it's angular diameter will as well.