The Kerbol Rant

What's wrong with the Sun in Kerbal Space Program? Short answer: "A Lot." Long Answer follows.

First of all, I'd like to establish some numbers. These are using the real world units.
KSP Sun Mass: 0.0088 Solar Masses.
KSP Sun Radius: 0.376 Solar Radii.
Kerbin Orbital Radius: 0.090909 au.
KSP Sun Light Color: White.
KSP Sun Surface Color: Yellow.

Problem 1: The mass is too low.
If taken in a realistic interpretation, where the sizes of the planets in the game are explained not by changed physics, but instead by some kind of magic degenerate cores, or superdense elements, then the Sun's mass is wrong. It's only 0.0088 solar masses, a full 10 times lower than the lowest possible mass for a star! That's brown dwarf or super-jupiter territory, and couldn't possibly be a star!

Solution to Problem 1: There is no real problem.
However, I personally believe that the solar system is best explained by changed gravitational physics, that the planet's high surface gravity for their size is related to a 10 to 11 times larger constant of gravity. In the context of this universe, the real sun would have 0.01 solar masses, and Kerbol only 0.088. Thus, the Kerbal sun has a mass of 0.88 kerbal-scale Solar masses. This is fine for a main sequence star.

Problem 2: The radius is too large.
When the Mun was added, it was given a radius of 200,000 meters, larger than 1/10 the size of the Moon. It was also given an orbit that was about three times smaller than 1/10 the Earth-Moon distance. This meant that the Mun was a little over three times larger than the Moon in Kerbin's sky. Eventually, the Sun ("Kerbol") was added (it was already kind of there, but it was just a bright light in the distance, not a physical object). The developers wanted solar ("Kerbolar?") eclipses to be possible, so they tweaked the radius of the sun until it was the same angular size as the Mun.

This results in the Sun being almost four times larger than it should be for its mass. While it could get to that scale while it is transitioning to the Red Giant Branch, it wouldn't stay that size (and more importantly, that luminosity) for long enough for Kerbin to evolve life.

Solution to Problem 2: Shrink the Sun. More details later.

Problem 3: The sun is the wrong color. (Kind of)
The Kerbal Sun emits white light, but its surface is yellow. If its light is white, its surface should be white too.

Actually it's more complicated than that. The coolest stars, often called "red," are actually a color of orange or orange-yellow. It turns out that the temperature of a star relates to its color. There's a handy calculator for this here: https://academo.org/demos/colour-temperature-relationship/ And it also turns out that the luminosity of a star depends upon its color and its radius. And it also turns out that the habitable zone of a star depends upon its luminosity. Do you see where I'm going? We know that Kerbin has to be orbiting in a location where it gets the same insolation (heat and light) as Earth does.

[Star Luminosity in Solar Luminosities]^0.5 = [Earth's Location in Habitable Zone.]
(Temperature of Star / Temperature of Sun)^4 * (Star Radius in Solar Radii)^2 = [Luminosity of the Star in Solar Luminosities].

Kerbin orbits at 0.0909. So the Kerbal Sun must have a luminosity of 0.0909^2 = 0.00826281 Solar luminosities. (In kerbal scale, this is normal for a star of Kerbol's mass) The color white is represented by a temperature of about 6600 Kelvin, but we'll pretend it's 5800 Kelvin, like the real Sun. But the temperature required for Kerbol's size and Kerbin's orbit in the hab zone is 2850 Kelvin. This corresponds to a color of slightly dull orange, a very cool star indeed.

But wait, the color of the light might be wrong, but the color of the surface, which is yellow, is actually not *totally* wrong! So really, the Sun's light needs to match its surface, not the other way around. (With a slight tweak to the exact coloring)

Solution to problem 3: Make the Sun's surface and the sun's light Orange.

Problem 4 and Solution: OK, so the sun is orange now, but I already said that the sun shouldn't be big. Also orange looks kind of ugly and no one wants to see that lighting instead of near white.

We have two ways of shrinking the sun to make it sensible. We could shrink it to match its white color, or we could shrink it to match its mass.

Kerbol has a mass of 0.88 kerbal-scale sol masses. This is equivalent to an early-K "Orange Dwarf" (Orange dwarfs are really pale yellow-white). This option makes the sun light visibly yellowish, but not so orange as to be overwhelming. It's subtle enough that the eye can white-balance this. Suggested values for radius and temperature: 0.11 Solar radii (1.1 in kerbal scale) and 5110 Kelvins.

Alternatively, we could make Kerbol a G2V star just like the sun, with a temperature of 5800K. This star would be 0.0909 solar radii (0.909 in kerbal scale).