Main sequence relationships

Some of this is my casual curve-fitting. Your curve-fits may vary.

Mass-Luminosity Relationship.

Mass less than 0.419 Msun
L = 0.42 M^1.99

Mass between 0.419 Msun and 4.54 Msun
L = M^4.23

Mass more than 4.54 Msun
L = 1.616 M^3.47

Mass-Radius Relationship.

R = M^0.7

(There's indications that the exponent varies substantially for stars below
0.7 solar masses, but the data is too skimpy to make definite curvefits.)

In the above R is in units of the solar radius, 6.96E+8 meters, L is in
units of the sun's luminosity, 3.826E+26 Watts, and M is in units of the
sun's mass, 1.989E+30 kilograms.

The Stephan-Boltzmann equation relates the radius and luminosity with the
star's effective temperature. Keeping the units in proportion to the sun's
dimensions, a lot of constants cancel out, leaving:

T = M^(a/4 - b/2)

Where (a) is the exponent that was used in the mass-luminosity relationship,
and (b) is the exponent used in the mass-radius relationship. Of course,
for lack of better information, b=0.7 (constantly).

For stars in the range of masses for habitable planets, a=4.23 (constantly),
and so for these stars:

T = M^0.7075

which (I happened to notice) is about the same as

T = M^[(2)^(-1/2)]

How strange.

Where T is in units of the sun's effective temperature, 5780 Kelvin.

Note, though. Every time I curvefit the data from eclipsing and
spectroscopic binary stars, I get slightly different values for the
coefficients and the exponents in my mass-luminosity relation. And I nail
down the middle section so that our sun is exactly on the line, which isn't
good procedure but it doesn't seem to hurt anything, as the data trends
right through M=1, L=1.

Jerry Abbott