Are these traits for my planet mathematically accurate? Could it support life?

Your star is not going to work, so the planet won't either.

Mass of star: 1.04 M☉

Radius of star: 0.69 R☉

Surface temperature of star: 4,620° K

Luminosity of star: 0.2 L☉

There is a well known set of relationships for mass-luminosity (and hence temperature) for stars. It's explained on this Wikpedia page.

For stars of around 1 solar mass that relationship says :

$$\frac L {L_\odot}= \left( \frac M {M_\odot}\right)^4$$

So your star with $M=1.04 M_\odot$ should have $L=1.17L_\odot$ and not $0.2L_\odot$ as you state.

The knock on from this is of course the temperature and conditions on your planet.

The star is basically about 16% more luminous than our own, but your planet is about half the distance we are from the Sun. It's going to be hot !

The (very rough) calculation for effective temperature of a planet will be :

$$T = T_\oplus \left( \frac {L(1-A)a_\oplus^2} {L_\odot(1-A_\oplus)a^2} \right)^{\frac 1 4}$$

With your number for the star this gives $T \approx 1.4 T_\oplus$. So $40$ % hotter than earth, or about $110^\circ K$ hotter. That puts it well into runaway greenhouse territory and it would likely be far worse.

Most of that is a result of your very close orbit - move it out past $1\, AU$ and you'll get better results.

The star's radius is actually a bit tricky - at around $M=M_\odot$ the typical mass-radius behavior has a distinct boundary - different behaviors on each side. Probably the simplest thing is to treat your star as being almost the same as the Sun in terms of mass and you get a radius of about the same as the Sun.

posted over 4 years ago

StephenG‭

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