# Long Life Star

The heating Sun will make the (unmodified) Earth uninhabitable in less than a billion years. How long would a lower mass star last, and for a closer planet with the same illumination as Earth, what would the system escape velocity be?

In the mass range near the suns ( 0.5 M⊙ < M < 2.0 M⊙), the luminosity is approximately L/L⊙ = (M/M⊙)⁴ . Assuming a 5 billion year lifetime for Earth, and an escape velocity of 30 km/s, what is the orbit radius in AU and the escape velocity for an "earthlike" planet?

NOTE 1 the "lifetime" should be scaled (somehow) to the amount of photosynthesis-friendly red light compared to the amount of life-scrambling heat. Life decays with thermal energy, and builds from red photons (blue is used by terrestrial photosynthesis, but probably is not necessary).

NOTE 2 Other (artificial?) photosynthetic systems may be more optimal, using different colors of light. Earth photosynthesis evolved for the wavelengths that penetrate water.

NOTE 3 Estimating Tidal effects: Tides from the Moon plus the Earth slow the earth's rotation by 2.3 milliseconds per century. Solar tidal effects are 46% of lunar tidal effects, so the day slows down due to the Sun alone is 7.3 microseconds/year. That would slow the earth to a stop in 12 billion years - though the Earth will be gone before then. Scale tidal locking to a 17 billion year tidal lock for our G2 Sun.

 M L r life vesc Temp 650nm Wien Scaled Orbit tide M⊙ L⊙ AU GY km/s K Power nm GY year GY 0.60 0.13 0.36 23.1 38.7 4400 2.29 658 53.0 0.279 1.3 0.65 0.18 0.42 18.2 37.2 4600 2.06 631 37.4 0.341 2.0 0.70 0.24 0.49 14.6 35.9 4780 1.85 606 26.9 0.410 2.9 0.75 0.32 0.56 11.9 34.6 4960 1.66 584 19.6 0.487 4.0 0.80 0.41 0.64 9.8 33.5 5130 1.49 565 14.6 0.572 5.8 0.85 0.52 0.72 8.1 32.5 5300 1.35 547 11.0 0.666 7.5 0.86 0.55 0.74 7.8 32.4 5330 1.32 543 10.4 0.686 8.0 optimum K0?G9 0.90 0.66 0.81 6.9 31.6 5460 1.22 530 8.3 0.768 10 0.95 0.81 0.90 5.8 30.8 5620 1.10 515 6.4 0.880 13 1.00 1.00 1.00 5.0 30.0 5780 1.00 501 5.0 1.000 17 1.05 1.22 1.10 4.3 29.3 5930 0.91 488 3.9 1.130 22 1.10 1.46 1.21 3.8 28.6 6080 0.83 477 3.1 1.269 27 1.15 1.75 1.32 3.3 28.9 6230 0.76 465 2.5 1.418 34 1.20 2.07 1.44 2.9 27.4 6370 0.69 455 2.0 1.577 42 1.25 2.44 1.56 2.6 26.8 6510 0.64 445 1.6 1.747 52 1.30 2.86 1.69 2.3 26.3 6650 0.59 436 1.3 1.927 63

Twice the escape energy for a star lasting 8 times as long. A "perfect" star system for star-faring life might be an M = 0.7 M⊙ star (K5?), with 3 times the stellar lifetime, 0.586 the tidelocking time, 20% more escape velocity.

 Class R/R☉ M/M☉ L/L☉ K Example F0 1.3 1.7 6 7,240 Gamma Virginis F5 1.2 1.3 2.5 6,540 Eta Arietis G0 1.05 1.10 1.26 5,920 Beta Comae Berenices G2 1.00 1.00 1.00 5,780 Sun G5 0.93 0.93 0.79 5,610 Alpha Mensae K0 0.85 0.78 0.40 5,240 70 Ophiuchi A

LongLifeStar (last edited 2016-07-03 07:52:07 by KeithLofstrom)