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Size: 4100
Comment:
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Size: 3967
Comment:
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| Deletions are marked like this. | Additions are marked like this. |
| Line 13: | Line 13: |
| || M || L || r || life || vesc || Temp || 650nm || Wien || Scaled || Orbit || tide || tide || || M⊙ || L⊙ || AU || GY || km/s || K || Power || nm || GY || year || ratio || GY || || 0.60 || 0.13 || 0.36 || 23.1 || 38.7 || 4400 || 2.29 || 658 || 53.0 || 0.279 || 0.078 || 1.3 || || 0.65 || 0.18 || 0.42 || 18.2 || 37.2 || 4600 || 2.06 || 631 || 37.4 || 0.341 || 0.116 || 2.0 || || 0.70 || 0.24 || 0.49 || 14.6 || 35.9 || 4780 || 1.85 || 606 || 26.9 || 0.410 || 0.168 || 2.9 || || 0.75 || 0.32 || 0.56 || 11.9 || 34.6 || 4960 || 1.66 || 584 || 19.6 || 0.487 || 0.237 || 4.0 || || 0.80 || 0.41 || 0.64 || 9.8 || 33.5 || 5130 || 1.49 || 565 || 14.6 || 0.572 || 0.328 || 5.8 || || 0.85 || 0.52 || 0.72 || 8.1 || 32.5 || 5300 || 1.35 || 547 || 11.0 || 0.666 || 0.444 || 7.5 || |
|| 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 || |
| Line 22: | Line 22: |
| || 0.87 || 0.57 || 0.76 || 7.6 || 32.1 || || || || || || 0.498 || 8.7 || | || 0.86 || 0.55 || 0.74 || 7.8 || 32.4 || 5330 || 1.32 || 543 || 10.4 || 0.686 || 8.0 || optimum || |
| Line 24: | Line 24: |
| || 0.90 || 0.66 || 0.81 || 6.9 || 31.6 || 5460 || 1.22 || 530 || 8.3 || 0.768 || 0.590 || 10 || || 0.95 || 0.81 || 0.90 || 5.8 || 30.8 || 5620 || 1.10 || 515 || 6.4 || 0.880 || 0.773 || 13 || || 1.00 || 1.00 || 1.00 || 5.0 || 30.0 || 5780 || 1.00 || 501 || 5.0 || 1.000 || 1.000 || 17 || || 1.05 || 1.22 || 1.10 || 4.3 || 29.3 || 5930 || 0.91 || 488 || 3.9 || 1.130 || 1.276 || 22 || || 1.10 || 1.46 || 1.21 || 3.8 || 28.6 || 6080 || 0.83 || 477 || 3.1 || 1.269 || 1.611 || 27 || || 1.15 || 1.75 || 1.32 || 3.3 || 28.9 || 6230 || 0.76 || 465 || 2.5 || 1.418 || 1.011 || 34 || || 1.20 || 2.07 || 1.44 || 2.9 || 27.4 || 6370 || 0.69 || 455 || 2.0 || 1.577 || 2.488 || 42 || || 1.25 || 2.44 || 1.56 || 2.6 || 26.8 || 6510 || 0.64 || 445 || 1.6 || 1.747 || 3.052 || 52 || || 1.30 || 2.86 || 1.69 || 2.3 || 26.3 || 6650 || 0.59 || 436 || 1.3 || 1.927 || 3.713 || 63 || |
|| 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 || |
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 |
|
|||||||||||
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 |