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| 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? | 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? |
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| '''NOTE''' the "lifetime" should be scaled (somehow) to the amount of photosynthesis-friendly red light compared to the amount of life-scrambling thermal infrared. Life decays with thermal energy, and builds from red photons (blue is used by terrestrial photosynthesis, but probably is not necessary). | '''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). |
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| '''NOTE 2''' Other photosynthetic systems may be more optimal, using different colors of light. | '''NOTE 2''' Other (artificial?) photosynthetic systems may be more optimal, using different colors of light. Earth photosynthesis evolved for the wavelengths that penetrate water. |
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| == not so good table == | || M || L || r || life || vesc || Temp || 650nm || Wien || Scaled || Orbit || tidelock || || M⊙ || L⊙ || AU || GY || km/s || K || Power || nm || GY || year || ratio || || 0.10 || 0.0001 || 0.0100 || 5000.0 || 94.8683 || 1694 || 0.95 || 1711 || 4764.2 || 0.003 || 0.032 || || 0.15 || 0.0005 || 0.0225 || 1481.5 || 77.4597 || 2103 || 2.39 || 1378 || 3533.9 || 0.009 || 0.058 || || 0.20 || 0.0016 || 0.0400 || 625.00 || 67.0820 || 2451 || 3.37 || 1182 || 2106.8 || 0.018 || 0.089 || || 0.25 || 0.0039 || 0.0625 || 320.00 || 60.0000 || 2761 || 3.80 || 1050 || 1216.5 || 0.031 || 0.125 || || 0.30 || 0.0081 || 0.0900 || 185.19 || 54.7723 || 3043 || 3.85 || 952 || 713.61 || 0.049 || 0.164 || || 0.35 || 0.0150 || 0.1225 || 116.62 || 50.7093 || 3303 || 3.69 || 877 || 430.81 || 0.072 || 0.207 || || 0.40 || 0.0256 || 0.1600 || 78.125 || 47.4342 || 3547 || 3.43 || 817 || 268.29 || 0.101 || 0.253 || || 0.45 || 0.0410 || 0.2025 || 54.870 || 44.7214 || 3777 || 3.14 || 767 || 172.13 || 0.136 || 0.302 || || 0.50 || 0.0625 || 0.2500 || 40.000 || 42.4264 || 3995 || 2.84 || 725 || 113.51 || 0.177 || 0.354 || || 0.55 || 0.0915 || 0.3025 || 30.053 || 40.4520 || 4203 || 2.55 || 689 || 76.74 || 0.224 || 0.408 || || 0.60 || 0.1296 || 0.3600 || 23.148 || 38.7298 || 4402 || 2.29 || 658 || 53.06 || 0.279 || 0.465 || || 0.65 || 0.1785 || 0.4225 || 18.207 || 37.2104 || 4594 || 2.06 || 631 || 37.44 || 0.341 || 0.524 || || 0.70 || 0.2401 || 0.4900 || 14.577 || 35.8569 || 4779 || 1.85 || 606 || 26.90 || 0.410 || 0.586 || || 0.75 || 0.3164 || 0.5625 || 11.852 || 34.6410 || 4958 || 1.66 || 584 || 19.65 || 0.487 || 0.650 || || 0.80 || 0.4096 || 0.6400 || 9.7656 || 33.5410 || 5132 || 1.49 || 565 || 14.57 || 0.572 || 0.716 || || 0.85 || 0.5220 || 0.7225 || 8.1417 || 32.5396 || 5300 || 1.35 || 547 || 10.96 || 0.666 || 0.784 || || 0.90 || 0.6561 || 0.8100 || 6.8587 || 31.6228 || 5464 || 1.22 || 530 || 8.34 || 0.768 || 0.854 || || 0.95 || 0.8145 || 0.9025 || 5.8318 || 30.7794 || 5624 || 1.10 || 515 || 6.42 || 0.880 || 0.926 || || 1.00 || 1.0000 || 1.0000 || 5.0000 || 30.0000 || 5780 || 1.00 || 501 || 5.00 || 1.000 || 1.000 || || 1.05 || 1.2155 || 1.1025 || 4.3192 || 29.2770 || 5932 || 0.91 || 488 || 3.93 || 1.130 || 1.076 || || 1.10 || 1.4641 || 1.2100 || 3.7566 || 28.6039 || 6081 || 0.83 || 477 || 3.12 || 1.269 || 1.154 || || 1.15 || 1.7490 || 1.3225 || 3.2876 || 27.9751 || 6227 || 0.76 || 465 || 2.49 || 1.418 || 1.233 || || 1.20 || 2.0736 || 1.4400 || 2.8935 || 27.3861 || 6370 || 0.69 || 455 || 2.01 || 1.577 || 1.315 || || 1.25 || 2.4414 || 1.5625 || 2.5600 || 26.8328 || 6510 || 0.64 || 445 || 1.63 || 1.747 || 1.398 || || 1.30 || 2.8561 || 1.6900 || 2.2758 || 26.3117 || 6648 || 0.59 || 436 || 1.33 || 1.927 || 1.482 || || 1.35 || 3.3215 || 1.8225 || 2.0322 || 25.8199 || 6783 || 0.54 || 427 || 1.10 || 2.118 || 1.569 || || 1.40 || 3.8416 || 1.9600 || 1.8222 || 25.3546 || 6915 || 0.50 || 419 || 0.91 || 2.319 || 1.657 || |
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| ||Class || Radius || Mass || Lum || Temp || Example || || B || V || R || H || Planet || vesc || || || R/R☉ || M/M☉ || L/L☉ || K || || GY || 445 || 551 || 658 || 1630 || AU || km/s || || 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 || |
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. |
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== not so good table == || M || L || r || life || vesc || Wp || Temp || B || V || G || R || H || || M⊙ || L⊙ || AU || GY || km/s || mag || K || 445 || 551 || || 658 || 1630 || || 0.50 || 0.0625 || 0.2500 || 40.0000 || 42.4264 || M1V || || || || || || || || 0.55 || 0.0915 || 0.3025 || 30.0526 || 40.4520 || || || || || || || || || 0.60 || 0.1296 || 0.3600 || 23.1481 || 38.7298 || M0V || || || || || || || || 0.65 || 0.1785 || 0.4225 || 18.2066 || 37.2104 || || || || || || || || || 0.70 || 0.2401 || 0.4900 || 14.5773 || 35.8569 || K5V || || || || || || || || 0.75 || 0.3164 || 0.5625 || 11.8519 || 34.6410 || K3V || || || || || || || || 0.80 || 0.4096 || 0.6400 || 9.7656 || 33.5410 || K2V || || || || || || || || 0.85 || 0.5220 || 0.7225 || 8.1417 || 32.5396 || G9V || || || || || || || || 0.90 || 0.6561 || 0.8100 || 6.8587 || 31.6228 || G7V || || || || || || || || 0.95 || 0.8145 || 0.9025 || 5.8318 || 30.7794 || G6V || || || || || || || || 1.00 || 1.0000 || 1.0000 || 5.0000 || 30.0000 || G2V || || || || || || || || 1.05 || 1.2155 || 1.1025 || 4.3192 || 29.2770 || G3V || || || || || || || || 1.10 || 1.4641 || 1.2100 || 3.7566 || 28.6039 || G1V || || || || || || || || 1.15 || 1.7490 || 1.3225 || 3.2876 || 27.9751 || F9V || 6130 || || || || || || || 1.20 || 2.0736 || 1.4400 || 2.8935 || 27.3861 || F7V || || || || || || || || 1.25 || 2.4414 || 1.5625 || 2.5600 || 26.8328 || F6V || 6520 || || || || || || 25 Cancri || || 1.30 || 2.8561 || 1.6900 || 2.2758 || 26.3117 || F4V || || || || || || || || || 1.35 || 3.3215 || 1.8225 || 2.0322 || 25.8199 || F3V || 6740 || 14.2 || 13.3 || || 13.1 || 11.7 || COROT-3 || || 1.40 || 3.8416 || 1.9600 || 1.8222 || 25.3546 || F1V || || || || || || || Twice the escape energy for a star lasting 8 times as long. A "perfect" star system for star-faring life might be a K5, with 3 times the lifetime and 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 || |
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.
M |
L |
r |
life |
vesc |
Temp |
650nm |
Wien |
Scaled |
Orbit |
tidelock |
M⊙ |
L⊙ |
AU |
GY |
km/s |
K |
Power |
nm |
GY |
year |
ratio |
0.10 |
0.0001 |
0.0100 |
5000.0 |
94.8683 |
1694 |
0.95 |
1711 |
4764.2 |
0.003 |
0.032 |
0.15 |
0.0005 |
0.0225 |
1481.5 |
77.4597 |
2103 |
2.39 |
1378 |
3533.9 |
0.009 |
0.058 |
0.20 |
0.0016 |
0.0400 |
625.00 |
67.0820 |
2451 |
3.37 |
1182 |
2106.8 |
0.018 |
0.089 |
0.25 |
0.0039 |
0.0625 |
320.00 |
60.0000 |
2761 |
3.80 |
1050 |
1216.5 |
0.031 |
0.125 |
0.30 |
0.0081 |
0.0900 |
185.19 |
54.7723 |
3043 |
3.85 |
952 |
713.61 |
0.049 |
0.164 |
0.35 |
0.0150 |
0.1225 |
116.62 |
50.7093 |
3303 |
3.69 |
877 |
430.81 |
0.072 |
0.207 |
0.40 |
0.0256 |
0.1600 |
78.125 |
47.4342 |
3547 |
3.43 |
817 |
268.29 |
0.101 |
0.253 |
0.45 |
0.0410 |
0.2025 |
54.870 |
44.7214 |
3777 |
3.14 |
767 |
172.13 |
0.136 |
0.302 |
0.50 |
0.0625 |
0.2500 |
40.000 |
42.4264 |
3995 |
2.84 |
725 |
113.51 |
0.177 |
0.354 |
0.55 |
0.0915 |
0.3025 |
30.053 |
40.4520 |
4203 |
2.55 |
689 |
76.74 |
0.224 |
0.408 |
0.60 |
0.1296 |
0.3600 |
23.148 |
38.7298 |
4402 |
2.29 |
658 |
53.06 |
0.279 |
0.465 |
0.65 |
0.1785 |
0.4225 |
18.207 |
37.2104 |
4594 |
2.06 |
631 |
37.44 |
0.341 |
0.524 |
0.70 |
0.2401 |
0.4900 |
14.577 |
35.8569 |
4779 |
1.85 |
606 |
26.90 |
0.410 |
0.586 |
0.75 |
0.3164 |
0.5625 |
11.852 |
34.6410 |
4958 |
1.66 |
584 |
19.65 |
0.487 |
0.650 |
0.80 |
0.4096 |
0.6400 |
9.7656 |
33.5410 |
5132 |
1.49 |
565 |
14.57 |
0.572 |
0.716 |
0.85 |
0.5220 |
0.7225 |
8.1417 |
32.5396 |
5300 |
1.35 |
547 |
10.96 |
0.666 |
0.784 |
0.90 |
0.6561 |
0.8100 |
6.8587 |
31.6228 |
5464 |
1.22 |
530 |
8.34 |
0.768 |
0.854 |
0.95 |
0.8145 |
0.9025 |
5.8318 |
30.7794 |
5624 |
1.10 |
515 |
6.42 |
0.880 |
0.926 |
1.00 |
1.0000 |
1.0000 |
5.0000 |
30.0000 |
5780 |
1.00 |
501 |
5.00 |
1.000 |
1.000 |
1.05 |
1.2155 |
1.1025 |
4.3192 |
29.2770 |
5932 |
0.91 |
488 |
3.93 |
1.130 |
1.076 |
1.10 |
1.4641 |
1.2100 |
3.7566 |
28.6039 |
6081 |
0.83 |
477 |
3.12 |
1.269 |
1.154 |
1.15 |
1.7490 |
1.3225 |
3.2876 |
27.9751 |
6227 |
0.76 |
465 |
2.49 |
1.418 |
1.233 |
1.20 |
2.0736 |
1.4400 |
2.8935 |
27.3861 |
6370 |
0.69 |
455 |
2.01 |
1.577 |
1.315 |
1.25 |
2.4414 |
1.5625 |
2.5600 |
26.8328 |
6510 |
0.64 |
445 |
1.63 |
1.747 |
1.398 |
1.30 |
2.8561 |
1.6900 |
2.2758 |
26.3117 |
6648 |
0.59 |
436 |
1.33 |
1.927 |
1.482 |
1.35 |
3.3215 |
1.8225 |
2.0322 |
25.8199 |
6783 |
0.54 |
427 |
1.10 |
2.118 |
1.569 |
1.40 |
3.8416 |
1.9600 |
1.8222 |
25.3546 |
6915 |
0.50 |
419 |
0.91 |
2.319 |
1.657 |
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 |