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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). |
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 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).
M |
L |
r |
life |
vesc |
Wp |
|
M⊙ |
L⊙ |
AU |
GY |
km/s |
mag |
|
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 |
est. |
0.80 |
0.4096 |
0.6400 |
9.7656 |
33.5410 |
K2V |
est. |
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 |
G4V |
|
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 |
est. |
1.20 |
2.0736 |
1.4400 |
2.8935 |
27.3861 |
F7V |
est. |
1.25 |
2.4414 |
1.5625 |
2.5600 |
26.8328 |
F6V |
est. |
1.30 |
2.8561 |
1.6900 |
2.2758 |
26.3117 |
F4V |
est. |
1.35 |
3.3215 |
1.8225 |
2.0322 |
25.8199 |
F3V |
est. |
1.40 |
3.8416 |
1.9600 |
1.8222 |
25.3546 |
F1V |
est. |
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.