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)