Help with a planet

[Gray Lensman]

HELP, what in the blankety blank blank am I doing wrong. How can the mean distance temperature be so far outside the temperatures at closest approach and farthest separation? Or am I finally losing my mind. :nonono:

19. Binary Effects (from page 67 WBH)

Main Star is

61 Cygni A K5.0 V
.7 Mass
.72 Diameter
.53 Luminosity
H-Zone .4 AU, Orbit 1

Companion Star is

61 Cygni B K7.0 V
.63 Mass
.67 Diameter
.418 Extrapolated Luminosity
H-Zone .4 AU, Orbit 1

a. Closest Approach

Luminosity for Companion K7 V (from table 3a) divided by the square root of companion distance minus world distance gives us .418 divided by 8.76 = .048 rounded + Main Star Luminosity of .53 = .577 effective luminosity.

.577*591.385*.62*1.15=243 kelvins (-273 = -30 c = -22 F)
(step 3e page 65, WBH Base Temperature = Luminosity of central star times Orbit factor times Energy Absorption factor time Greenhouse Factor)


b. Farthest Separation

Luminosity for Companion K7 V (from table 3a) divided by the square root of companion distance plus world distance gives us .418 divided by 8.81 = .047 rounded + Main Star Luminosity of .53 = .577 effective luminosity.

.577*591.385*.62*1.15=243 kelvins (-273 = -30 c = -22 F)
(step 3e page 65, WBH Base Temperature = Luminosity of central star times Orbit factor times Energy Absorption factor time Greenhouse Factor)

(Hundreths of Difference between these two calculations.)

c. Mean Distance

Luminosity for Companion K7 V (from table 3a) divided by the square root of companion distance plus world distance divided by 2 gives us .418 divided by 6.23 = .067 rounded + Main Star Luminosity of .53 = .597 effective luminosity.

.597*591.385*.62*1.15=252 kelvins (-273 = -21 c = -6 F)
(step 3e page 65, WBH Base Temperature = Luminosity of central star times Orbit factor times Energy Absorption factor time Greenhouse Factor)

Where have I went wrong,


or have I finally went quite insane.:rofl:

 

[Jame]

or have I finally went quite insane.:rofl:

You weren't already? For shame! :nonono:


:devil:

 

[Spinward Scout]

or have I finally went quite insane.:rofl:

Er, well... yeah!

:rofl:

Sorry, I'm boggled just looking at it. Math is all Greek to me (some of it literally!).

 

[Jame]

Er, well... yeah!

:rofl:

Sorry, I'm boggled just looking at it. Math is all Greek to me (some of it literally!).

This goes for me as well. Sorry I couldn't help.

 

[Lycanorukke]

Mmm, working through

Okay base temp = L x O x E x G

Where
L = Luminosity (in this case primary + companion)
O = Orbit factor (581.395)
E = Energy absorb (0.62 - an atm 9 world)
G = Greenhouse (1.15)

This bit seems OK

Lc = L / SQRT( Cd - Wd)

W(d) = World from primary (0.4 AU)
C(d) = Companions distance - this isn't given.
L = luminosity factor of companion (0.418)

There seems to be a problem with the companion luminosity. From the table a K5V has a lum of 0.53, and a M0V has a lum of 0.45. Your number of 0.418 is roughly between a M0V and a M1V star and not a K7V.

So a K7V should have a factor of 0.45 + 3*( (0.53-0.45)/5) or about 0.498. Though the effect of this I cant work out yet as I dont have C(d) companion distance.

On Edit: I can't plug in the numbers from the real 61 Cygni either as they dont seem to co-relate. While the orbital distance is about 80 AU the high eccentricity means it varies from 44-120 AU, and the luminosity of A and B are 0.215 and 0.15 retrospecivley which dont match up with the WBH numbers.

 

[Lycanorukke]

Okay...finally got some time to do the calculations - and your sums are right with the numbers you gave.
Reversing the sums gives me a companion distance of about 70 AU, so I'll go with that

The problem seems to be with the Mean Separation which is given in the books as:

Lm = Lc / SQRT((Cd+Wd)/2)

This halves the distance of both the world (negligable) and the companion (a lot) essentially bringing the companion 35 AU closer.

Fiddling with the equation it would seem better to half the world distance (as it moves around the primary) and leave the companion star alone. This gives the equation...

Corrected: Lm = Lc / SQRT(Cd+(Wd/2))

Plugging in all the numbers with the a luminosity of 0.418 I get

T(close)= -29.4C
T(far)= -29.5C
T(mean)= -29.47C

Which seems more in line with being a mean.
Fixing the luminosity to 0.498 and it comes out

T(close)= -25.4C
T(far)= -25.7C
T(mean)= -25.6C

I couldn't find any errata for the WBH mentioning this, so you're not wrong on the sums, though I can't say anything about sanity.

 

[Gray Lensman]

Corrected: Lm = Lc / SQRT(Cd+(Wd/2))

Plugging in all the numbers with the a luminosity of 0.418 I get

T(close)= -29.4C
T(far)= -29.5C
T(mean)= -29.47C

Which seems more in line with being a mean.
Fixing the luminosity to 0.498 and it comes out

T(close)= -25.4C
T(far)= -25.7C
T(mean)= -25.6C

I couldn't find any errata for the WBH mentioning this, so you're not wrong on the sums, though I can't say anything about sanity.

http://www.solstation.com/stars/61cygni2.htm is where I got the real star info. I intentionally circularized the orbit of the secondary at Orbit 10

"The star and its stellar companion B have a highly elliptical orbit (e= 0.40) that swings them between 51.7 and 121.0 AUs apart in an orbit that lasts about 722 years "

I too looked for WBH errata but couldn't find any. I think your corrected Equation is probably right.

For the K7 V Luminosity I extrapolated from the chart.

You see, my math skills t'aint that great either like some of the responders, I just couldn't believe I was that far off.

I tried using real world numbers for luminosity as well but I wanted a (at least marginally) Habital Planet around both stars not one with a base temp of -237 c (-394 F).

As far as my sanity, well......you should talk to my better half .

Thanks Lycanorukke.

 

[Gray Lensman]

Possible Errata for WBH

Okay look at page 68 of DGPs World Builders Handbook under temperature worksheet.

The 12th column says Column 11 times Column 12. This has to have been meant to read Column 10 times Column 11. :nonono:

Okay, finished the temperature worksheet (only needed to do one since the effective luminosity is the same for all three to 3 decimal places)

So, we have a world where the maximum temperature at the equator is [note 1] 26 C (79 F) in summer time and the minimum temperature at the poles is -160 C (-256 F) in the winter time.

But, with the binary having the same effective luminosity addition except when the planet passes behind the primary and the orbital period is 109.5 days, JUST HOW LONG IS THAT WINTER REALLY GONNA BE? (The base temp of the planet was -50C before I added the companion luminosity which brought it up to -22C)

[NOTE 1] +26C is the maximum temp allowed by step 7c on page 66 of WBH (it was actually up to +29C)

I think when I do up the habitable planet around the companion I will move it to orbit 0 and see what kind of temperature range I come up with.

One thing this exercise has taught me is that Handwavium does look good right now. :nonono:

I have this entire nightmare in a word file if anyone wants to look at it, may actually convert it to pdf and post it as an example in a couple of weeks when I am done with it ("NO, don't do it". "Shush boy I'm talking here".):rofl: