[SPACE] Tidal braking

[dataweaver]

Originally Posted by Schedim

I still worrying this old bone... I tried to apply this in my systemgenerator, but one thing is bugging me,. Shouldnt you begin with the SHORTEST moon orbit time when you do the iterations. So the planet rotation progression go:

Starting Rotation -> Shortest Moon Orbit time -> Next Moon Orbit Time -> <repeat until S2 >= S1 or you run out of Moons -> Planet Orbital Time

Or has I gravely misread something?

S1 is the set of tidal forces conspiring to lengthen the planet's day, while S2 is the set of tidal forces conspiring to shorten its day. As long as S2 < S1, the net forces are conspiring to lengthen the day; so you should indeed go from shortest to longest rotational period.

[Schedim]

Originally Posted by dataweaver

S1 is the set of tidal forces conspiring to lengthen the planet's day, while S2 is the set of tidal forces conspiring to shorten its day. As long as S2 < S1, the net forces are conspiring to lengthen the day; so you should indeed go from shortest to longest rotational period.

Ah! Good then I got that right, now I only have to figure out a way to have the Axial Tilt affect the Tidal Breaking ... torque was always a hate subject back in school, so I'm inclined to just wing something!

[dataweaver]

Ignore it. If you introduce the axial tilt and its effects with respect to tidal slowing, then you'll also have to introduce orbital inclinations - both for the planet as it orbits the sun, and for each satellite as it orbits the planet. After all, a moon in a polar orbit would have a very different effect on the planet's rotation than one orbiting directly above the equator.

[Schedim]

Ah ... true ... I just put in an extra mod to the Axial tilt to reduce it for older systems, and then ignore it further.

[Artifact]

I have a quick planetary orbit question - slightly off topic, but close.

In order to calculate the blackbody T for a planet in a binary system, how do you factor in the effect of the second star if it is close enough to have a measureable effect?

For example, I generated a system with 2 K0 stars. The companion star orbits with an average radius of 12 au's. This makes a forbidden zone starting at 1.98 au's for the primary planet. The inner limit of the primary star is 0.08, so there is room for a few planets (in this case 4 were generated).

The 3rd planet has an orbital radius of 0.55, density of .9, diameter of 1.35. The blackbody Temp using the primary star is 302, making it a garden world. But with an average radius of only 12, th blackbody T based on the companion star would be 64.9. If the T is additive (T = 302 + 65 = 367), then the world would be considered a greenhouse world instead of Garden. I used the same Luminosity for both stars for simplicity as 0.4280.

So what is the correct way to calculate the combined Blackbody T?

Thanks

[whswhs]

Originally Posted by Artifact

So what is the correct way to calculate the combined Blackbody T?

The simple technique is to figure the blackbody T for the primary star, using the planet's mean orbital radius; figure the blackbody T for the distant star, using the mean separation between the stars as the "orbital radius"; raise both temperatures to the fourth power; add them; and take the fourth root. This won't account for fluctuations resulting from changes in separation as the planet orbits its star and the two stars orbit each other, but those fluctuations will usually be only a fraction of the mean temperature.

If you want to verify, you can try taking the minimum and maximum separations (minimum stellar separation minus maximum planetary orbital radius; maximum stellar separation plus maximum planetary orbital radius) and seeing whether using them in figuring the blackbody T for the distant star makes a noticeable difference.

Bill Stoddard

[Artifact]

Originally Posted by whswhs

The simple technique is to figure the blackbody T for the primary star, using the planet's mean orbital radius; figure the blackbody T for the distant star, using the mean separation between the stars as the "orbital radius"; raise both temperatures to the fourth power; add them; and take the fourth root. This won't account for fluctuations resulting from changes in separation as the planet orbits its star and the two stars orbit each other, but those fluctuations will usually be only a fraction of the mean temperature.

If you want to verify, you can try taking the minimum and maximum separations (minimum stellar separation minus maximum planetary orbital radius; maximum stellar separation plus maximum planetary orbital radius) and seeing whether using them in figuring the blackbody T for the distant star makes a noticeable difference.

Bill Stoddard

Thanks -

That seems like it really reduces the effect of the second star. I don't want to hijack this thread though, so I will think through it more carefully and start a seperate thread.

[dataweaver]

The formula is based on the fact that the blackbody temperature is proportional to the fourth root of the effective luminosity to which the planet is subjected. If there's only one source of luminosity, all you have to do is to apply the inverse square rule to that source's luminosity rating (i.e., Leffective = Lactual/R²). If you have more than one source, you need to add their effective luminosities together before taking the fourth root. So:

Leffective = L1/R1² + L2/R2².

B = 278 × 4√Leffective

B = 278 × 4√(L1/R1² + L2/R2²)

Bill merely phrased this using B1 and B2 rather than the various L's and R's; but the results are the same:

B = 4√(B1^4 + B2^4)

[Artifact]

So I have another question - this one more relevant to Tidal Braking.

Starting on pg 116 in the Space book, the calculations for Satellite orbital Radius are based on Planetary Diameters.

To calculate the Orbital Period, the formula says to use Earth Diameters.
The same is true for the Tidal Braking formulas.

I assume this is so the answer is in Earth Days? It is easy enough to adjust to Earth Diameters, but I wanted to make sure that (a) that is correct, and (b) that it is in fact so that the anwer is in Earth Days (the last part so I can convert to the relevant "day" in the system I have).

Sorry for the barrage of questions - I have only recently picked up GURPS and I am trying to convert material I created for a different system (Space Opera). I think once I get all of these little questions ironed out it all seems pretty straightforward - the math is not difficult and can be streamlined pretty easily in a spreadsheet. My shortcoming is I don' have a huge background in astronomy and physics - once we get to the ecology and biology parts of world creation I am good to go.

Thanks!

T

[Agemegos]

Originally Posted by Artifact

Starting on pg 116 in the Space book, the calculations for Satellite orbital Radius are based on Planetary Diameters.

To calculate the Orbital Period, the formula says to use Earth Diameters.
The same is true for the Tidal Braking formulas.

I assume this is so the answer is in Earth Days?

Correct. Note well published corrigenda for an erratum in that formula.