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Author Topic: formula for distance to nadir-zenith?  (Read 6013 times)

Taharqa

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formula for distance to nadir-zenith?
« on: 13 May 2011, 17:58:21 »
is there a formula for determining distance to nadir-zenith based on spectral class and subtype or is all just a set of arbitrary values?
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cray

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Re: formula for distance to nadir-zenith?
« Reply #1 on: 13 May 2011, 19:41:30 »
It's arbitrary. Only two stellar types show a relation to the star's mass; the rest are just selected arbitrarily.
« Last Edit: 14 May 2011, 20:14:01 by cray »
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Frabby

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Re: formula for distance to nadir-zenith?
« Reply #2 on: 14 May 2011, 05:29:09 »
(scrap that, misunderstood the question - move on, nothing to see here...)  ::)
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Taharqa

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Re: formula for distance to nadir-zenith?
« Reply #3 on: 14 May 2011, 19:44:01 »
Thanks for the info.
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Giovanni Blasini

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Re: formula for distance to nadir-zenith?
« Reply #4 on: 17 May 2011, 14:24:35 »
Out of curiosity, and a lack of desire to run the equations myself, which two stellar classes do show a gravitational relationship?
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Re: formula for distance to nadir-zenith?
« Reply #5 on: 17 May 2011, 17:49:13 »
Out of curiosity, and a lack of desire to run the equations myself, which two stellar classes do show a gravitational relationship?

That's a Fallguy question. Fallguy crunched the numbers. I think it's an M-class and the G2V.
Mike Miller, Materials Engineer

**"A man walks down the street in that hat, people know he's not afraid of anything." --Wash, Firefly.
**"Well, the first class name [for pocket WarShips]: 'Ship with delusions of grandeur that is going to evaporate 3.1 seconds after coming into NPPC range' tended to cause morale problems...." --Korzon77
**"Describe the Clans." "Imagine an entire civilization built out of 80’s Ric Flairs, Hulk Hogans, & Macho Man Randy Savages ruling over an entire labor force with Einstein Level Intelligence." --Jake Mikolaitis


Disclaimer: Anything stated in this post is unofficial and non-canon unless directly quoted from a published book. Random internet musings of a BattleTech writer are not canon.

Fallguy

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Re: formula for distance to nadir-zenith?
« Reply #6 on: 06 June 2011, 20:22:54 »
The two stellar classes that have similar solar constants at the canon safe jump distances are Class G2 (Sol) and Class M5. (Proxima Centauri) To understand why, I would need to explain the correlation of Spectral class to Bolometric Magnitude (the amount of total EM energy emitted by a star across the entire EM spectrum) and the discrepancy between the Canon Safe Jump Distances and the Charge Time Table.
 
The rules give very specific Minimum Safe Jump Distance (MSJD) for each spectral class, giving us a basis to work from. Using Stefan-Boltzmann law of blackbody emission, (P=AεσT4 where P is Power in watts, A is surface area in meters2, ε is emissivity, σ is the Stefan-Boltzmann Constant, and T is the temperature of the surface in °K) inverse square law for a point source, (I=P/4r2 where I is Intensity in w/m2 and r is the radius in meters) and a table of surface temperatures and radii for each spectral class on the Main Sequence, we can find the Bolometric Magnitude of each star at the canon MSJD listed for each spectral class.
 
Cross-referencing this data with the canon Charge Time for each spectral class reveals the error. A Jumphip's solar sail has to collect a certain amount of power in joules, therefore the charge time is different over smaller and dimmer stars because they produce less total energy. When you take the charge time for Sol of 183 hours (658,800 seconds) and multiply it by the Solar Constant at MSJD (13.21 w/m2 at 1,517,879,732 km distance) that gives a total power collected of 8.7 mj per square meter of sail.
 
Comparing this to a class M5 star with a charge time of 206 hours (741,600 seconds) multiplied by the solar constant at an M5's MSJD (11.76 w/m2 at 109,080,037 km distance) gives a total power collected of 8.72 mj per square meter of sail. However, when you apply the same set of equations to the rest of the spectral classes, the net result shows that these two are the only two that come close to the same result.
 
The following table is the result:
 
 Type
 Time (hrs)
 MSJD (km)
 Temp °K)
 Radius (km)
 Stellar Const @ MSJD (w/m²)
 Deviation
 M9
 210
 75,000,000
 2,550
 158,897
 10.77
 94%
 M8
 209
 82,192,147
 2,650
 161,176
 10.76
 93%
 M7
 208
 90,197,803
 2,750
 165,935
 10.98
 95%
 M6
 207
 99,120,895
 2,850
 169,482
 10.94
 94%
 M5
 206
 109,080,037
 2,950
 180,460
 11.76
 100%
 M4
 205
 120,210,786
 3,050
 196,515
 13.12
 111%
 M3
 204
 132,668,292
 3,150
 234,020
 17.38
 147%
 M2
 203
 146,630,374
 3,250
 282,689
 23.53
 198%
 M1
 202
 162,301,133
 3,350
 334,529
 30.36
 254%
 M0
 201
 179,915,179
 3,450
 388,255
 37.43
 311%
 K9
 200
 199,742,590
 3,575
 428,594
 42.67
 353%
 K8
 199
 222,094,749
 3,725
 461,491
 47.16
 388%
 K7
 198
 247,331,200
 3,875
 490,987
 50.41
 413%
 K6
 197
 275,867,748
 4,025
 516,629
 52.22
 426%
 K5
 196
 308,186,014
 4,175
 538,488
 52.62
 427%
 K4
 195
 344,844,735
 4,325
 556,853
 51.76
 417%
 K3
 194
 386,493,164
 4,475
 572,083
 49.84
 400%
 K2
 193
 433,886,958
 4,625
 584,547
 47.11
 376%
 K1
 192
 487,907,078
 4,775
 594,592
 43.79
 348%
 K0
 191
 549,582,283
 4,925
 602,533
 40.11
 317%
 G9
 190
 620,115,976
 5,050
 614,690
 36.25
 285%
 G8
 189
 700,918,272
 5,150
 631,174
 32.36
 253%
 G7
 188
 793,644,393
 5,250
 646,056
 28.55
 222%
 G6
 187
 900,240,718
 5,350
 659,463
 24.94
 193%
 G5
 186
 1,023,000,099
 5,450
 671,517
 21.56
 166%
 G4
 185
 1,164,628,460
 5,550
 682,327
 18.47
 141%
 G3
 184
 1,328,325,100
 5,650
 691,995
 15.69
 119%
 G2
 183
 1,517,879,732
 5,750
 700,616
 13.21
 100%
 G1
 182
 1,737,789,950
 5,850
 708,274
 11.03
 83%
 G0
 181
 1,993,403,717
 5,950
 715,048
 9.15
 68%
 F9
 180
 2,291,092,549
 6,075
 732,905
 7.91
 59%
 F8
 179
 2,638,462,416
 6,225
 754,332
 6.96
 52%
 F7
 178
 3,044,611,112
 6,375
 783,790
 6.21
 46%
 F6
 177
 3,520,442,982
 6,525
 805,073
 5.38
 39%
 F5
 176
 4,079,054,583
 6,675
 836,316
 4.73
 34%
 F4
 175
 4,736,208,289
 6,825
 859,296
 4.05
 29%
 F3
 174
 5,510,915,132
 6,975
 901,264
 3.59
 26%
 F2
 173
 6,426,153,651
 7,125
 943,963
 3.15
 23%
 F1
 172
 7,509,758,447
 7,275
 976,361
 2.69
 19%
 F0
 171
 8,795,520,974
 7,425
 1,026,776
 2.35
 17%
 A9
 170
 10,324,556,364
 7,675
 1,037,975
 1.99
 14%
 A8
 169
 12,147,004,515
 8,025
 1,052,341
 1.77
 12%
 A7
 168
 14,324,152,109
 8,375
 1,067,639
 1.55
 11%
 A6
 167
 16,931,086,050
 8,725
 1,115,418
 1.43
 10%
 A5
 166
 20,060,019,352
 9,075
 1,173,895
 1.32
 9%
 A4
 165
 23,824,470,101
 9,425
 1,261,178
 1.25
 9%
 A3
 164
 28,364,525,294
 9,775
 1,346,648
 1.17
 8%
 A2
 163
 33,853,487,850
 10,125
 1,460,976
 1.11
 7%
 A1
 162
 40,506,291,619
 10,475
 1,590,154
 1.05
 7%
 A0
 161
 48,590,182,199
 10,825
 1,764,007
 1.03
 7%
 B9
 160
 58,438,309,136
 11,700
 1,721,707
 0.92
 6%
 B8
 159
 70,467,069,133
 13,100
 1,649,382
 0.91
 6%
 B7
 158
 85,198,295,036
 14,500
 1,667,052
 0.96
 6%
 B6
 157
 103,287,722,257
 15,900
 1,770,294
 1.06
 7%
 B5
 156
 125,561,609,863
 17,300
 1,891,514
 1.15
 7%
 B4
 155
 153,063,985,045
 18,700
 2,089,993
 1.29
 8%
 B3
 154
 187,117,766,777
 20,100
 2,427,023
 1.56
 10%
 B2
 153
 229,404,075,188
 21,500
 3,041,270
 2.13
 13%
 B1
 152
 282,065,439,915
 22,900
 3,941,907
 3.05
 19%
 B0
 151
 347,840,509,855
 24,300
 5,535,233
 5.01
 31%

Yes, I know I'm insane.  :D
 
Thoughts welcome as always.
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cray

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Re: formula for distance to nadir-zenith?
« Reply #7 on: 07 June 2011, 06:37:42 »
Can you make a guess where the deviation comes from? For example, was some other value of luminosity used?
Mike Miller, Materials Engineer

**"A man walks down the street in that hat, people know he's not afraid of anything." --Wash, Firefly.
**"Well, the first class name [for pocket WarShips]: 'Ship with delusions of grandeur that is going to evaporate 3.1 seconds after coming into NPPC range' tended to cause morale problems...." --Korzon77
**"Describe the Clans." "Imagine an entire civilization built out of 80’s Ric Flairs, Hulk Hogans, & Macho Man Randy Savages ruling over an entire labor force with Einstein Level Intelligence." --Jake Mikolaitis


Disclaimer: Anything stated in this post is unofficial and non-canon unless directly quoted from a published book. Random internet musings of a BattleTech writer are not canon.

Fallguy

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Re: formula for distance to nadir-zenith?
« Reply #8 on: 07 June 2011, 13:07:45 »
My guess is that they started with a value of 75,000,000 km for type M9 and then applied an arbitrary calculation for the rest of the star types. I was able to reverse engineer the table, but it's not a straightforward calculation.
 
D=Dt-1(1.005+(0.00005n))
 
where D is the MSJD (in km) for this star type, Dt-1 is the MSJD (in km) for the previous star type, and n is the numerical value of the star type. (M9=0, M8=1, M7=2, etc.)
 
For example, to find the MSJD for type M8, the equation is:
 
75000000(1.00505) = 82192146.56
 
which rounds off to 82,192,147... the value on the table. Then to find type M7 the equation is:
 
82192146.56(1.0051) = 90197802.61 
which rounds off to 90,197,803... again, the same value as on the table.
 
So to determine the MSJD for any given star type, you have to know all the MSJDs for all star types lower than itself. There's a way to simplify the equation further into a single line that doesn't require knowing all previous star types, but this can replicate the data perfectly and doesn't require calculus, so I call that good enough.  8)
 
A zipped Excel sheet is attached showing the math in detail. Also included is my HR overlay showing the various star types (and subtypes) on the same table as the canon MSJD table. The canon values cut across all subtypes except VII (white dwarf stars) and it crosses subtype V (main sequence stars) at types M5 and G2... Sol and Proxima Centauri. (the two closest stars to Earth) Whether that was coincidence or design is debatable, but it is rather interesting that those two stars match so closely for Solar Constant at the canon MSJDs listed.
 
Thoughts welcome as always.
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Urban Kufahl

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Re: formula for distance to nadir-zenith?
« Reply #9 on: 22 June 2011, 16:57:48 »
For the relation between mass/radius and luminosity check that

http://www.dil.univ-mrs.fr/~gispert/enseignement/astronomie/3eme_partie/etoiles.php#animation

(just move the red bare with you mousse)

For you power calculation, did you check the UV ratio in each stellar spectrum ?  :P

Daryk

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Re: formula for distance to nadir-zenith?
« Reply #10 on: 22 June 2011, 19:35:45 »
It's arbitrary. Only two stellar types show a relation to the star's mass; the rest are just selected arbitrarily.
I wonder if that's how I derived a suspiciously simple field strength (3.45E-6) back in college that I've never been able to reproduce.  Fallguy's explanation makes much more sense.

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Re: formula for distance to nadir-zenith?
« Reply #11 on: 22 June 2011, 19:47:24 »
Fallguy, I get an error when I open your spreadsheet in Excel2010.  It tells me there's a "problem" with the file, and that editing it may be dangerous.  Any idea what it could be?

Fallguy

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Re: formula for distance to nadir-zenith?
« Reply #12 on: 23 June 2011, 21:14:31 »
 

For the relation between mass/radius and luminosity check that

http://www.dil.univ-mrs.fr/~gispert/enseignement/astronomie/3eme_partie/etoiles.php#animation

(just move the red bare with you mousse)

I'm familiar with that. (except in english  :P  ) In fact I used similar calculations to estimate stellar mass and radius in my master spreadsheet as it is the most accurate way to estimate those unknowns in stellar dynamics.
 
Quote

For you power calculation, did you check the UV ratio in each stellar spectrum ?  :P

Power output of each stellar type was calculated using Planck Radiation Density equation:

E = ((2phc2)/l5)/(e(hc/lkT)-1) 
 
to calculate total energy output in all wavelengths of each star type. My master spreadsheet includes a breakdown of each star type by frequency in 1 nm steps from 1 nm (Extreme UV / X-Ray transition) up to 10,000 nm. (Far Infrared) That covers the vast majority of EM energy output for every star type in existence.
 
Even a star with a surface temperature of 65,000°K (type O0V) would have a peak wavelength of 41.58 nm with less than 5 w/m² output below 6 nm. (less than 0.0000000005% of the star's total EM energy output) Close enough I'd say.  8)
 

Fallguy, I get an error when I open your spreadsheet in Excel2010.  It tells me there's a "problem" with the file, and that editing it may be dangerous.  Any idea what it could be?

 
Not a clue. Possibly a corrupted download. I just downloaded my own ZIP file and opened it without errors. Try clearing your Temp Internet files and re-download the file.
 
Thoughts welcome as always.
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Daryk

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Re: formula for distance to nadir-zenith?
« Reply #13 on: 24 June 2011, 05:16:22 »
The new download has the same "problem", whatever it is.  At the very least, I can still read it.  Thanks!

Urban Kufahl

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Re: formula for distance to nadir-zenith?
« Reply #14 on: 24 June 2011, 11:47:56 »
Was talking about color index ;).

To charge your KF drive you need to convert light into electricity, unfortunately great wave length carries not enough of energy.

To make short with the same luminosity a O star give more power than a M star

Betelgeuse (M2I)
Magnitudes
U = 4.38
B = 2.27
V = 0.42
J = -2.99
H = -4.01
K = -4.38

Antares A (M2I)
Magnitudes
U = 3.13
B = 2.96
V = 1.09

Almost 1 magnitudes difference between 2 star it's probably more than 0.00...005%, no ?

PS : But nevermind it's probably a really bad idea to try to jump around 150 millions km from one of this monster
PS2: sometime a picture is better than a long sentence

« Last Edit: 24 June 2011, 12:04:01 by Urban Kufahl »

Fallguy

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Re: formula for distance to nadir-zenith?
« Reply #15 on: 04 July 2011, 01:12:40 »
Was talking about color index ;) .

To charge your KF drive you need to convert light into electricity, unfortunately great wave length carries not enough of energy.
Not quite sure what you're trying to say there. If you mean that low frequency EM doesn't transfer much energy, I am assuming that the solar collectors on a Jumpship are "broad spectrum" EM collectors and are able to collect energy from all wavelengths of EM from the Far Infrared to the extreme ultraviolet.

Quote
To make short with the same luminosity a O star give more power than a M star

{snip}

Almost 1 magnitudes difference between 2 star it's probably more than 0.00...005%, no ?
What you're doing is applying lumiosity differences with different visual filters that astronomers use to classify objects. You're also using non-main sequence stars as examples. That has no bearing on the difference in bolometric luminosity (absolute luminosity across all EM wavelengths) for main sequence stars as:
 
a) we don't care what frequency the energy is emmited at... all are assumed to be collectable by the solar sail

Quote
PS : But nevermind it's probably a really bad idea to try to jump around 150 millions km from one of this monster
...and...
 
b) only main sequence stars are covered in the BT Charge Time table and Minimum Safe Jump Distance table

Quote
PS2: sometime a picture is better than a long sentence


What you show in that image can be calculated using the Planck Radiation Density equation I gave earlier. For a more simplified equation of total energy output, you can use Stefan-Boltzmann law:
 
E=sT4ε
 
where s is the Stefan-Boltzmann constant, (5.67x10-8 W m-2 K-4) T is the surface temperature of the star, (°K) and ε is the emissivity of hydrogen at high temperature and pressures. (ε =1) The two equations yield the same result for total broad-spectrum energy emission.
« Last Edit: 04 July 2011, 01:16:04 by Fallguy »
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Re: formula for distance to nadir-zenith?
« Reply #16 on: 13 August 2011, 16:07:58 »
My guess is that they started with a value of 75,000,000 km for type M9 and then applied an arbitrary calculation for the rest of the star types. 

I would also guess that the original designers didn't twig that star classifications (B,A,F,G,K,M) do not relate in a linear way to either mass or luminosity.

It gives some odd results for the proximity distance too, SiriusA has an incredible 40 billion km distance for a smallish white star (~2 solar masses), while Betelgeuse has a miniscule 2.86 days transit & 150 million km distance to Zenith point. Rather problematic, as Betelgeuse's radius is estimated at least 500 million km, putting the Zenith point inside the surface of the star.
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cray

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Re: formula for distance to nadir-zenith?
« Reply #17 on: 13 August 2011, 22:05:57 »
I would also guess that the original designers didn't twig that star classifications (B,A,F,G,K,M) do not relate in a linear way to either mass or luminosity.

They also emphatically did not recognize the implications of the roman numeral at the end of the stellar classification. Hence the Betelgeuse problem, and so many habitable planets circling non-main sequence stars.
Mike Miller, Materials Engineer

**"A man walks down the street in that hat, people know he's not afraid of anything." --Wash, Firefly.
**"Well, the first class name [for pocket WarShips]: 'Ship with delusions of grandeur that is going to evaporate 3.1 seconds after coming into NPPC range' tended to cause morale problems...." --Korzon77
**"Describe the Clans." "Imagine an entire civilization built out of 80’s Ric Flairs, Hulk Hogans, & Macho Man Randy Savages ruling over an entire labor force with Einstein Level Intelligence." --Jake Mikolaitis


Disclaimer: Anything stated in this post is unofficial and non-canon unless directly quoted from a published book. Random internet musings of a BattleTech writer are not canon.

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Re: formula for distance to nadir-zenith?
« Reply #18 on: 18 August 2022, 15:29:47 »
Sorry for the necro but this is directly relevant to this discussion, since I just figured out how to actually calculate the the jump points based on gravitational field strength...

http://evildrganymede.net/wp/2022/08/07/battletech-realistic-gravity-based-jump-point-distances/

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Re: formula for distance to nadir-zenith?
« Reply #19 on: 18 August 2022, 15:35:49 »
For ease of reference here, could you post the field strength you selected?  8)

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Re: formula for distance to nadir-zenith?
« Reply #20 on: 18 August 2022, 15:53:48 »
0.000059 m/s² - same as the field strength at the G2 (Sol) jump distance (i.e. for a 1 solar mass star at 10.146 AU). That way the distances for sun-like stars shouldn't be too different from canon, but it'd diverge for lower and higher mass stars.

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Re: formula for distance to nadir-zenith?
« Reply #21 on: 18 August 2022, 17:28:52 »
Thanks again!  Only three posts to go before you're done with "prove you're human"!  :thumbsup:

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Re: formula for distance to nadir-zenith?
« Reply #22 on: 18 August 2022, 18:32:28 »
Mod intervening here. Normally we'd discourage necros but I'll post with my own stamp of approval for the other mods that I think having Fallguy's calculations here in context is valuable enough to let it slide this time.
Alas poor Photobucket. I knew him Horatio, a fellow of infinite jest, of most excellent fancy.

SeeM

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Re: formula for distance to nadir-zenith?
« Reply #23 on: 21 August 2022, 14:58:01 »
Yes, I know I'm insane.  :D
 
Thoughts welcome as always.
I always love the need to "de-magic" space travel in SF, especially when modern equimpent starts to obsolete some of the story concepts. My today favorite thing is a scout ships, which are plainly useless. Just let population build dozens of big space telescopes and let them do planet hunt all the time. While teleportation itself is still unsolved, I appreciate it's limitations. they add consistency to the story and make predictable scenarios, without space bandits hops out of a space forest.

Since 99% of stars are very similar (with rare exception of neutrons, or strongly pulsating ones), mass of the star is the only definitive difference. I wonder if double of triple star systems would have like "phases" of it's jump points, that would make them tricky to use once in a while.
(+)

cray

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Re: formula for distance to nadir-zenith?
« Reply #24 on: 21 August 2022, 18:31:07 »
I always love the need to "de-magic" space travel in SF, especially when modern equimpent starts to obsolete some of the story concepts. My today favorite thing is a scout ships, which are plainly useless. Just let population build dozens of big space telescopes and let them do planet hunt all the time.

That's what BattleTech now refers to - a number of Touring the Stars products mention the large telescopes used by the Western and Terran Alliance to map out the millions of stars in the Inner Sphere. Scout ships provided services that telescopes couldn't, like ecological sampling.

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I wonder if double of triple star systems would have like "phases" of it's jump points, that would make them tricky to use once in a while.

That's addressed in Campaign Operations star system creation rules and Touring the Stars: Mizar. Close binaries can increase the proximity limit of a star (like Mizar), while distant binaries do not interfere (like Rigil Kentaurus).
Mike Miller, Materials Engineer

**"A man walks down the street in that hat, people know he's not afraid of anything." --Wash, Firefly.
**"Well, the first class name [for pocket WarShips]: 'Ship with delusions of grandeur that is going to evaporate 3.1 seconds after coming into NPPC range' tended to cause morale problems...." --Korzon77
**"Describe the Clans." "Imagine an entire civilization built out of 80’s Ric Flairs, Hulk Hogans, & Macho Man Randy Savages ruling over an entire labor force with Einstein Level Intelligence." --Jake Mikolaitis


Disclaimer: Anything stated in this post is unofficial and non-canon unless directly quoted from a published book. Random internet musings of a BattleTech writer are not canon.

EDG

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Re: formula for distance to nadir-zenith?
« Reply #25 on: 21 August 2022, 19:10:14 »
That's addressed in Campaign Operations star system creation rules and Touring the Stars: Mizar. Close binaries can increase the proximity limit of a star (like Mizar), while distant binaries do not interfere (like Rigil Kentaurus).

With close binaries there's actually an L1 point between the stars too. The reason the Earth-Sun L1 point is so close to Earth is because the Earth's mass is tiny compared to the sun, but if you replaced Earth with a 1 solar mass star then the L1 point would actually be at the halfway point between the two stars.

If the stars were really close (a few stellar radii apart?) then the proximity limit would be increased since I think the stars would be indistinguishable from a single larger mass at sufficient distance, but with greater stellar separation you may end up with a two-lobed (peanut-shaped) proximity limit as each star would have its own (overlapping) spherical limit. If the separation is far enough, you'd just end up with two separate proximity limits for each star.

cray

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Re: formula for distance to nadir-zenith?
« Reply #26 on: 22 August 2022, 16:30:53 »
With close binaries there's actually an L1 point between the stars too.

Good point.

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If the stars were really close (a few stellar radii apart?) then the proximity limit would be increased since I think the stars would be indistinguishable from a single larger mass at sufficient distance

Mizar's an example of that. The resulting proximity limit is ridiculous, so the planetary-solar L1 point is favored.

Quote
If the separation is far enough, you'd just end up with two separate proximity limits for each star.

Rigil Kentaurus is an example of that.
Mike Miller, Materials Engineer

**"A man walks down the street in that hat, people know he's not afraid of anything." --Wash, Firefly.
**"Well, the first class name [for pocket WarShips]: 'Ship with delusions of grandeur that is going to evaporate 3.1 seconds after coming into NPPC range' tended to cause morale problems...." --Korzon77
**"Describe the Clans." "Imagine an entire civilization built out of 80’s Ric Flairs, Hulk Hogans, & Macho Man Randy Savages ruling over an entire labor force with Einstein Level Intelligence." --Jake Mikolaitis


Disclaimer: Anything stated in this post is unofficial and non-canon unless directly quoted from a published book. Random internet musings of a BattleTech writer are not canon.

EDG

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Re: formula for distance to nadir-zenith?
« Reply #27 on: 22 August 2022, 17:35:26 »
Mizar's an example of that. The resulting proximity limit is ridiculous, so the planetary-solar L1 point is favored.

Mizar is a quadruple system (a double-double, Mizar A and Mizar B) - the two pairs are far enough apart at least that they'd have separate proximity limits (they take thousands of years to orbit eachother). The A pair orbit eachother in about 20.5 days (probably a few tenths of an AU, maybe about Mercury's orbit equivalent? I can try to calculate that later) - that might actually be far enough apart to have a two-lobed proximity limit at least. The B pair orbit eachother in 6 months so they'd probably have their own proximity limits.

Of course since system is about 350 million years old and the stars are pretty massive, there aren't really going to be habitable worlds there.

Daryk

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Re: formula for distance to nadir-zenith?
« Reply #28 on: 22 August 2022, 18:20:47 »
*snip*
Mizar's an example of that. The resulting proximity limit is ridiculous, so the planetary-solar L1 point is favored.
*snip*
FTFY

cray

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Re: formula for distance to nadir-zenith?
« Reply #29 on: 27 August 2022, 09:30:51 »
FTFY

Traffic to the planet Mizar prefers to use a jump point near the star-planet L1 point, a type of jump point noted in Strategic Operations (Revised) p. 122. Mizar has a common orbit around its two primaries, which are close enough to function as a single mass for something at Mizar's distance. Hence there should be a star-planet Lagrange-1 point, if a bit less stable than normal, and an associated "pirate" L1 point.
Mike Miller, Materials Engineer

**"A man walks down the street in that hat, people know he's not afraid of anything." --Wash, Firefly.
**"Well, the first class name [for pocket WarShips]: 'Ship with delusions of grandeur that is going to evaporate 3.1 seconds after coming into NPPC range' tended to cause morale problems...." --Korzon77
**"Describe the Clans." "Imagine an entire civilization built out of 80’s Ric Flairs, Hulk Hogans, & Macho Man Randy Savages ruling over an entire labor force with Einstein Level Intelligence." --Jake Mikolaitis


Disclaimer: Anything stated in this post is unofficial and non-canon unless directly quoted from a published book. Random internet musings of a BattleTech writer are not canon.

 

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