Min, max distances betwen planets

[sralica]

I am trying to make a RemoteTech network.

spreadsheet that I'm using (if anyone will be able to read it)

But I need min and max distances betwen Kerbin and all other planets.

Max(distance)= Ap(kerbin)+Ap(x)

Min(distance)= Pe(kerbin)+Pe(x) (exemple: minD betwen Kerbin and Moho is 9.389.329.628m)

I juts figure it out that for inner planets (moho, eve) it should go like this:

Min(distance)= Pe(kerbin)+Ap(x) (exemple: minD betwen Kerbin and Moho actually is 7.284.074.276m)

Is my math correct?

This is true for cases where Ap and Pe of both planets are in line. (because Kerbin Ap=Pe, no problem) For other planets (like Eloo and Dres) this is not the case.

Is there a tool that calculates Min and Max distance between any two planets? Could someone make it please?

I may be pushing it but could it also take in to account planets orbital inclination?

Thanks

Edited February 24, 2015 by sralica

[Kryxal]

I think you're going to a bit too much trouble over this ... just use sum of the apoapses and have done, the actual number can't exceed that but will probably be fairly close.

By the way, the minimum distance too high, it's more like the difference of the two.

[WuphonsReach]

Short answer: Worst-case distance is the sum of Ap values.

For links between Kerbin and the inner planets -- Comm 88-88 for Duna/Eve/Moho, KR-14 for Dres, GX-128 for Jool/Eeloo.

[LethalDose]

I am trying to make a RemoteTech network.

Best Answer for this is Wuphon's response:

Short answer: Worst-case distance is the sum of Ap values.

For links between Kerbin and the inner planets -- Comm 88-88 for Duna/Eve/Moho, KR-14 for Dres, GX-128 for Jool/Eeloo.

With the addition that the CommTech-1 has a similar range to the GX-128, and 88-88 is probably the best dish for intra-system communication in the Jool system.

I think you're going to a bit too much trouble over this ... just use sum of the apoapses and have done, the actual number can't exceed that but will probably be fairly close.

By the way, the minimum distance too high, it's more like the difference of the two.

Kryxal is right on both counts.

Overall, it's really better to design your RT system to link directly between the target and Kerbin ("Kerbin" meaning a satellite relay in the Kerbin system). Bouncing between the planets gets messy and really doesn't save your any effort.

[sralica]

thanks for the answers, but you are completely missing the point of this thread.

I would like to get Min, max distances between planets.

[Rokmonkey]

BAM

http://remotetechnologiesgroup.github.io/RemoteTech/tutorials/long_range/

There is a table there with the distance you'd like.

[OhioBob]

		Minimum (km)	Maximum (km)
Moho	Eve	3,546,900	16,117,600
Moho	Kerbin	7,289,400	19,913,500
Moho	Duna	14,641,100	26,768,900
Moho	Dres	30,052,400	51,629,500
Moho	Jool	60,949,000	76,594,200
Moho	Eeloo	60,715,300	119,514,300
Eve	Kerbin	3,668,900	23,530,800
Eve	Duna	9,792,200	31,665,400
Eve	Dres	25,237,900	56,462,800
Eve	Jool	55,583,200	81,962,500
Eve	Eeloo	56,927,000	123,317,100
Kerbin	Duna	6,069,300	35,383,000
Kerbin	Dres	21,402,600	60,320,600
Kerbin	Jool	51,735,000	85,811,900
Kerbin	Eeloo	53,183,400	127,081,700
Duna	Dres	13,732,500	68,079,200
Duna	Jool	44,584,600	92,947,000
Duna	Eeloo	45,095,900	135,224,000
Dres	Jool	24,543,300	113,355,000
Dres	Eeloo	28,733,500	151,339,300
Jool	Eeloo	11,617,100	169,943,700

It sounds like what you want is the minimum/maximum distance between the orbits of the planets, which would be the theoretical minimum/maximum distance between the planets. I'm sure that can be determined mathematically, but that's not what I did. I projected the motions of all the planets over a 1000-year period and searched for the minimum and maximum true separations. These results are tabulated above.

 

Edited February 13, 2017 by OhioBob
Revised numbers to fix error in formula

[sralica]

... I projected the motions of all the planets over a 1000-year period and searched for the minimum and maximum true separations. These results are tabulated above.

OOoo great! that is what I need. I think 1000 years will be enough.

Did you simulate this in-game, or in another program?

[Renegrade]

It sounds like what you want is the minimum/maximum distance between the orbits of the planets, which would be the theoretical minimum/maximum distance between the planets. I'm sure that can be determined mathematically, but that's not what I did. I projected the motions of all the planets over a 1000-year period and searched for the minimum and maximum true separations. These results are tabulated above.

+1 internets and/or cookies or whatever for you sir. That's definitely going the extra mile.

(My own solution back in the day was just a very simplistic and pessimistic comparison of PEs and APs, but it resulted in some impossible combinations)

[OhioBob]

OOoo great! that is what I need. I think 1000 years will be enough.

I'm glad I could help. I stopped searching when I reached the end of year 1000. There may be closer/farther distances in later years, but I figured it would take a seriously addicted individual to play the game that far into the future. (In fact, I know Jool and Eeloo have closer encounters in the second millennia but I had to stop somewhere.)

Did you simulate this in-game, or in another program?

I put all the orbital parameters into an Excel spreadsheet and computed the planet positions vs. time, from which I calculated the separation distances. I then just searched for the minimums and maximums.

[WuphonsReach]

And looking just at the Kerbin -> X numbers:

[TABLE=class: cms_table_grid, width: 500, align: center]

[TR]

[TD]Kerbin[/TD]

[TD]Duna[/TD]

[TD=align: center]6,069,400[/TD]

[TD=align: center]35,383,000[/TD]

[/TR]

[TR]

[TD]Kerbin[/TD]

[TD]Dres[/TD]

[TD=align: center]21,400,100[/TD]

[TD=align: center]60,322,000[/TD]

[/TR]

[TR]

[TD]Kerbin[/TD]

[TD]Jool[/TD]

[TD=align: center]51,737,900[/TD]

[TD=align: center]85,810,200[/TD]

[/TR]

[TR]

[TD]Kerbin[/TD]

[TD]Eeloo[/TD]

[TD=align: center]53,145,700[/TD]

[TD=align: center]127,108,600[/TD]

[/TR]

[/TABLE]

Kerbin Ap/Pe = 13.600 Mm / 13.600 Mm

Jool Ap/Pe = 72.212 Mm / 65.335 Mm

72.212 + 13.600 = 85.812 Mm (max distance)

65.335 - 13.600 = 51.735 Mm (min distance)

Eeloo = 66.688 Mm Pe / 113.550 Mm Ap

113.550 + 13.600 = 127.15 Mm (max distance)

66.688 - 13.600 = 53.088 (Min distance)

So the simple method of looking at just the Ap/Pe numbers is accurate to under 1% with any differences likely due to rounding.

[OhioBob]

So the simple method of looking at just the Ap/Pe numbers is accurate to under 1% with any differences likely due to rounding.

That works for Kerbin because Kerbin's orbit is circular. It's not so simple when both orbits have a significant eccentricity.

[WuphonsReach]

Well, for worst-case it holds true:

[TABLE=class: cms_table_grid, width: 500, align: center]

[TR]

[TD]Jool[/TD]

[TD]Eeloo

[/TD]

[TD=align: center]13,455,800[/TD]

[TD=align: center]183,859,900[/TD]

[/TR]

[/TABLE]

Jool Ap/Pe = 72.212 Mm / 65.335 Mm

Eeloo = 66.688 Mm Pe / 113.550 Mm Ap

Jool Ap + Eeloo Ap = 185.762 Mm (within about 1%)

The 13.455 Mm number is more difficult to match because it takes more then 1000 years for Jool and Eeloo to get within touching distance. (Technically, they could collide at some undetermined point in the future because Jool's Ap > Eeloo's Pe value.)

For Moho to Jool/Eeloo:

[TABLE=class: cms_table_grid, width: 500, align: center]

[TR]

[TD]Moho[/TD]

[TD]Jool[/TD]

[TD=align: center]61,128,600[/TD]

[TD=align: center]78,522,500[/TD]

[/TR]

[TR]

[TD]Moho[/TD]

[TD]Eeloo[/TD]

[TD=align: center]62,496,600[/TD]

[TD=align: center]119,839,800[/TD]

[/TR]

[/TABLE]

Moho = 6.316 Mm (Ap) / 4.210Mm (Pe)

Jool Ap/Pe = 72.212 Mm / 65.335 Mm

Eeloo = 66.688 Mm Pe / 113.550 Mm Ap

Moho-Jool Maximum = 6.316+72.212 = 78.528 (almost spot on)

Moho-Eeloo Maximum = 6.316+113.550 = 119.866 (pretty close as well)

Moho-Jool Minimum = 65.335 - 6.316 = 59.019 (might take > 1000 years to line up)

Moho-Eeloo Minimum = 66.688 - 6.316 = 60.372 (might take > 1000 years to line up)

So "minimum within a defined time range" may or may not line up with the "larger Pe minus smaller Ap" number. It depends heavily on resonance of the two orbits.

[strongest_2hu]

Technically, they could collide at some undetermined point in the future because Jool's Ap > Eeloo's Pe value.

Technically, they could never collide because Jool and Eeloo are in 3:2 resonance and also their orbits don't intersect.

Edited February 25, 2015 by strongest_2hu

[Negana]

On 2/24/2015 at 5:38 PM, OhioBob said:

I'm glad I could help. I stopped searching when I reached the end of year 1000. There may be closer/farther distances in later years, but I figured it would take a seriously addicted individual to play the game that far into the future. (In fact, I know Jool and Eeloo have closer encounters in the second millennia but I had to stop somewhere.)

I put all the orbital parameters into an Excel spreadsheet and computed the planet positions vs. time, from which I calculated the separation distances. I then just searched for the minimums and maximums.

 

On 2/24/2015 at 1:24 AM, OhioBob said:

		Minimum (km)	Maximum (km)
Moho	Eve	3,546,900	16,117,600
Moho	Kerbin	7,289,400	19,913,500
Moho	Duna	14,641,100	26,768,900
Moho	Dres	30,052,400	51,629,500
Moho	Jool	60,949,000	76,594,200
Moho	Eeloo	60,715,300	119,514,300
Eve	Kerbin	3,668,900	23,530,800
Eve	Duna	9,792,200	31,665,400
Eve	Dres	25,237,900	56,462,800
Eve	Jool	55,583,200	81,962,500
Eve	Eeloo	56,927,000	123,317,100
Kerbin	Duna	6,069,300	35,383,000
Kerbin	Dres	21,402,600	60,320,600
Kerbin	Jool	51,735,000	85,811,900
Kerbin	Eeloo	53,183,400	127,081,700
Duna	Dres	13,732,500	68,079,200
Duna	Jool	44,584,600	92,947,000
Duna	Eeloo	45,095,900	135,224,000
Dres	Jool	24,543,300	113,355,000
Dres	Eeloo	28,733,500	151,339,300
Jool	Eeloo	11,617,100	169,943,700

It sounds like what you want is the minimum/maximum distance between the orbits of the planets, which would be the theoretical minimum/maximum distance between the planets. I'm sure that can be determined mathematically, but that's not what I did. I projected the motions of all the planets over a 1000-year period and searched for the minimum and maximum true separations. These results are tabulated above.

 

Hi OhioBob !
 

I'm looking to create a web app for satellite constellation calculation for KSP and KSP2. I saw that you simulated on Excel the planets orbits.

Would it be possible to have this Excel file please ?

Edited February 7, 2022 by Negana

[OhioBob]

4 hours ago, Negana said:

Would it be possible to have this Excel file please ?

I'll have to look and see if I still have it.  I don't remember how user friendly it is, because it was never made to share.  If I find it, I'll send you a private message.

[Blaarkies]

On 2/22/2015 at 7:45 PM, sralica said:

I am trying to make a RemoteTech network.

 

Maybe this can help?
It doesn't handle RemoteTech parts yet, but it has everything sorted for stock KSP

 

[Poodmund]

@OhioBob, I got bored this afternoon and went down this rabbit hole after seeing this question on reddit: 

I remembered your spreadsheet which I used to get the min/max distances over the first 1000 years for my CommNet spreadsheet but couldn't remember how granular the calculation was with respect to the time steps during calculation...

...

...

... ended up just writing a python script to calculate the distances where you can change the time step by editing it in the script. Ran it for 1000 years at a time step of 1 hour between Kerbin and Duna. It took just under 20 seconds to calculate and I got the results of:

Enter name of the first body: Kerbin
Enter name of the second body: Duna
Enter the number of Kerbin years to run for: 1000
Minimum Distance: 6069286587.329437 meters
Maximum Distance: 35383027778.77004 meters
Calculation Time: 18s

Made a repo for the script here: https://github.com/Poodmund/KSP-Celestial-Body-Distances-Calculator

From your spreadsheet we got:

• Min: 6,069,326,656 meters
• Max: 35,382,969,611 meters

So they are very close, with the difference probably being due to the duration of the calculation step. If we wanted to do it on a per second iteration, it'd take about 10 days for me to calculate Kerbin - Duna over 1000 years.  

Edited November 23, 2023 by Poodmund

[OhioBob]

@Poodmund, as I recall, I think my time step was 1 day.  So clearly 1 hour would be a bit more accurate.

[Poodmund]

Ah, nice. I will like edit the script to take in all the bodies and then crunch the numbers and spit the distances out in a nice format... and then see how small I can make the time step without turning my PC into an inferno.  

EDIT: Well it seems it works well:

>calcAll.py
Enter name of the first body: Kerbin
Enter the number of Kerbin years to run for: 1000
Minimum Distance between Kerbin and Moho: 7289394665.366949 meters
Maximum Distance between Kerbin and Moho: 19913537675.695507 meters
Minimum Distance between Kerbin and Eve: 3668829002.2021995 meters
Maximum Distance between Kerbin and Eve: 23530850549.623432 meters
Minimum Distance between Kerbin and Duna: 6069286587.329437 meters
Maximum Distance between Kerbin and Duna: 35383027778.77004 meters
Minimum Distance between Kerbin and Dres: 21402499252.618446 meters
Maximum Distance between Kerbin and Dres: 60320788648.104256 meters
Minimum Distance between Kerbin and Jool: 51735044326.640366 meters
Maximum Distance between Kerbin and Jool: 85812057514.17293 meters
Minimum Distance between Kerbin and Eeloo: 53183312062.062584 meters
Maximum Distance between Kerbin and Eeloo: 127081686577.7892 meters
Minimum Distance between Kerbin and Sarnus: 105481066687.77617 meters
Maximum Distance between Kerbin and Sarnus: 146115998963.23166 meters
Minimum Distance between Kerbin and Urlum: 229218369395.3892 meters
Maximum Distance between Kerbin and Urlum: 279415565156.50653 meters
Minimum Distance between Kerbin and Neidon: 390533362776.5709 meters
Maximum Distance between Kerbin and Neidon: 428177031309.7583 meters
Minimum Distance between Kerbin and Plock: 382964985022.1354 meters
Maximum Distance between Kerbin and Plock: 688705050769.595 meters
Total Calculation Time: 3m 3s

EDIT EDIT: I've projected it for 1000 years for all bodies and noticed that some min/max distances occur around the 1000 year limit... especially the minimum encounter between Jool and Eeloo... which occurs at Y999:D30 only 11,617,098km apart.
 

Edited November 25, 2023 by Poodmund

[Poodmund]

Body 1	Body 2	Minimum (km)	Time Min (Kerbal)	Maximum (km)	Time Max (Kerbal)
Moho	Eve	3,546,908	Y5553:D356:3h:0m:40s	16,117,621	Y6108:D68:3h:3m:33s
Moho	Kerbin	7,289,385	Y8871:D45:2h:0m:40s	19,913,539	Y6528:D48:2h:59m:47s
Moho	Duna	14,641,065	Y7765:D233:4h:1m:57s	26,768,895	Y5796:D117:2h:2m:2s
Moho	Dres	30,052,322	Y7554:D306:2h:56m:14s	51,629,702	Y7906:D21:2h:0m:34s
Moho	Jool	60,949,012	Y9406:D10:1h:2m:50s	76,594,332	Y528:D176:4h:56m:58s
Moho	Eeloo	60,715,266	Y7873:D316:4h:1m:28s	119,514,349	Y9434:D365:0h:7m:39s
Moho	Sarnus	113,689,188	Y1873:D58:0h:59m:14s	137,899,413	Y8359:D46:4h:57m:25s
Moho	Urlum	238,529,726	Y412:D357:4h:3m:40s	270,103,862	Y9916:D226:2h:56m:8s
Moho	Neidon	397,824,635	Y7373:D239:4h:3m:5s	420,885,782	Y2500:D406:4h:56m:10s
Moho	Plock	390,654,083	Y2225:D425:1h:50m:11s	681,013,388	Y9523:D98:3h:0m:8s
Eve	Kerbin	3,668,829	Y643:D75:4h:1m:41s	23,530,852	Y2430:D23:4h:3m:46s
Eve	Duna	9,792,174	Y6246:D255:3h:49m:44s	31,665,478	Y8507:D237:5h:1m:37s
Eve	Dres	25,237,843	Y7185:D136:0h:58m:58s	56,462,866	Y3612:D76:0h:1m:57s
Eve	Jool	55,583,201	Y841:D232:0h:42m:9s	81,964,576	Y2234:D379:3h:46m:37s
Eve	Eeloo	56,926,652	Y7191:D155:2h:8m:48s	123,317,186	Y921:D130:1h:51m:13s
Eve	Sarnus	109,151,911	Y5080:D95:1h:52m:43s	142,445,164	Y704:D276:1h:7m:30s
Eve	Urlum	233,057,384	Y6479:D216:4h:1m:10s	275,576,891	Y5953:D330:2h:6m:51s
Eve	Neidon	394,262,257	Y6877:D28:1h:51m:22s	424,448,344	Y3160:D279:2h:50m:47s
Eve	Plock	386,792,768	Y8905:D30:1h:18m:47s	684,877,156	Y9770:D357:4h:9m:50s
Kerbin	Duna	6,069,283	Y4808:D380:0h:56m:24s	35,383,028	Y3095:D225:5h:59m:26s
Kerbin	Dres	21,402,402	Y1558:D365:1h:19m:1s	60,320,789	Y728:D290:3h:8m:53s
Kerbin	Jool	51,735,042	Y7427:D91:1h:3m:13s	85,812,078	Y2212:D47:4h:13m:57s
Kerbin	Eeloo	53,183,306	Y844:D229:4h:22m:10s	127,081,754	Y9554:D161:5h:5m:20s
Kerbin	Sarnus	105,481,041	Y1028:D97:2h:13m:47s	146,116,001	Y8020:D300:5h:0m:21s
Kerbin	Urlum	229,218,312	Y6722:D38:2h:10m:41s	279,415,713	Y8218:D173:0h:0m:7s
Kerbin	Neidon	390,533,330	Y9355:D83:3h:53m:48s	428,177,052	Y3987:D26:3h:4m:41s
Kerbin	Plock	382,964,603	Y3463:D39:2h:44m:18s	688,705,350	Y7049:D362:1h:42m:20s
Duna	Dres	13,732,281	Y3208:D290:5h:24m:11s	68,080,257	Y8645:D69:4h:57m:23s
Duna	Jool	44,584,550	Y2205:D371:0h:4m:2s	92,947,049	Y7841:D347:0h:41m:9s
Duna	Eeloo	45,090,424	Y6781:D388:0h:35m:54s	135,225,589	Y7165:D338:3h:5m:41s
Duna	Sarnus	99,018,997	Y8288:D250:1h:56m:38s	152,572,434	Y6783:D67:1h:58m:55s
Duna	Urlum	222,352,244	Y8015:D19:3h:24m:52s	286,277,601	Y1342:D107:0h:48m:56s
Duna	Neidon	382,771,145	Y1100:D248:3h:2m:30s	435,937,665	Y8450:D349:2h:58m:50s
Duna	Plock	374,816,799	Y2721:D10:5h:22m:54s	696,857,247	Y1360:D211:5h:21m:27s
Dres	Jool	24,526,513	Y2232:D114:5h:43m:56s	113,360,807	Y5605:D65:0h:19m:35s
Dres	Eeloo	28,689,105	Y2020:D420:5h:25m:50s	151,339,309	Y5305:D185:5h:15m:26s
Dres	Sarnus	72,640,229	Y156:D34:0h:4m:43s	179,121,564	Y536:D22:1h:45m:6s
Dres	Urlum	204,800,506	Y1471:D189:0h:41m:34s	303,705,198	Y1997:D39:4h:24m:49s
Dres	Neidon	359,526,182	Y5538:D197:4h:7m:40s	459,178,956	Y3638:D295:4h:39m:2s
Dres	Plock	358,888,476	Y5935:D149:1h:12m:44s	712,736,293	Y3338:D60:1h:8m:23s
Jool	Eeloo	11,420,136	Y9973:D153:0h:24m:24s	169,943,756	Y19:D260:2h:19m:15s
Jool	Sarnus	47,661,437	Y6544:D293:0h:30m:21s	203,907,221	Y1972:D83:0h:0m:59s
Jool	Urlum	177,434,493	Y9634:D54:2h:32m:35s	331,199,563	Y9998:D45:3h:12m:3s
Jool	Neidon	332,155,657	Y1587:D25:4h:37m:19s	486,552,250	Y3486:D243:4h:36m:41s
Jool	Plock	327,504,530	Y246:D376:3h:13m:15s	744,265,120	Y8038:D103:4h:23m:55s
Eeloo	Sarnus	16,988,828	Y547:D272:0h:47m:43s	243,123,110	Y6722:D324:0h:23m:39s
Eeloo	Urlum	135,614,911	Y1961:D2:3h:52m:19s	373,212,340	Y9928:D273:5h:41m:37s
Eeloo	Neidon	299,993,717	Y4675:D131:3h:17m:10s	519,198,233	Y3105:D287:3h:46m:23s
Eeloo	Plock	331,236,639	Y247:D163:1h:53m:4s	740,539,150	Y9767:D230:3h:41m:42s
Sarnus	Urlum	112,410,337	Y3:D415:0h:22m:37s	396,177,919	Y8051:D352:4h:15m:28s
Sarnus	Neidon	276,249,934	Y7567:D31:5h:38m:35s	542,407,147	Y6328:D421:5h:41m:2s
Sarnus	Plock	267,100,128	Y9648:D224:4h:28m:3s	804,676,295	Y4330:D99:3h:51m:23s
Urlum	Neidon	138,500,523	Y5550:D274:0h:0m:16s	680,197,580	Y1667:D336:1h:6m:41s
Urlum	Plock	140,799,541	Y3461:D218:5h:29m:17s	932,918,586	Y1358:D314:3h:6m:14s
Neidon	Plock	227,326,991	Y9812:D74:0h:21m:34s	1,079,565,277	Y129:D372:5h:26m:45s

Manage to get this down to a 1 second resolution projected over the first 10,000 years. I think the game gets all wonky when you start getting to these dates as precision starts getting reduced so I don't think we need to go any further in time. Also, I expanded the calcs to incorporate all of the OPM bodies too.