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sralica

Min, max distances betwen planets

Question

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 by sralica

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    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 by OhioBob
Revised numbers to fix error in formula

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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.

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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.

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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.

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

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

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... 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?

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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)

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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.

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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.

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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.

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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.

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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 by strongest_2hu

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