maltesh

[Scenario]Tetrahedral Satellite Configuration: 4-sat full-surface coverage

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0aPGw17.png

In 1985, J.E. Draim wrote the article "Three- and four-satellite continuous-coverage constellations" (paywalled, sorry) for the Journal of Guidance, Control, and Dynamics. The article described using four satellites in a tetrahedral configuration of inclined, elliptical orbits to provide complete surface coverage of Earth at all times, as the minimal number of satellites necessary to do so.

Draim was subsequently awarded patentson the idea.

A couple months ago, a discussion in the IRC channel came up on the minimum number of satellites necessary to get constant, full coverage on a planetary surface, and Draim's concept was mentioned.

Using Draim's parameters, I worked out a set of parameters for a Kerbin Tetrahedral Satellite Configuration, and that's the genesis of this scenario.

Objective: Launch and place four satellites in the Tetrahedral Satellite Configuration.

Load the scenario. Build a satellite lifter to place the four satellites at the required positions The satellite must meet the following criteria:

1) A Probe Pod for control.

2) A Satellite dish for routing communications.

3) Some kind of onboard propulsion system for stationkeeping and deorbiting.

4) A power source (either solar panels+batteries, or an RTG) to keep the

5) Some sort of on-sat maintenance provision; Either a docking port to allow the satellite to be moved, or ladder sections to allow you to pretend that the satellite is set up for service by Kerbals.

The Scenario file contains four marker objects, marked as debris, in the following orbital positions.

[TABLE=width: 500]

[TR]

[TD]Target Orbital Elements[/TD]

[TD]Marker 1[/TD]

[TD]Marker 2[/TD]

[TD]Marker 3[/TD]

[TD]Marker 4[/TD]

[/TR]

[TR]

[TD]Semimajor Axis (m)[/TD]

[TD]4350000[/TD]

[TD]4350000[/TD]

[TD]4350000[/TD]

[TD]4350000[/TD]

[/TR]

[TR]

[TD]Eccentricity[/TD]

[TD]0.28[/TD]

[TD]0.28[/TD]

[TD]0.28[/TD]

[TD]0.28[/TD]

[/TR]

[TR]

[TD]Inclination[/TD]

[TD]33°[/TD]

[TD]33°[/TD]

[TD]33°[/TD]

[TD]33°[/TD]

[/TR]

[TR]

[TD]Argument of

Periapsis[/TD]

[TD]270°[/TD]

[TD]90°[/TD]

[TD]270°[/TD]

[TD]90°[/TD]

[/TR]

[TR]

[TD]Longitude of the

Ascending Node[/TD]

[TD]0[/TD]

[TD]90[/TD]

[TD]180[/TD]

[TD]270[/TD]

[/TR]

[TR]

[TD]Mean Anomaly at Epoch[/TD]

[TD]0[/TD]

[TD]-1.57078[/TD]

[TD]3.14159[/TD]

[TD]1.57078[/TD]

[/TR]

[TR]

[TD]Epoch[/TD]

[TD]0[/TD]

[TD]0[/TD]

[TD]0[/TD]

[TD]0[/TD]

[/TR]

[/TABLE]

Requirements for completion:

The player must launch, get into orbit, and rendezvous with each of the four the Marker Objects. The player must deploy one satellite within 10m of each Marker object.

GRbbA0bl.jpg

Upon placement of the last satellite, the player must take a screenshot of the completed constellation from the Tracking Station, showing the Universal Time in the upper left corner. Ranking will be based on the Universal Time displayed in the image.

w0tOnEtl.jpg

Universal TIme: Year 1, Day 3, 04:32:58 (larger image here: http://i.imgur.com/w0tOnEt.jpg )

Optional Achievements:

Chemset
: Using solely chemical rockets to place the satellites. No LV-N, no Ion drives.

Sliderule
: Using solely the in-game rendezvous system; No mechjeb/KER/ORDA, etc to provide rendezvous assistance

Stopwatch
: Not using Kerbal Alarm Clock or other timekeeping/launch timing mods to set up rendezvous.

Tidy
: No debris from launches left on orbit.

Major Clean
: Deorbit the rendezvous targets; Each one masses about 0.38t and has 1m shrouded docking ports.

R
3
: Use a completely reusable spacecraft to place the satellites.

Oneshot
: Use one launch to deploy all four satellites.

Download the Scenario: Tetrasat_v0.20.zip

An example Satellite: XMPLsat.craft (screenshot )

[TABLE=width: 500]

[TR]

[TD]Ranking[/TD]

[TD]User[/TD]

[TD]Timestamp[/TD]

[TD]Achievements[/TD]

[/TR]

[TR]

[TD]1[/TD]

[TD]
[/TD]

[TD]Day 1, 08:56:32[/TD]

[TD]Chemset, Sliderule,Stopwatch,Tidy, Major Clean, Oneshot[/TD]

[/TR]

[TR]

[TD]2[/TD]

[TD][/TD]

[TD][/TD]

[TD][/TD]

[/TR]

[TR]

[TD]3[/TD]

[TD][/TD]

[TD][/TD]

[TD][/TD]

[/TR]

[TR]

[TD]4[/TD]

[TD][/TD]

[TD][/TD]

[TD][/TD]

[/TR]

[TR]

[TD]5[/TD]

[TD][/TD]

[TD][/TD]

[TD][/TD]

[/TR]

[/TABLE]

Edited by maltesh
Providing information about the originator of the concept. Clarification of Orbital Parameters.

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I've done this sort of thing with the Remote tech mod. One hub station in geosynchronous orbit over KSC and 4 relays in 300Km orbits separated by inclination increments of 45 Degrees

It's not EXACTLY the kind of thing the challenge is looking for but I'm still happy about it xD

Edited by Reavermyst

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Aye, the tetrahedral configuration manages it with four, rather than five.

Can't say I've really made much use of RemoteTech; I like the line-of-sight indicators, at least.. That said, figured I'd throw some remotetech parts on satellites in the configuration to see what would happen.

aSIkmdjl.jpg

Some screwing around seems to indicate that, in the provided configuration (Where the satellites have an apoapsis just shy of 5000km altitude over Kerbin), satellites outfitted with the 8000-km-range omnidirectional RemoteTech Deployable Antenna appears to be able to keep constant contact with any object anywhere on the surface of Kerbin, although the range limit does require a bit of awkward routing at times. And of course, assuming that you've got similar range on your commset at KSC.

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That paper is a very nice find, thanks. I might try that challenge if I find the time. This constellation could replace my non-expandable sats when I need more dishes soon. My current network has three sats spaced evenly in geosync orbit, plus two in highly elliptical orbits with a period of 6 hours. The polar sats have proven very usefull because they can reach vessels on the far side of Mün an Minmus, helping with injection burns.

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(Sorry for the necro.)

I want to try out this configuration, so it can replace my inefficient 8-satellite constellation in 0.21. But I'm drawing a blank on the parameters... what are the longitude of periapsis, longitude of the ascending node and mean anomaly? And more importantly, how do I control them; how do I actually get into those orbits? I understand inclination, eccentricity and the semi-major axis, and I use Kerbal Engineer, if that helps. I know I could just try to rendezvous with the markers, but I'd like to have a better understanding of it and be able to use it in a new game.

(On a different note, is there a convenient way to work this out for any given body, e.g. the Mun, Duna or Laythe? Might be worth posting on the wiki.)

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The longitudes of the periapsis and ascending node are simply the geographical longitude on Kerbin over which those points lie. So you can get these parameters from the surface tab in KER. They describe the orientation of the elipsis in space.

Say you start from a circular equatorial orbit with the same radius as the periapsis of your target orbit. Then you can do the burn for the inclination change at the latitude of the ascending node (or on the other side of the planet). If you then still have a circular, but inclined orbit, you can burn to raise your apoapsis when you are over the longitude of periapsis. In the end, you will end up precisely in the right orbit.

The mean anomaly provides the timing information. It progresses between 0 and 2 Pi proportionally to the area swept by the line between Kerbin (in this example) and your ship. Kepler's second law says that the area swept by this line is constant for a given time-interval. 2 Pi means it's once around and starts back at 0. I think the data here are given for an interval of -Pi ... +Pi. So this means Marker 1 is at periapsis when Marker 3 ist at apoapsis, and the same for 2 and 4. I hope I got that right. If not, please correct me! :confused:

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Actually, Longitude of Periapsis and Longitude of the Ascending Node are not surface-relative coordinates. They're celestial-relative coordinates; that is, relative to the fixed celestial sphere.

Gs49xch.png

Image by Wikipedia User Lasunncty, CC-BY-SA-3.0-MIGRATED; Licensed under the GFDL by the author; Released under the GNU Free Documentation License.

In the case of the Kerbin System, the reference plane (analagous to Earth's ecliptic plane), is the plane in which Kerbin orbits.

In the kerbin System, if you were to draw a line from Kerbin through the sun at UT=0.0. the Reference Direction would be a little counterclockwise of that direction. (I don't think the Kerbin System has any obvious feature on the skybox that points in the Refeerence direction.)

If you were to place a plane that passed through the center of Kerbin parallel to the Reference Plane (Since it's kerbin, this would be the reference plane,), the Ascending Node would be the point at which your orbit passes through the reference plane headed in the Northward direction.

The Longitude of the Ascending Node is the angle, measured counterclockwise in that plane, between the Reference Direction and your orbit's Ascending Node.

Argument of Periapsis (Which is what I should have written, instead of Longitude, and will go back and change it), is the angle between your orbit's Ascending Node and your orbit's periapsis, measured counterclockwise in the plane of your orbit.

KSP's persistent.sfs files use the abbreviation "LPE" for Argument of Periapsis.

As for "How do I get into an orbit that has those parameters?", I don't really have a good answer for you. The stock game doesn't really give you good information for that. Really, there needs to be some kind of targeting capability that lets you enter orbital parameters and gives you a target box you can aim for when rendezvousing.

A longer discussion of the orbital parameters can be found in my signature.

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Thanks for the correction, I should have realised surface-relative coordinates would be no good way to describe an orbit.:)

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Thanks for the information, guys. I think I understand it better, now...but considering the precise timing of the different orbits and the overall complexity of this scenario, suddenly my eight-satellite constellation (four geosynchronous, two in an eccentric orbit over the north pole, two in an eccentric orbit over the south pole) doesn't sound so bad anymore. XD

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Yeah, I had that thought, too. I'll have to reconstruct my comsat network in 0.21 too. Maybe someone can construct an orbit that makes it possible to release the satellites from a bus-vehicle at their periapses at the right time and place...I'll have to think about this.

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Aughh! And here I thought I was being clever when I constructed my 4-sat Keostationary RT network by creating a bus-vehicle that coasted an elliptical orbit with a period 3/4ths of a Kerbin day...

Just looking at this, markers 1 & 3 share a common AN/DN (only reversed from each other -- one is ascending while the other is descending). But I haven't worked out what the time difference is between their passing of that point. My intuition says its half their period, but I'm pretty sure that's wrong. The same AN/DN relationship is true of 2 & 4, but they're shifted 90 degrees off from the others.

So you could create an equatorial, elliptical orbit whose apoapsis touches 1 & 3's common AN/DN point, and whose period is whatever the time is between those two passings (or some multiple/fraction thereof), if that makes sense... You'd drop the first satellite just before reaching that point, then have it make a burn to simultaneously affect a 33-degree plane change and a circularization. In theory, 90 (or 270?) degrees later, the satellite would encounter the marker at its periapsis, and be able to burn to match its velocity (thus raising its apoapsis). Then, at a later point, your deployment ship would reach apoapsis again, and deploy the second satellite.

But you'd need a second one of these bus orbits, shifted by 90 degrees, to deploy 2 & 4 from. You almost need 3 buses: one for 1&3, one for 2&4, and one "megabus" to deploy the first two buses into their deployment orbits. :confused:

The trick is getting the timing right between all these deployments. I'm not quite sure how to do that...

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(On a different note, is there a convenient way to work this out for any given body, e.g. the Mun, Duna or Laythe? Might be worth posting on the wiki.)

Ah, didn't answer this question. With regards to this, you just need to adjust the semimajor axis of the configuration to get the periapsis high enough over the surface. I haven't gone back to revisim my orignal calclation and went for round numbers just above the limit for Kerbin. The resulting altitude scales with radius, though, so, using my Kerbin Numbers...

For body X with radius r, the semimajor axis of the Draim Tetrahedral Configuration orbits needs to be at least 7.25*r.

Also, congrats to Mesklin, who's become the first person to submit a completion (now linked in the original post), though he hasn't yet posted his completion in the thread. Hopefully soon?

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I've been working out the math this weekend, and I think I have a valid flight-plan for a one-shot/tidy/major-clean (and it's a bit simpler than my previous post). Now if only I can design the ship and figure out how to stick it into the right initial orbit at just the right moment.

Just saw the update with Mesklin's time. Under 9 hours? My flight plan would take a few hours longer than that, unfortunately... I wonder if it could be squeezed down some.

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My flight plan was very simple: insert bus with four ships on high equatorial orbit (0 inclination). Then, in AN(DN) node for mark, deckouple sat, change sat inclination to 33 deg. After it make transfer orbit for docking with mark and finally math velocites and dock with mark. Repeat same actions for all 4 marks. I am very like KISS principle (keep it simple - stupid).

Only one problem you should track several operations simulateneous, it is can be hard without MJ and Kerbal Alarm Clock.

See album with screeshots. Also I did second try with help from MJ and Kerbal Alarm Clock, in this case my time is 4h 26m 51s. I did all actions with all 4 sattelites simulateneous and it was not simply.

http://imgur.com/a/HNjJL#0

http://imgur.com/a/OEVGc#0

Edited by Mesklin

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