Proposal for Kerbin Satellite System

[benschwab]

Hi All:

Overview:

I would like to develop and then deploy a satellite system around Kerbin. This would consist of 10 communication satellites, 6 scientific satellites, and potentially a global positioning system. I have developed ideas of what I want for the communication and scientific satellites though I have yet to do much work on the global positioning system. If anybody wants to review this proposal in whole or in part and offer advice, comment, or criticism then I would be thankful. I feel I should let you’all know that the only add-on to Kerbal Space Program I have is mechJeb.

Kerbostationary Communication (Sunshine) Satellites:

The communication satellites would consist of 4 on the equatorial plane and 6 in Molynia orbit (3 serving the northern hemisphere and 3 serving the southern hemisphere). The 4 in the equatorial plane would be in synchronous orbit and equally spaced. I believe this would provide adequate coverage for Kerbals who live in between 50 degrees south and 50 degrees north and would allow them to use the communication satellites without needing tracking systems. I have achieved this in the past using 4 launches (one for each satellite). I get the satellites equally spaced by first getting into a circular low Kerbin orbit with zero inclination and then doing a Hohmann transfer to get the kerbosynchornous orbit at 2868.75 km. I start the Hohmann transfer when each satellite is above a particular longitude which are spaced 90 degrees apart. Since I don’t care what points the satellites are over, I chose one of the four longitudes at random. I am thinking about using one launch vehicle to get all four satellites into orbit to save costs. The launch vehicle would be used to get four smaller rockets into LKO which would then detach and Hohmann transfer at the appropriate points.

Molynia Orbit Communication (Lightning in the North and Thunder in the South) Satellites:

I had a harder time figuring out how to get the 6 communication satellites into orbit to serve the polar regions. The goal is to have three satellites equally spaced in Molynia orbits. The orbits would have an inclination of 63.4 degrees (I know this isn’t important for Kerbin but I want to use it for historical reasons) with a perigee at 80 km and an apogee of 3090.36 km. From looking at a map of Kerbin I think that the Lightning Satellites achieving apogees above 63.4 degrees north, 90 degrees east and at 63.4 degrees north, 90 degrees west would provide the best coverage for the Kerbin landmass north of 50 degrees north. I also think that the Thunder Satellites achieving apogees above 63.4 degrees south, 26 degrees west and 63.4 degrees south, 154 degrees east would provide the best coverage to the small landmass south of 50 degrees south.

I have considered three methods of putting one satellite into this orbit:

1: Launching to LKO with zero degrees inclination, doing an inclination maneuver at the right point to get the satellite in the correct place (63.4 degrees south 0 degrees east/west or 63.4 degrees south 180 degrees east/west) to make the desired final orbit the first time the satellite is in the southern hemisphere, and then making the final orbit at that point.

2: Launching to LKO with 63.4 degrees inclination and waiting until the southernmost point achieved is at either 63.4 degrees south 0 degrees east/west or 63.4 degrees south 180 degrees east/west and then making the final orbit at that point.

3: Launching to Kerbin orbit with 63.4 degrees inclination with an apogee after launch at a particular altitude “a†and longitude “l†and making a perigee burn to raise the perigee to 80 km. “a†and “l†would be chosen such in its first orbit the satellite passes over either 63.4 degrees south, 0 degrees east/west or 63.4 degrees south, 180 degrees east/west. At this point I would then make the final orbit.

The benefit to option 1 is that the instructions can be worked out beforehand and are exact with simple calculations. Kp. diomedea pointed out to me that the inclination burn would require nearly 2,500 delta v to make making this an expensive option.

In respect to option 2, from a LKO at 80 km altitude at 63.4 degrees inclination, every time the satellite passes 63.4 degrees south its longitude would be 31.25 degrees west of its previous longitude. This means that the satellite will take 288 orbits to put itself about the same longitude again (which would take 75 hours or 25 Kerbin sidereal days to happen). This would mean that if I wait long enough the satellite should be within one degree of longitude of either 63.4 degrees south, 0 degrees east/west or 63.4 degrees south, 180 degrees east/west. I believe this to be the most efficient option but requires patience.

The calculations for option 3 are the hardest. Either I would have to aim for the correct point at launch (which I don’t know how to do) or to use a(n) (anti-)radial burn along with a prograde burn to get the argument of perigee at -90 degrees and the right altitude for the appogee once I launch and get into orbit. In either case since the orbit is changing while I launch to the correct perigee, the latitude the satellite will pass over once it gets to 63.4 degree north will be changing while I raise the apogee. I might be able to perform the calculations but I suspect this wouldn’t be as efficient as option 2.

As I believe it to be the cheapest way to get the Molynia satellites in orbit, I prefer option 2 even though it may take up to a couple Earth days to be able to complete the orbits (Is the day counter in Universal Time 24 hours or 6 hours?). My initial thought of getting the satellites properly spaced would be to use three satellites to time how long it takes from launch to get to apogee of the final orbit and time the launches of the second and third satellites at the appropriate times after the first satellite as achieved apogee. Kp. diomedea has suggested a more efficient method of getting the three satellites in orbit of using one launch vehicle for three satellites and using maneuvers and separate separations to get the right spacing.

My proposed method for getting the correct orbits and spacings is as fallows. I would launch a single launch vehicle with three separately separable smaller rockets for each individual satellite. I would launch to an inclined circular orbit of 80 km. I would wait until the launch vehicle is above 63.4 degrees south, 30n degrees east/west for some integer n. I would raise the apogee at this point for the launch vehicle to 821.05 km (a period of 1 hour). I would separate each smaller rocket every second visit to perigee and raise the apogee of the orbit to 2055.2 (a period of 2 hours). After all three rockets have been separated they should be in orbits rotated 120 degrees from each other and they should arrive at perigee simultaneously (or pretty close).

Each time the satellites reach perigee, one of the satieties should be above either 63.4 degrees south 0 degrees east/west or 63.4 degrees south 180 degrees east/west. During one of these times I raise the apogee to 3090.36 km for the final Molynia orbit. Two hours latter another satellite should be in the spot the first satellite was above Kerbin and I raise that satellite’s apogee to 3090.36 km. Another two hours later the third satellite should be in position and I raise that satellite’s apogee to 3090.36 km.

At this point I should have my Lightning constellation in place. When each satellite is at apogee it should be over 63.4 degrees north and either 90 degrees east or 90 degrees west. One hour after one of the satellites is above one of those two coordinates another satellite should be above the other coordinate. I will use a similar process for the Thunder constellation with the appropriate reference points.

Scientific (Typhoon) Satellites:

Ideally I would wish these to be in sun-synchronous orbit. Other than for Kerbostationary orbits, I believe this to be imposable for Kerbin given that Kerbin is modeled (for now) as a perfect sphere. Geocentric sun-synchronous orbits make use of the oblateness of Earth to stay synchronized to both the earth’s surface and to the position of the sun relative to the Earth. With a sidereal day of 6 hours and a solar day of 6 hours and 50.813 seconds it would require an orbit with a period of just less than a second for a satellite in an inclined orbit to cross the equatorial plane of Kerbin at the same longitude at the same time of day every day. This is imposable.

I desire to have the Typhoon Satellites pass over the equatorial plane of Kerbin at the same time each day (under the belief that this would be more valuable to science than would having the satellites pass over the same point at the same time every day). I also chose for it to pass the equatorial plane 4 times each day (one time in daylight on each side of the planet) so the orbital period would be 3 hours and 25.41 seconds. A circular orbit with an altitude of 1588.60 km achieves this (actually it is off by .02 seconds).

I propose to put 6 Typhoon Satellites in circular polar orbit with an altitude of 1588.60 km. I want each orbit to be separated by 60 degrees. I propose to use one launch vehicle to put all 6 satellites into orbit. At the finished orbit, Kerbin rotates 180.42 degrees each orbit (meaning that after two orbits the satellite is about .84 degrees west of where it was). An orbit with a perigee of 1588.60 km and an apogee of 1669.10 km has an orbital period of 3 hours, 5 minutes, and 25.39 seconds during which Kerbin rotates 185.42 degrees (a 5 degree difference).

Thus once I get the first orbit in place, I release the first satellite retrograde when it is almost above the north pole, turn prograde and raise my apogee to 1669.10 km, wait 6 orbits, then circularize back at 1588.6 km when I’m almost at the north pole, and repeat. This should give me the desired orbital configuration though I am at a loss as to how to time it so that one of the satellites (perhaps the first released) crosses the equatorial plane at noon every other crossing.

Conclusion:

I would also like to set up a GPS system and while getting the right number of satellites in the right orbits is somewhat easy to work out (now that I’ve done the above work), the satellites need to be in a specific configuration in their orbits to ensure that enough satellites are visible at all times from every point on Kerbin. I could just put enough satellites in orbit so I don’t have to figure out what this configuration is but that seams expensive.

The above is my proposal as it stands right now. This would put enough communication satellites up to be able to broadcast Kerbtoons to all of the Kerblets on Kerbin as well as scientific satellites for weather prediction, mapping, and other purposes. Anybody with comments, suggestions, criticism, or whatnot would be appreciated delivering them. I should also let you’all know that I am playing through KSP rather slowly and it will probably be a week (maybe two) before I finalize a plan of action and start implementing it. I am willing to provide details on calculations and delta-v budgets if asked.

In Gratitude

Ben Schwab

[Taki117]

Wow, that is a very thought out plan. What you could do for your GPS sats is to put them on a 750 x 750 km polar orbit, that way you could have two perpendicular sets of 4 sats to cover the entire surface. Alternatively you could take a look at the actual GPS sat contellation.

[Jimbimbibble]

One thing you could do about the molynia orbits is use MechJeb's "launch into plane of target" feature. Use hyperedit to position a target where you intend to put your satellite and launch for it. I wouldn't consider this to be unrealistic/cheating because if you were going to do something like this for real you would be able to calculate how to do the launch and program the rocket.

[diomedea]

As I had the opportunity to tell you already, please ask if you have specific issues.

It seems to me you are setting for the more suitable strategy (option 2 IMO) about Molniya orbits, so you don't need much more advice, but just to experiment them in KSP.

The kerbstationary orbits may prove tricky at first to get right. Actually (as in reality on Earth) we only need orbits to be within some margin of error to call a success: for kerbstationary, what is important is inclination close to 0°, orbital period very close to 6 hrs, and a very low eccentricity. But success can be called only if you can place the satellite above a specific longitude. So, in my planning to achieve those, inclination comes first, and apoapsis to 2868.75 Km. At apoapsis, I then raise periapsis looking at the orbital period (you use MJ, it gives you that), I know each minute beyond 6 hrs means 1° in longitude more to the west when a full orbit is completed. After one orbit I should be exactly matching longitude and back at altitude 2868.75, so burn to have periapsis at the same altitude and therefore eccentricity =0.

I am not sure about the scientific satellites. KSP science is based on situations, like different biomes. So I would use vessels headed to make experiments in all different situations. But I understand you like to simulate realistic orbits (like used on Earth).

About the GPS constellation, I am sure you can find all info you need from Internet. GPS-Navstar in reality uses 6 orbits with 4 sats on each (all needed data from that Wiki page), but coverage would be obtained with many other possible configurations (perhaps, not all able to ensure an all time coverage as the chosen ones). If you can successfully make kerbstationary and Molniya orbits, you won't have issues making those inclined GPS orbits too.

Edited April 19, 2014 by diomedea

[cantab]

You could emulate a sun-synchronous orbit with periodic stationkeeping manouvres. For a relatively small satellite an ion drive would do the trick. Pick an orbit with apopasis above the north or south poles and as high as you're happy with to minmise delta-V needed. I reckon you can get a few years between xenon topups.

Drawback is needing to do the stationkeeping, of course.

[Rokker]

Now, While I do understand wanting to do the Molniya orbits for historical reasons, I must point out that for the purpose of coverage of the North and South in general, they would be rather poor as opposed to something with the same apo/peri and a 90 degree inclination, with 3 (or 2 if you are talented at constellation placing) placed equally apart time-wise (or as close as possible to it, wont really matter too much) in a North serving orbit, and 3 (once again, 2 if you are really good) satellites placed similarly in a South serving orbit. Or, a simple 3 or 4 satellite circular orbit at a 90 deg inclination.

Now, as for launching anything like a Molniya, if you still want to go with that, I would launch the first one with a 70-75 degree heading and see where it gets you. I have a feeling that it may land you relatively close to that 63.4 degree mark, but I could be way off.

Also, it wouldn't matter if they ever modeled Kerbin as an oblate spheroid because, and I may be mistaken, but I'm pretty sure KSP models gravity itself as a single point within the body.

Edited April 19, 2014 by Rokker