How do I calculate required delta-V for a maneuver?

[Leicontis]

Basically, I want to set up a ring of communications satellites, and was hoping I could pull this off by packing a number of compact relays onto a single larger carrier vessel. What I'd like to be able to do is set the carrier into a phasing orbit, launching each comsat at the same point in the mother-craft's orbit, with the comsat circularizing its orbit with a single burn. I want to be able to work out the delta-V required for the circularization burn, and ideally tailor the orbits so that a set of separatrons provide the exact amount I need, so inserting them into their orbit is a fire-and-forget operation.

[Rhomphaia]

Assuming you are circularizing at an apsis It is a matter of calculating the difference between the orbital speed of the circular orbit and the speed at the apsis.

http://en.wikipedia.org/wiki/Apsis

the first formulas here are what you need.

[Mr.Rocket]

I don't understand exactly what you need, but if you need to know delta-v for a manuver, click on your flight path and click create manuver, as you drag the icons it will show how much delta-v you need. If that is not what you need, to get into a basic orbit is 4500 delta-v, and you can use a delta-v map for other places

[Vrana]

Be warned, if you are trying to setup a ring on the same circular orbit... It will never be perfect. If you do the job really good it will be very close to perfect but never perfect.

A difference in say, apoapsis height on the 4th decimal spot might not seem big, you might not even notice it without mods which provide more detailed info. But in the long run (timewarping, years pass) your sats will drift from their perfect postions along the ring. A very small error in orbit will build up over a long period of time in relation to other sats on the (almost) same orbit. No way around this afaik.

You will have to do small manuvers every few years(or months depening on how well you positioned them and how "fast/low" thier orbit is) to place sats which drifted out of position to their right spot in the ring.

I have seen a few explanantions for why this happens... From floating point errors, to theories that orbit is claculated from the "nose" of a ship instead of its center. Whatever the cause fact is perfect orbits are not possible and this is why it is a good idea to include some means of propulsion on satellites which form "rings" on the same orbit. RCS or an Ion drive can cover you for a very long time.

Just saying this cause you mention postioning them with separatrons. If these satellites need to maintain their postion relative to each other for a long (in)game time they will need more then a single shot propulsion system.

EDIT: Forgot to answer your question.

Easiest way to get the dV info you want would be to do a test run in the orbit you want your carrier to use for launching.

Get a ship into that orbit, setup a manuver node on intended satellite separation spot, circulize the orbit on the node, your manuver node will now dispaly the needed amount of dV. Basicly... What Mr.Rocket said.

Edited December 5, 2013 by Vrana

[Taki117]

...No way around this afaik...

I had a similar situation in my Long Term Laythe Mission (Still in progress) in order to get it perfect, such that they don't move around you need to set the following

alt = (desired Altitude Synchronous and Semi-Synchronous values can be found in the wiki)

ORBIT
			{
				SMA = Semi-Major Axis (Desired Value can be found in the Wiki)
				ECC = 0 (This gives you a perfectly circular orbit)
				INC = 0 (This gives you an equatorial orbit)
				LPE = 0 (This determines craft position in orbit)
				LAN = 0 (This must be 0 for an equatorial orbit)
				MNA = (This value must be the same for all probes)
				EPH = 23200961.363508 (This value must be the same for all probes AND the same as UT)
				REF = 9 (Don't worry about this)
				OBJ = 1 (Or this)
			}

More Detailed data here!

[Vrana]

I had a similar situation in my Long Term Laythe Mission (Still in progress) in order to get it perfect, such that they don't move around you need to set the following

*snip*

I stand corrected. Make it: No ingame way around this afaik.

[Taki117]

I stand corrected. Make it: No ingame way around this afaik.

But yes, in game it is extremely difficult to get right mainly because if it is not the active vessel it gets put "On rails." and matching velocity (So that it doesn't move relative to your target) doesn't work to well when you are 90 degrees apart. As far as a fire-and-forget system you could do that for the initial departure, but for station keeping you are going to need RCS. (two small tanks and 8 thrusters will give you just over 1k dV depending on weight). Also, each time you switch to one of the satellites it's information get's updated and it gets taken off the rails which could potentially throw off everything that you have worked so hard to achieve.

[Yasmy]

To calculate the delta-v required for most non-atmospheric maneuvers, use the vis-viva equation.

For your particular problem, the answer is well known. It is the second burn in a

Hohman transfer orbit:

And, of course, to calculate the comsat delta-v: dV = 981 ln(m / (m - 2*0.06)) m/s,

where m is the initial comsat mass, 981 = g * Isp for sepratrons, and 2*0.06 is the fuel mass for 2 sepratrons.

Note that altitudes reported by ksp are relative to the planet sea level, so you have to add in the planet's radius:

So pick some low Kerbin initial orbit, such as r1 = 90,000 m altitude + 600,000 m Kerbin radius.

Then solve for r2, and subtract off Kerbin's radius to find your desired comsat altitude.

Surprisingly, this gives a cubic equation, rather than the quartic I was expecting,

but given the nastiness of the general solution to the cubic equation, I would still solve this numerically.

Edited December 5, 2013 by Yasmy
Going overboard in my answers again...

[Yasmy]

Let's forget the delta-V issues for a moment, and the drifting over time issues.

Suppose you want to set up N roughly equally spaced satellites in a ring, all on the same circular orbit of radius R, dropping them off from a single spacecraft.

Suppose the satellites are responsible for the delta-V required to circularize.

The easiest way, if you know the period T0 of a circular orbit at R, is simply to set your spacecraft apogee to R,

and at apogee, move your perigee until your orbital period is a reduced fractional number of orbits: k/N * T0,

where k and N are relatively prime. (k runs from 1 to N-1, and k and N have no common factors.)

Or you can do the math ahead of time to determine the correct periapsis:

Let T0 = the period of the circular orbit at radius R.

Let T1 = the period of the delivery spacecraft.

Put your delivery spacecraft on an orbit with its apoapsis at R, and choose its periapsis, r, so that its period is a reduced rational fraction of the circular orbit period: T1/T0 = k/N

T0 = c * (2R)^(3/2)

T1 = c * (R+r)^(3/2)

T1/T0 = k/N = ((R+r)/2R)^(3/2)

r = R * (2 (k/N)^(2/3) - 1)

Then just try a few values of k. You can pick the first value of k relatively prime to N that gives an r outside the parent's atmosphere.

Or if you want to minimize the delta-V for each satellite, choose k = N-1.

Note that r and R are distances from the center of the parent, not from the surface of the parent like the Ap and Pe markers in game.

If you prefer altitudes like KSP, set your periapsis marker to Pe = (Ap + Rp) * (2 (k/N)^(2/3) - 1) - Rp, where Rp is the parent's radius.

Edited December 6, 2013 by Yasmy

[luchelibre]

Wow, you guys are trying way to hard.

Don't forget that getting a perfectly circular orbit for your probe is not what you're going for. You want an orbital period of 6 hours on the dot. Use KER to get that information.

For the mothership, get it's apoapsis up to 2868. Once your ship gets there, adjust the periapsis until your orbital period is either 4 hours for a three-sat setup, or 4.5 hours for a four-sat setup. Again, use KER. Release a sat a few minutes before you get back to your apoapsis and have it do its circ burn when it gets there. Repeat for the next two or three revolutions.

It helps a lot to release them either normal or anti-normal.

Edited December 8, 2013 by luchelibre