Intermediate Question: What is the ideal orbital altitude for Mun & Minmus transfer?

[cornmacabre]

Assuming I'm at near equatorial plane inclination with Kerbol - or can transfer to that plane within two orbits - what is the ideal orbital altitude to transfer to either Mun or Minmus (whichever I impulsively fancy... )?

Should I transfer from a near circular orbit, or is there a specific elliptical (AP/PE) orbit ideal for transfer to both satellites? Basically what my n00b self wants to know is after AP circularization burn, what orbit do you genius rocketeers go for before transferring to either moons? Hope this isn't too redundant a question - however - I'm looking for specifics. Thanks!

[Enture]

I usually use a 260km orbit as my typical parking orbit in preparation of TMI/TmI burns; but there's no special reason for it, it's just a habit. I read several people saying they only went to 100km orbits for their burns, however I would try to be at least 155km high, so the game stops updating Kerbin's surface, which causes a slight lag.

I guess there's no such thing as an ideal orbit (fellows rocketeers, correct me if I'm wrong!): you may save energy by staying on a lower orbit, but only to need more later during the TMI burn. Certainly the "burn at munrise" method doesn't work anymore at a certain altitude, but that's the sole impact I can think of.

[AncientAstronaut]

lol.

I use <100km for my parking orbit altitude.

[Cykyrios]

you may save energy by staying on a lower orbit, but only to need more later during the TMI burn.

Actually, due to the Oberth effect, burning at a lower altitude (and thus, higher speed) can save more fuel than at a higher altitude, but going at a lower speed. I haven't calculated the difference though, but I tend to orbit around 80-90 km for transfers.

[togfox]

My parking orbit is 125km. Just enough to hit a higher warp.

[Serratus]

Parking orbit for me, is best at 100km, but for transfers I do use 200km (to prevent lag from Kerbin generation) because 150km is the satellite orbit... Sometimes 300km for Minimus, but that's only because I align planes before the transfer burn, and it's easier to do it with slightly bigger orbit - smaller error...

[AncientAstronaut]

If going to Minmus, be sure to launch into the correct azimuth. Launching and then plane changing in orbit is just a huge waste of Delta-V.

[maltesh]

Depends where you do the plane change.

Do the plane change in LKO at 100km, and it's 234 m/s to change a velocity of 2245 m/s by six degrees.

Do the plane change just after you've burned for the transfer (I don't know why you'd do that, but hey), and it's 330 m/s to change a velocity of 3151 m/s by six degrees

Do the plane change mid-tranfer at 30,000 km altitude, and it's 87 m/s to change a velocity of 287 m/s by 17 degrees (the maximum you'd need to change it to hit Minmus.).

A significant amount, but not a huge waste.

[Enture]

Do the plane change in LKO at 100km, and it's 234 m/s to change a velocity of 2245 m/s by six degrees.

Do the plane change just after you've burned for the transfer (I don't know why you'd do that, but hey), and it's 330 m/s to change a velocity of 3151 m/s by six degrees

Do the plane change mid-tranfer at 30,000 km altitude, and it's 87 m/s to change a velocity of 287 m/s by 17 degrees (the maximum you'd need to change it to hit Minmus.).

Could you briefly expose us the math maltesh? So I could learn how to calculate orbital plane changes ∆v-costs...

[Cykyrios]

http://en.wikipedia.org/wiki/Orbital_inclination_change#Circular_orbit_inclination_change

This formula works for circular orbits only (general one is above), and is in practice the minimum you need with a perfect execution.

[bsalis]

Well the ideal may depend a little on the rocket, in what the optimal ascent profile is.

It seems to me that 100Km is considered the standard LKO, and a good place to do a transfer orbit to benefit from the Oberth effect. If you go higher, you can save delta-V from atmosphere drag, but lose on Oberth effect. There are always tradeoffs.

[maltesh]

The circular orbit inclination formula actually works to find the minimum delta-v for any change in direction you want to make, as long as you know the angle you want to change your direction of motion by (ÃŽâ€i in the formula), and you want to have the same speed when you're done as when you started.

All orbits of the same semi-major axis have the same Specific Orbital Energy. Once you know the radial distance and velocity for any point in your orbit, you can use the specific orbital energy equation to find the velocity at any other radius that your orbit reaches.

Edited August 25, 2012 by maltesh

[maltesh]

Thinking about this a little more, I wound up postulating the following:

Assuming your spacecraft is in an equatorial, circular orbit at an altitude 100 km above Kerbin's surface(700km from its center), and you burn into an equatorial transfer orbit to take you out to 46400 km altitude(47,000 km from its center). At the time you do so, Minmus will be at its maximum distance above the plane of its orbit. At some point during the orbit, you will perform a plane change to meet it. At what radial distance from Kerbin should you perform the plane change to minimize the delta-V cost ?

That produced this graph

Your best bet appears to be at about 23,000 km altitude for the plane change, where the required delta-V bottoms out at 81 m/s. You can save a litte more by waiting all the way out to apoapsis to do the plane change (72 m/s), but I only calculated the delta-V for the plane change itself; The savings you get by waiting that long are eaten by the extra oomph you need to reach Minmus before it leaves the vicinity.

Of course, as mentioned upthread, a real space program on a tight fuel budget would probalby just wait for one of Minmus' orbital nodes to pass overhead, and launch directly into its plane. Waiting up to three hours for a window isn't all that onerous on a 54 hour trip, and the extra delta-V necessary to make orbit at a 6°-inclination angle is about 18 m/s by my reckoning.

But who has time for that? LAUNCH NOW!

Edited August 27, 2012 by maltesh
Minor math error

[Vanamonde]

I hope this isn't a dumb question, but why isn't the most efficient time to alter plane at the beginning of the transfer? My thinking is that any deflection you achieve there will be magnified by the length of the flight. By contrast, at 47,000km you need to deflect 6 degrees, but at 23,500km you have to deflect 11.87 degrees, to cover the same 4939.9km that Minmus is above the ecliptic at that point, right? (This game is forcing me to re-learn math I haven't used in 20 years. Not that I'm complaining. ) If not, what am I overlooking?

[maltesh]

You're moving a lot slower at 23,500 km altitude than you are at the beginning of the transfer. At the beginning of the transfer, 100km up, you're moving at 3151 m/s. By 23,500 km, you're moving at about 395 m/s. And the slower you're going, the easier it is to deflect your direction of motion by a particular amount.

[sneezedr424]

I use about an 80 KM circular orbit (thanks MechJeb!) to transfer to places. You don't waste as much fuel getting to a higher altitude.

Fun Fact: Going to Minimus is actually more fuel efficient (if you know what you're doing), because Minimus has lower gravity. Take off's a lot easier too. Burn for 7 seconds and you get pretty high up.

[MissStabby]

why not use a orbit of 70 km

[sal_vager]

I read somewhere that the most efficient altitude for the trans Munar burn was as low as possible, so that would be just over 69,100m

I can't remember where I read this though, I think it was one of Closette's comments, or maybe Kosmo-not's.

[Secular_Response]

Rather than making another topic, I would like to ask a related question here. Why would I want to achieve orbit and THEN change my inclination to match Minmus, when I can simply set my launch attitude to be aligned with Minmus when I reach orbit? The question, then, is: What is that launch attitude? Would 96° do it?

[sal_vager]

Secular_Response, this is what I do, and Minmus is on a 6 degree inclination.

[Secular_Response]

Thanks for the response, sir. If I understand you, instead of merely adding 6° to my 90° (newb mistake) I should launch at 6°? That's great!

[maltesh]

Rather than making another topic, I would like to ask a related question here. Why would I want to achieve orbit and THEN change my inclination to match Minmus, when I can simply set my launch attitude to be aligned with Minmus when I reach orbit? The question, then, is: What is that launch attitude? Would 96° do it?

Bearing 096° would do it, if Minmus' Descending node is directly above KSC on launch.

Bearing 084° will do it, if Minmus's Ascending node is above KSC on launch.

At any other time...Things get complicated. You won't be able to match Minmus' orbital plane until you pass through a point that's in Minmus' orbital plane. Depending on how and when you fly your ascent, this might not happen until you are already in orbit. If you decide not to match the plane, and just fly into a plane that will intersect Minmus' orbit when you get out there, you have to look ahead to figure out when you're going to be burning, and put your parking orbit into that plane, if you're going to be super-efficient about it.

All told, flying out equatorially and plane-changing halfway out does cost up to several dozen meters per second more of delta-V than waiting for a node window, and launching directly in plane. However:

1. If Minmus is equatorial at your intercept point, it will cost less than matching the plane.

2. Several dozen m/s of delta V is generally chump change. Unless your ship is operating on a razor-thin fuel budget, you can easily eat that.

3. You don't have to care whether Minmus is above or below the equatorial plane when you launch equatorially. You only have to care when it's time to do that plane change, halfway out.

[Secular_Response]

Thanks very much for the detailed response! I should do fine now.

[SciMan]

Thanks for the response, sir. If I understand you, instead of merely adding 6° to my 90° (newb mistake) I should launch at 6°? That's great!

hold on a second there, don't forget that launching from KSC at a 90° HEADING (due east) will put you in a 0° inclination orbit, while launching at a 0° heading will put you in a 90° inclination orbit (aka polar orbit)

This means if you are putting numbers into MechJeb's ascent autopilot to set up for a Minmus transfer orbit, you need to put in 6°, as it is asking for orbital inclination, not launch heading.

Now, if you are launching manually (no MechJeb) you should hold the heading at 96°, which is indeed "merely adding 6° to my 90°"

[Kosmo-not]

I launch on a heading of 083° or 097° (depending) when the launch site reaches the node. Bear in mind there's a velocity component you have to factor in due to the rotation of Kerbin when trying to get a certain inclination from launch.