Periapse delay maneuver

[Nicias]

Hello,

I have developed a standard procedure for getting to moons like Val. 

1. Come in as low as possible to the planet (Jool in this case)
2. Burn enough at PE to capture with a high AP (about a year period)
3. At AP burn to accomplish two things:
   1. Raise PE to Val's orbit (prograde)
   2. Change arrival time to create an intersect at PE (so Val as there when the probe gets to the probe's PE) this is a radial/anti-radial burn.
4. (match planes on the way down)
5. circularize at low Val orbit.

I can calculate all of the maneuver dv requirements. Except for 3.2. I'm having a hard time figuring out how to calculate how much I would need there.

Any suggestions on how to calculate that?

 

 

 

 

[FleshJeb]

I can't find any good information on the cost of radial burns. In general, I think it's more efficient to adjust your time to intersect by changing your Ap or Pe; leaving radial burns for minor corrections.

You might be able to derive it from Figure 4.12 on the Orbit Maneuvers section of this website: http://www.braeunig.us/space/index.htm

[king of nowhere]

if your orbit has a time of one year, then a radial correction to make sure you match time with vall's passage is going to cost a few m/s at most. And you are performing it as part of another bigger manuever, so it's going to be completely negligible.

incidentally, i must point out that using a gravity assist from tylo or laythe is a much more efficient way to get captured in jool's orbit

[Nicias]

The burn that includes the syncing is just raising the PE. It is actually only abut 200 m/s (And that is with a 10x rescale). 

I'll keep mathing away at the problem. thanks @FleshJebfor the link!

@king of nowhereI know the gravity assist method is better, but I haven't sorted out the math on it. Part of the fun for me is doing the math.

 

 

[king of nowhere]

4 minutes ago, Nicias said:

The burn that includes the syncing is just raising the PE. It is actually only abut 200 m/s (And that is with a 10x rescale). 

I'll keep mathing away at the problem. thanks @FleshJebfor the link!

@king of nowhereI know the gravity assist method is better, but I haven't sorted out the math on it. Part of the fun for me is doing the math.

Ok. the thing is, the radial burn is only a few m/s. Most of your burn is prograde to raise PE, so you end up with a burn of 1 m/s, 10 at most, against a 200 m/s prograde burn. the total burn is calculated by pitagora's theorem as sqrtr(200^2+10^2), which is almost equal to 200. I'd be surprised if it was more than 201 m/s.

If you want a more detailed calculation for fun, then I won't deprive you of your fun and will let you do a calculation.

[Zhetaan]

10 hours ago, king of nowhere said:

I'd be surprised if it was more than 201 m/s.

200.25, in point of fact.

@Nicias:

Since you are a dedicated mathochist, at the least you'll need to get to eccentric anomaly so that you can figure your time-of-flight and ensure that you'll intersect Vall's orbit at a time that Vall is actually there.  Which means that you'll need true anomaly, and well, it becomes an avalanche at that point.  Do you use Kerbal Engineer?  You'll need a way to get the true anomaly, which you cannot do with celestial observation in KSP (the skybox is just painted on; there's no First Point of Aries, and if there were, it wouldn't stay in the same place).

Alternatively, if you're feeling extra insane, you can simply define a coordinate system and solve for it there.  So long as you have the relative positions of your vessel, Vall, and their orbits correct, then you can solve for the burn in any convenient system without needing to use mod tools.

[magnemoe]

Is it better to use Jool low orbit or an Tylo flyby to brake into Jool orbit? I tend to use Tylo but velocity at low Jool orbit has to be higher, yes your Pe will be low but you can use an Tylo flyby to raise Pe up a lot. This assumes target is Pol or Bop, if its Laythe i assume low Jool burn is best. 

[Nicias]

On 3/3/2022 at 8:49 AM, magnemoe said:

Is it better to use Jool low orbit or an Tylo flyby to brake into Jool orbit? I tend to use Tylo but velocity at low Jool orbit has to be higher, yes your Pe will be low but you can use an Tylo flyby to raise Pe up a lot. This assumes target is Pol or Bop, if its Laythe i assume low Jool burn is best. 

Aside from the issue in this question, the procedure of burning at low Jool to capture, (with Ap about 1,6000,000,000m), burn at Ap to raise Pe to Laythe, and then burn at Laythe costs: 184 then 40 then 949m/s. That gets you into a circular orbit around Laythe, but it might in inclined.

For Pol the same procedure costs 184, 152, and 281 m/s.

I have a spreadsheet. The only caveat is that I am using a 10x rescale, which multiplies all my deltaV by Sqrt(10). I have divided my numbers by that factor here, but the 10x rescale also make Oberth more effective since the atmospheres don't scale by 10x, so you can get even closer.

I don't have calculations on doing a flyby to capture, but my three-step procedure saves 100 m/s when going to Tylo, compared to directly hitting Tylo at your incoming Pe and burning once to get to low Tylo orbit, if that helps.

@Zhetaan

Yes, My plan is to fight that avalanche. At least to work out worst-case numbers. On the actual mission, I just mess with radial/prograde to get the intercept.