Direct insertion to Tylo orbit (math check)

[Nicias]

Hi, I recently had the idea to try and capture directly into low Tylo orbit from a Kerbin-Jool transfer. The thought was to add Tylo's Oberth to cut down on required dV. 

What I did was make a node to set my perijool to be the same as Tylo's orbit while far away (thanks MechJeb)

Then once I was in Jool's SOI, I made a node almost right away and put in some retrograde to get an intercept with Tylo. Fiddling with this node (adding normal and radial components) I was even able to get the correct peritylo. This cost about 50m/s. Then I coasted down into Tylo's SOI, and burned at peritylo to capture. It saved a TON of dV. I didn't get an accurate estimate because MechJeb's dv calculator had a bug in it for a couple of days. But I had a whole spare stage!

So I decided to run the numbers, to see what the savings really was. Here are my calculations. I used vis-viva for everything.

Jool orbital velocity:  4129 m/s. 

Transfer orbit 2372 m/s. 

Excess velocity at Jool: 1756s m/s.

That velocity at the edge of Jool's SOI (2.46 E 9) with Jools mu (2.83 E 14) gives a SMA of -9.90 E 7 (hyperbolic)

That SMA and Jools mu gives a velocity of 3332 m/s at Tylo's orbit (6.85 E 7). Tylo's orbital velocity is 2031m/s, so excess velocity relative to Tylo is 1301 m/s.

 

1301 m/s at the edge of Tylo's SOI (1.09 E 7) with Tylo's mu (2.83 E 12) gives a SMA of -2.41 E 06 (hyperbolic)

 That SMA and Tylo's mu gives a velocity of 3141 m/s at 50km (target orbit radius 650,000 ). Circular orbit at that radius is 2049 m/s so the actual burn needs to be 1056 m/s. 

The delta-v map gives 160+400+1100=1660.  So the direct injection method saves 36%

That seems like way to good to be true. Is my math off?

[Blaarkies]

The cheapest way to capture into Tylo orbit is when your vessel is in an orbit very similar to that of Tylo around Jool. This insures that when you reach Tylo SOI, you will be in an almost elliptical orbit.

To get in an orbit similar to Tylo, you could use an unpowered slingshot around Tylo in order to slow down from you initial interplanetary Kerbin>Jool transfer. If you keep an eye on the orbital plane via the inclination relative to Tylo orbit, the slingshots should be really easy. Tylo is pretty powerful for getting into Jool orbit for free and much safer that the Jool aerocapture method.

So the point is, if you finish all your maneuver nodes far outside Jool's SOI and put yourself into such an "almost" Tylo orbit, you will only need the amount of dv it takes to go from Tylo escape velocity -> Tylo orbital velocity, you should be able to reach Tylo high elliptical orbit with very little dv, much less than the dv maps suggest

[ManEatingApe]

On 3/22/2019 at 6:56 PM, Nicias said:

That seems like way to good to be true. Is my math off? 

Nope, it's spot on, taking advantage of Oberth effect at Tylo is a great way to capture on the cheap at Jool.

If you leave the ship in a high elliptical Tylo orbit, then it's also possible to eject to Laythe, Vall, Pol & Bop intercepts for max ~20 m/s, so it can function as a handy staging area.

Edited March 29, 2019 by ManEatingApe

[Superfluous J]

3 hours ago, ManEatingApe said:

If you leave the ship in a high elliptical Tylo orbit, then it's also possible to eject to Laythe, Vall, Pol & Bop intercepts for max ~20 m/s, so it can function as a handy staging area.

Yup it's the only way I'll Jool-5

[Nicias]

I was thinking if doing a Jool 5 with separate Landers going directly to each moon in a flotilla and and crew shuttle going moon to moon. I used to do insertion into a gateway orbit for this kind of mission but had a screwup with my relay sats carrier and so tried the direct insertion and saved a bunch of DV.  

This is at 10x rescale. 

[Starhawk]

7 hours ago, 5thHorseman said:

Yup it's the only way I'll Jool-5

Interesting.

My preferred 'staging area' for a Jool-5 mission is in Jool orbit halfway between Vall and Tylo.

Happy landings!