gilly to moho saving fuel (orbital mechanics mastery)

[king of nowhere]

i have this ship (actually a rover with rockets, but we can consider it a ship for this purpose) with a fuel capacity of 3500 m/s. it has a convert-o-tron, so it can refuel wherever it can land. i wanted to send it to moho on its own power, as a challenge. gilly is the closest i can refuel, so i use that as my start. according to the launch window calculator it never takes less than 5500 m/s, landing included. I managed to bring it down to around 4500 with some clever manuevering, but nowhere near enough for my purpose.

I was about to post this in the questions, but then i thought, i already spent one hour trying to optimize trajectories and still haven't explored all the possibilities; this is challenge material. may as well turn it into one, and see if the best score is enough for my rover's fuel capacity.

 

So, the rules are simple. you start on the surface of gilly. you must reach the surface of moho with as little deltaV as possible. I would say no time limit, but i don't want some crazy trajectory using nothing but gravity assists and taking several centuries, so for every day of travel past the 1000th, you gain one point.

Final score is deltaV used + 1 for every traveling day over the 1000th. lowest score is better, of course.

 

 

may the winner find a route cheaper than 3500

[sevenperforce]

No possible trajectory can do Gilly to Moho in less than 3,710 m/s.

[king of nowhere]

3 minutes ago, sevenperforce said:

No possible trajectory can do Gilly to Moho in less than 3,710 m/s.

interesting statement. how do you know? is there a way of knowing? does that include gravity assists?

[sevenperforce]

8 hours ago, king of nowhere said:

interesting statement. how do you know? is there a way of knowing? does that include gravity assists?

To get off Gilly and leave its sphere of influence, entering Eve’s orbit, will cost you a minimum of 440 m/s.

It will cost more to burn out of Eve’s SOI, although not very much. You can then use a series of gravity assists off Eve to lower your Kerbol periapsis until it crosses Moho and get the correct inclination.

However, Moho has no atmosphere. Accordingly, you will have to brake into low Moho orbit propulsively. Even if you could somehow use gravity assists to enter a Kerbol orbit exactly matching Moho’s (which is not possible) it would still cost you a minimum of 2400 m/s to get from even the lowest-energy hyperbolic orbit into a low circular orbit. It will then cost another 870 m/s to deorbit and land.

So those are the minimum energy requirements. And that is not even counting the reserves you need to get out of Eve‘s sphere of influence, or to complete your gravity assists, or to brake your excess hyperbolic velocity at Moho.

[arctangent]

@sevenperforce are you getting those numbers from the dV map? that 2400 isn't from the lowest energy hyperbolic orbit, it's from a Hohmann transfer from Kerbin.

[sevenperforce]

10 minutes ago, arctangent said:

@sevenperforce are you getting those numbers from the dV map? that 2400 isn't from the lowest energy hyperbolic orbit, it's from a Hohmann transfer from Kerbin.

Ah, dammit, you're right. I just took a quick look and you only need 315 m/s to leave Moho's SOI.

However, you still need 2287 m/s to reach an Eve-crossing orbit, so even if you can use all manner of gravity assists to correct inclination, your minimum braking dV from hyperbolic Moho entry to landing is going to be 3157 m/s. No possible gravity assists can get you to have a Kerbol apoapsis lower than the orbital altitude of Eve. 

[king of nowhere]

45 minutes ago, sevenperforce said:

However, you still need 2287 m/s to reach an Eve-crossing orbit, so even if you can use all manner of gravity assists to correct inclination, your minimum braking dV from hyperbolic Moho entry to landing is going to be 3157 m/s. No possible gravity assists can get you to have a Kerbol apoapsis lower than the orbital altitude of Eve. 

can't you have a moho intercept that you use as gravity assist to lower your apoapsis? i think the messenger probe did something similar.

[sevenperforce]

21 minutes ago, king of nowhere said:

can't you have a moho intercept that you use as gravity assist to lower your apoapsis? i think the messenger probe did something similar.

You can use a gravity assist off a planet or moon to correct your inclination relative to that planet or moon, but you cannot use a gravity assist off a planet or moon to circularize to a closer orbit. You have to use a different body.

If you have two bodies close together, you’re in luck because you can build up assists between them to go to a third destination. For example you can go Kerbin - Eve - Kerbin - Eve - Kerbin to get a very cheap trajectory to literally anywhere. But unless there are multiple bodies so you can use gravity assists at your destination (e.g. Jool) then you still have to either aerobrake or brake propulsively.

Gravity assists bend your trajectory. For example, it’s cheaper to go from Eve to Kerbin than from Eve to Moho. So you could burn out of Eve’s SOI from Gilly, wait a year, and get a very close hyperbolic pass to Eve for maximum Oberth effect so a very small burn will kick you up to Kerbin. Use a reverse gravity assist off Kerbin to lower your Kerbol periapsis to cross below Moho’s orbit, and then use a gravity assist off Eve to raise your periapsis to match Moho and lower your apoapsis to match Eve. You can then use Moho to correct your inclination over a few orbits before you burn for capture. But that capture burn will never be less than 2300 m/s.

[king of nowhere]

50 minutes ago, sevenperforce said:

You can use a gravity assist off a planet or moon to correct your inclination relative to that planet or moon, but you cannot use a gravity assist off a planet or moon to circularize to a closer orbit.

 

Actually, you can.

apoapsis was 7.023 Gm, at day 169. gravity assist with moho was at day 261, you can see i set a manuever there only to keep visualizing the trajectory, but it has 0 m/s. after that encounter, the new apoapsis is 6.909 Gm.

Not particularly efficient, it is tricky to set up a gravity assist in those conditions. Somebody will be more skilled than i am. but it is indeed possible.

doing a gravity assist work a bit like bouncing a ball on a wall. you change direction, but since the wall/planet is moving, you also get some of that speed. if you bounce the ball when the wall is moving away from you, the ball will bounce back slower. that's what happens when you pass behind a planet.

circularizing orbit with gravity assists is indeed possible.

 

problems with the manuever are many, though.

- you must get a very precise encounter. to do that, you have to manuever. manuevering this close to the sun is very expensive, to the point that you risk losing more in course correction manuevers than you gain in the assist itself.

- the faster you speed by the planet, the less you can get out of your gravity assist. with such high intercept speed, your assist is not very efficient. as shown by apoapsis being lowered only by 100000 km (roughtly 50 m/s gained)

- you must pass behind the planet, but when you focus the visual on the planet it is in a different position, so it is very difficult to figure out exactly where is "behind". you may end up setting the encounter poorly and gaining speed in the wrong directions

[sturmhauke]

Yeah, I managed to get a free capture around Laythe once after a slingshot around Tylo, and several braking maneuvers before that. It was mostly luck that everything lined up exactly right.

[Muetdhiver]

On 8/20/2020 at 4:37 PM, king of nowhere said:

can't you have a moho intercept that you use as gravity assist to lower your apoapsis? i think the messenger probe did something similar.

Yes you can. It is indeed possible to do a moho pump down via multiple flyby's. Keep in mind that in order to chain them, you need to aim for partial resonant orbits. I usually stop when I get down to 11:10 as it becomes very long for a low gain.

3-4 flyby's pump down is doable and worth it, so long as you stay very precise.

Moho is my favorite solar pinball target. You can lower the DV needs quite a lot.

Here is a ~3.85 km/s flight plan for the Kerbin-Eve-Eve-Moho route :

Spoiler

Ejection angle:          142.1

First Leg:           Kerbin to Eve
Departure:           626.5 KUT
Duration:            200.4 days
VINF:                1172.3 m/s
VINF (x,y,z):        [ -219.8 -1127.3   234.8] m/s
V_p  (x,y,z):        [1732.8 9121.9   -0. ] m/s
R_p  (x,y,z):        [ 1.33609129e+10 -2.53804279e+09  0.00000000e+00] m
Ejection DV:         1139.8 m/s, from 100.0 km parking orbit
DSM after 5.009353741551316 days
DSM magnitude: 67.7538865403578m/s

leg no. 2: Eve to Eve
Duration: 65.48253347166666days
Fly-by epoch: 2000-Jul-25 17:07:03.762611 (206.7132379931881 mjd2000) 
Fly-by radius: 10.741838492344863 planetary radii
DSM after 7.032141856866231 days
DSM magnitude: 0.00011881148988023844m/s

leg no. 3: Eve to Moho
Duration: 22.725021000272108days
Fly-by epoch: 2000-Sep-29 04:41:54.654563 (272.1957714648547 mjd2000) 
Fly-by radius: 1.6647120065468768 planetary radii
DSM after 15.44081262100048 days
DSM magnitude: 1.7313492100751497e-05m/s

Arrival at Moho
Arrival epoch:       1179.7 KUT
Arrival Vinf:        2693.7 m/s
Injection DV:        2172.9 m/s, to 100.0 km parking orbit
Total mission time:  553.2 days
Total DV w.o. IJB :  1139.8 m/s
Total DV with IJB :  3833.5 m/s

With a bit of pump-down you might be able to fit it in the 3.5 km/s enveloppe.