Gravity well vs. refueling

[uncle_jew]

Hello,

assume I have a fully fueled probe in the low Kerbin orbit that I am planning to fly to Moho.

I have two ways of ejecting from LKO towards Moho:

1) Direct ejection burn from LKO

2) Go to my refueling base in a high Kerbin orbit (between Mun and Minmus), refuel there, then eject from that orbit to Moho.

What is a better option if I want to arrive at Moho with as much delta-v remaining as possible?

I understand an ejection burn from LKO has the advantage of the gravity well, which is lacking if I eject from a high orbit. So is the advantage from the gravity well effect bigger or smaller than the advantage of leaving fully fueled from a high Kerbin orbit, thus needing less energy to escape Kerbin?

Edited April 22, 2016 by uncle_jew

[Empiro]

There's the concept of a gate orbit that determines the optimum altitude for transfer (note that it doesn't consider the fuel required to get to that altitude, which in your case is true since you'll be refueling).

I believe in your case, you'll have the most fuel remaining if you refuel and then lower your PE to close to Kerbin, and then burn into a transfer to Moho. The timing might be a bit challenging, however.

[Starhawk]

According to this thread, which I believe essentially has the calculated gate orbits, the ideal ejection altitude from Kerbin to Moho is 700 km.

Happy landings!

[Superfluous J]

The best option - ignoring the PITA aspect and just looking at "arriving at Moho with as much fuel as possible" your best bet is to go up to Minmus, fuel up your ship so it's fully fueled, and then when Minmus is 180 degrees from what your LKO ejection burn WOULD HAVE BEEN, burn to escape Minmus BACKWARDS so you fall back down low to Kerbin. Then, at your Kerbin Periapsis, burn to Moho.

It's convoluted and prone to error, but if done correctly it's the most efficient.

And if you nail it you feel like a baws. Source: I nailed it. I felt like a baws.

Edited April 22, 2016 by 5thHorseman

[mhoram]

In addition to what @5thHorseman said, which covers the ideal departing method you can lower the amount of fuel needed by departing from Kerbin while Mohos Periapsis is exactly on the opposite side of the Sun:

Your Kerbin-Moho transfer orbit has a Periapsis that touches the orbit of Moho, and an Apoapsis that touches the orbit of Kerbin.
Since the Orbit of Moho has a strong eccentricity (Periapsis ~4.2e9m, Apoapsis ~6.3e9m), it matters quite a lot where you meet Moho.

The nearer you meet Moho at it's Periapsis, the less fuel you need.

When using this method you will probably not meet Moho the first time you reach Mohos Orbit, but you can decelerate at Mohos Orbit Periapsis, so that your transfer-orbit gets smaller and adjust it so that one orbit later you meet Moho.

 

To explain this effect, you need to consider the Kerbin-departure-burn and the Moho-circularization-burn.

The departure burn costs more the lower you push your transfer orbit Periapsis (reaching Moho at it's Periapsis ist more expensive that reaching Moho at it's Apoapsis)

The circularization burn costs more the farther you are away from the Sun, which is caused by the Oberth effect.

And the second effect seems to have a larger impact than the first effect. During my tests with simple transfer paths, the DV-difference was about 100 m/s between the two extremes (meeting Moho at it's Periapsis vs meeting Moho at it's Apoapsis).
However using the method mentioned by 5thHorseman the difference should be larger.

Edited April 22, 2016 by mhoram