Flight Planning?

[Elroy Jetson]

Are there any tutorials or texts describing how to plan and execute transfers beyond the simple flights I have accomplished so far?  

My entire collection of flights has been LKO, Mun orbit and return to Kerbin and kerbin to Mimnus and back.  I recently tried a flight from Mimnus to Mun but I think I had to orbit Kerbin several years to get an encounter with Mun.   How do I learn when to launch in order to get a reasonable encounter window?

 

i am playing on console so I don't have any mods to help with this.

[FleshJeb]

This has a good guide and an online calculator: http://ksp.olex.biz/

This is a slightly more sophisticated calculator: https://alexmoon.github.io/ksp/

If you don't already know, always do your transfer and capture burns as low around the planet as possible. It's counter-intuitive but Dr. Oberth explains it all: https://en.wikipedia.org/wiki/Oberth_effect

[Zhetaan]

15 hours ago, Elroy Jetson said:

I recently tried a flight from Mimnus to Mun but I think I had to orbit Kerbin several years to get an encounter with Mun.   How do I learn when to launch in order to get a reasonable encounter window?

Transfer windows occur once per what is called the synodic period.  The synodic period is a way of calculating conjunctions, which are helpful in astronomy to determine the best opportunities to observe other planets, but it also works for figuring the best time to travel to other planets.  When applied to moons, synodic period also means the time to complete a cycle of phases, but we want the first definition for this.

The synodic period is the reciprocal of the difference between the reciprocals of the orbital periods of the two planets in opposition.  If that makes no sense to you, it means this:

1 / T_syn = 1 / T_p1 - 1 / T_p2

Where:
T_syn = synodic period
T_p1 = orbital period of inner planet
T_p2 = orbital period of outer planet

For Minmus and the Mun in orbit of Kerbin, the synodic period is:

1 / T_syn = 1 / (138984 s) - 1 / (1077311 s)
1 / T_syn = 7.1950728 x 10^-6 - .9282371 x 10^-6
1 / T_syn = 6.2668357 x 10^-6
1 / T_syn = 159570.2 s
1 / T_syn = 7 days, 2 hours, 19 minutes, 30.2 seconds

There was no reason to wait years.  Sometimes, that is necessary:  an important thing to remember about the synodic period is that the closer together two planets are, the longer the synodic period.  Good transfer windows to Duna and Eve are far more rare than good transfers to Jool.  This is because the closer two planets are, the closer their orbital velocities and thus the less difference there is.  That difference in velocity is also the rate at which the inner planet will catch up to the outer, so as that difference goes to zero, the time to catch up stretches to infinity.  You see this when you put up a communication constellation in synchronous orbit; if the satellites are all in the same orbit, then they will never rendezvous.

On the other hand, the farther away a planet is, the more frequent the transfer windows.  Eventually, the window occurs essentially once per inner-planet year as the inner planet goes round the sun and the outer planet moves so imperceptibly as to remain essentially still.  Theoretically, the window can be more frequent than that if one of the planets orbits retrograde, but that's not an issue in KSP.

Next is the alignment.  It's not enough to know that there's an opportunity for a good window; you also need to know when it is.  For this, you need a few pieces of information.  You need to know the amount of time it will take to transfer from one body to the other, you need to know how far your destination will move in that time, and from that, you need to calculate what the angle between your origin and destination needs to be at the time of departure to ensure a good transfer.

Assuming a Hohmann transfer, your transfer orbit will have a periapsis at the inner body's orbit and an apoapsis at the outer body's orbit.  Going from Minmus to the Mun, this gives 47,000,000 metres and 12,000,000 metres, respectively.  For planets in non-circular orbits, it gets a bit more complex, but the error is small unless the orbit is very eccentric.  To figure the time to traverse this orbit, you use Kepler's Third Law:

T = 2π * √ [(r₁ + r₂)³ / 8μ]

Where:
T = transfer orbit period (in seconds)
r₁ = origin orbit radius
r₂ = destination orbit radius
μ = standard gravitational parameter of the primary (for Kerbin, 3.5316 x 10¹² m³/s²)

Since we want only one half of the period (we are only travelling half of the orbit), we divide this result by two.  You may be familiar with the T = 2π * √ (a³ / μ) version of Kepler's law; a is the semi-major axis of the orbit whose period you want.  The semi-major axis can also be calculated as the average of the periapsis and apoapsis (that should make sense; the average of the minimum and maximum major-axis distances from the centre is the average major-axis distance to the centre), and since a Hohmann transfer uses the origin and destination orbits as the apsides, averaging them gives the semi-major axis of the transfer orbit.  [(r₁ + r₂) / 2]³ = (r₁ + r₂)³ / 2³ = (r₁ + r₂)³ / 8, which is where we get the 8 in the formula.

Thus, the Hohmann transfer time from Minmus to the Mun is:

T = π * √ [(47000000 + 12000000)³ / 8 * (3.5316 x 10¹²]
T = π * √ (59000000³ / 2.82528 x 10¹³)
T = π * √ (2.05379 x 10²³ / 2.8258 x 10¹³)
T = π * √  7.267995 x 10⁹
T = π * 8.525254 x 10⁴
T = 267828.7 s
T = 12 days, 2 hours, 23 minutes, 48.7 seconds

The destination angular velocity, in radians per second, is:

ω = √ (μ / r₂³)

Which for the Mun is:

ω = √ [(3.5316 x 10¹²) / (12 x 10⁶)³]
ω = √ [(3.5316 x 10¹²) / 1.728 x 10²¹]
ω = √ 2.04375 x 10^-9
ω = 4.520785 x 10^-5 s^-1

That is obviously very small, but how far do you expect a moon to move in a second?

Anyway, the angular distance, α, covered in the transfer time is equal to T * ω.  However, what we want is how far away from the destination point (exactly π radians from our origin point) the destination will be when we start, so what we need to do is subtract the angular distance from the destination point:

α = π - T * ω
α = π - (267828.7 * 4.520785 x 10^-5)
α = π - 12.107960
α = -8.9664 radians

To get a more intuitive angle, convert from radians to degrees:

-8.9664 radians * (180 degrees / π radians) = -513.7 degrees

To turn that into more useful angles:

-513.7 + 360 = -153.7 degrees
-153.7 + 360 = 206.3 degrees

This means that, as you begin from Minmus orbit, the Mun needs to be a bit (a tiny bit over twenty-five degrees) past the exact opposite side of Kerbin.  During the transfer, the Mun will complete all of one orbit and most of a second before you encounter it.

Also note that this calculation is not exactly correct; Minmus is inclined, and the calculation is two-dimensional.  Because there is three-dimensional space to traverse in this transfer, that will add to travel time and thus move the target point.  However, you don't actually need to do any of these calculations (do you like how I waited until the end to tell you that?) because KSP provides helpful intercept markers provided that you set your destination as the target.  I do not know whether they will work when you are inside a different sphere of influence, but you can use the alexmoon planner or any calculator of your choice to figure the phase angle ahead of time, write it down, and use that.  The phase angles do change a bit from orbit to orbit (inclination and eccentricity strike again) but they do not change much.

[Snark]

On 3/21/2019 at 4:06 PM, Elroy Jetson said:

How do I learn when to launch in order to get a reasonable encounter window?

One way is to use a launch window planner like http://ksp.olex.biz (as was linked above)-- you just tell it that your origin is Minmus, your target is Mun, and have it calculate.  It'll show you what's what.

Or you can do math, as @Zhetaan's excellent post above describes. 

Another approach (less refined, but doable in-game) is to let the map view help you.  Let's say you want to go from Kerbin to Duna.  So, in LKO, plop down a maneuver node on Kerbin's night side and crank it up in the direction until it's escaping from Kerbin in a direction that's parallel to Kerbin's orbital path around the sun.  Keep dragging until your solar Ap rises to the point that it just touches Duna's orbit.  You'll see something like this:

I've drawn a couple of red arrows to aid illustration.  See where it says "Closest Approach" up top... but "Target Position" is way off there to the left side.  That means that this isn't a good transfer window-- because what you want is for Duna to be right there at the Ap marker at the time you get up there.

So... look at the angle between the two red arrows.  In this particular example, it looks like Duna will be about 85 degrees ahead of your Ap, when you reach Ap... if you were to launch right now.  So all you need to do is to let Kerbin "catch up" about another 85 degrees, relative to Duna, and then try this same exercise again.

In other words:

1. Plan out a launch to Duna as if it were about to happen now.
2. Note how far "off" it is, e.g. "I have an error of N degrees" (where N is around 85 in the sample picture here)
3. Note the relative positions of Kerbin and Duna right now, and then subtract N.  That's the angle relative to each other than you want them to be.
4. Timewarp until they get to the positions you want.

I've used Kerbin and Duna in this example, but it'll work with other combinations, too.

Personally, though, I usually just use http://ksp.olex.biz and be done with it. 

[Wildcat111]

For me, I used http://ksp.olex.biz/ when trying to figure out transfer windows, but once you send enough things there, it starts to come to you from memory.