# Earth Moon Pork chop plot

Does pork-chop plots exist for Earth-Moon System? I could only find pork-chop plots for Earth-planet systems.Could someone please shed some light on this topic?

• Hi, and welcome. Please take the time to explain your terms. Never assume your audience is familiar with them (in this case, "pork-chop"). In this particular case, you might also explain what you intend to learn, or implement, if you find this information. – Carl Witthoft Mar 12 '20 at 13:07
• I don't know what a pork-chop plot is. – Bob516 Mar 12 '20 at 14:24
• Nobody demanded the author of this question to define the term, nor does it look like anybody threatened to close that question. – uhoh Mar 12 '20 at 15:47
• It's probably HNQ because "what the bleep is a pork chop plot; I'm gonna click to find out" – Joshua Mar 12 '20 at 21:10
• So instead of whining and close voting, I made an edit with the appropriate link to wikipedia that explains what a porkchop plot is. If a question can be rescued with a quick edit, please don't jump on the close bandwagon. – Ingolifs Mar 12 '20 at 22:21

So let's break down the answer into bite sized chunks...

## How do you transfer a spacecraft from one solar system body to another?

There are two main things you need to do.

1. Set up an orbit that intercepts the orbit of your target planet/moon.
2. Time it so that your spacecraft intercepts the target orbit at the same time as the planet/moon you're trying to reach.

The second point is the key to all this. The planets orbit the sun at different rates, so you have to wait for a launch window so that the target planet will be there when you arrive.

## Why are there launch windows? Why can't you just launch whenever?

If you had a torchship, you could just launch whenever. In actual modern day spaceflight, propulsion systems are not near efficient enough to get away with it. The tyranny of the rocket equation means that the spaceship's mass needs to be mostly fuel, and a small increase in the delta-v requirements means a much larger increase in the fuel you have to carry.

The most fuel efficient transfer maneuver is called the Hohmann transfer, because the apoapsis only just touches the target orbit, which means the amount of fuel you have to expend to reach this transfer orbit is minimised, and the amount of fuel needed to match velocities with the target planet is also minimised.

But what if you miss this launch window? Or you're impatient and want to launch now? You can still make it, but you have to expend more fuel to intercept with the target planet, and more fuel still to match velocities so you can go into orbit or land. When I play Kerbal Space Program, I often 'eyeball' these launch windows, and often find that I have to expend extra fuel to make the rendezvous work and compensate for my sloppy play.

## Ok, so what are pork chop plots though?

There is often a bit of leeway built into a mission when it comes to timing, etc. Launches can be delayed or scrubbed for any number of reasons. So the mission has to be designed with some allowance for things going wrong. When planning for these eventualities, they use Pork Chop plots.

The x and y axis are launch date and arrival date, respectively. The isobars represent the relative difficulty of the launch window, with the easiest Hohmann transfer being at the centre. (Strictly speaking, the isobars represent the characteristic energy of the transfer orbit. For our purposes, the higher the characteristic energy, the more eccentric and extreme the transfer orbit is, and the more delta-v you need for the mission. I don't know why they use characteristic energy rather than delta-v, but this thread on physicsforums might help.)

If the orbits of Earth and Mars were perfectly circular and coplanar, these plots would just look like concentric circles. But because they orbit in slightly different planes and have slightly different eccentricities, the energy requirements to reach Mars in a given timeframe change over time. This is what gives the plot it's asymmetric 'porkchopiness'.

## On to the actual question. Why don't we see Earth-Moon porkchop plots?

(This part may be a bit conjecture-y. I don't know for sure, but I've arrived at an answer that makes sense to me. Please if you have a better idea, inform me).

If you think about it naively, there's no real difference between a transfer between Earth and Mars, and between Low-Earth-orbit and the Moon. You're just going from a lower orbit to a higher orbit.

But the real difference is the ability to try again. If you miss your Earth-Mars launch window, you have to wait a long time to try again. The closer the orbital periods of two bodies is, the rarer the launch windows. For earth-mars, this occurs once every 780 days. (this is called the Synodic period. Look here for other synodic periods.)

On the other hand, for the Earth-Moon transfer it only takes about 90 minutes to orbit the earth once at LEO, so if you were to miss your Launch Window, you can just try again in an hour and a half.

It's not that a porkchop plot can't be drawn, it certainly can (and with differences in LEO inclination and the Moon's inclination and eccentricity, it would have some degree of 'porkchopiness'). It's just there's not much reason to, as it doesn't really help the planning phase of the mission.

• Thanks for the explanation and for everyone for the comments – SSS Mar 13 '20 at 7:39
• @SSS No worries! The process can be a bit alarming here, like watching sausages being made from their base constituents, but we get there in the end. – Ingolifs Mar 13 '20 at 8:11
• @Ingolifs I've never seen sausage made, but if it's anything like Stack Exchange it sounds frightening! :-) – uhoh Mar 13 '20 at 9:57
• I, for one, :-) don't think those look like pork chops! – Carl Witthoft Mar 13 '20 at 12:20

Does pork-chop plots exist for Earth-Moon System?

No, because the concept doesn't make much sense. The Earth-Mars configuration and Mars' eccentricity makes the cost to send a vehicle from Earth to Mars vary by a huge amount. Pork chop plots are a useful way to visualize these huge variations. The cost of sending a vehicle to the Moon on the other hand varies so little with launch time that it isn't part of the picture. The key concerns with sending something to the Moon are the time of lunar day and the position relative to the Moon correct at lunar orbit insertion.

• You mention two key variables, why couldn't a porkchop plot be made using those two variables? – 2012rcampion Mar 12 '20 at 21:55
• @2012rcampion: Because the pork chop plot is about describing cost. If you wish to ascribe a cost function to the position of the Sun with respect to the Moon and so on, then sure, you could draw such a plot; I encourage you to do so. – Eric Lippert Mar 12 '20 at 22:23

I agree with Ingolifs' answer; you can create a porkchop plot for a transfer between any two orbits. For an Earth-Moon porkchop you could pick either a point on the Earth's surface or a particular low Earth orbit as your start. For example, here's a porkchop plot showing the delta-v required for transfer from Apollo 13's initial Earth orbit to the Moon (orbital elements from SpaceTrack catalog, orbit positions calculated using JPL Horizons)

(Notes: delta-v in km/s; the red mark shows the actual burn end time.)

As you can see, the "porkchop" shape is due to the particular relationship between the Earth and Mars, different transfers have different shapes.

I produced an Earth-Mars porkchop using the same code which you can compare with the one on Wikipedia.

• So, there are no porkchop plots for Moon, because they look like butterfly plots. – asdfex Apr 23 '20 at 16:37