Mun orbit calculation?

[Zambaku]

Hello everyone, I'm new to this wonderful game, and I've made about 20 trips to space and brought the astronaut back alive about 8 times, and I've just managed to get my ship in orbit for the first time, that was majorly difficult, but I managed. I have a mun lander mounted on my rocket and I'm now trying to figure out how to get to Mun. I have problems figuring it out. I can make the orbit of my chip change so I go out to the mun's orbital range, but how do I figure out if the mun will be at the place I'm going?

Here's my current orbit, I'm so proud. "Salutes the astronaut"

[Red Iron Crown]

Welcome aboard!

Click the Mun and select "Set Target", then when you get the orbit out there it will show markers for your closest approach or, when you get one, the path for the encounter with it.

[Superfluous J]

Do this all with maneuver nodes. Get your orbit around Kerbin circular and (at least mostly) equatorial. Create a maneuver node to burn prograde out to Mun's orbit. Then drag the maneuver node around until you get an encounter.

[Wemb]

Here's my current orbit, I'm so proud. "Salutes the astronaut"

http://i308.photobucket.com/albums/kk355/Zambaku/Namnloumls_zpsvsiebpv2.png

Nice - first of all, get into a circular orbit - not strictly necessary - but makes life easier. Do this by burning either exactly retro at the Pe or pro-grade at the Ap nodes (though not so much to re-enter Kerbin's orbit). Slow the burn down when it's getting close to circular - when it's just goes beyond being circularly you'll notice the Ap and Pe nodes flip around - when that happens cut the engines.

Now check your inclination - set the Mun as your target (right click on it) and look at the AN and DE nodes - or just eyeball it by rotating the map - is your orbit in the same plane as the mun's? If not, but normal or antinormal (up or down) at the AN or DN nodes - where your orbit crosses the mun's plane. Use the manoeuvre node to plan it. Note you may need to re-circularise your orbit if you have to make a big change.

Once you'e circular and coplanar orbit - make a manoeuvre node anywhere, and drag the prograde vector out till your Ap node meets the moon's orbit - that's the point when your ship will reach the moon's orbit. Now all you have to do is work out when to make that burn so you get there the same time as the mun does. Drag the maneaouver node arround the orbit till you get it to hit the mun - you'll see it when it does. That's when you should go.

Once you arrive there, though, you'll need to do a another burn which will have the effect of a) circularising your orbit arround kerbin and causing you to orbit the Mun as well.

This is called a Hohmann transfer. Good luck!

Wemb

[Zambaku]

Thank you for all your help, thanks to you I finaly landed on Mun. Boy was it a hard landing! I came in to fast and my astronauts barely survived...All that remains of my glorious rocket is the pod. Not even the engine nor the landing gear survived. Now the question is, how do I get them off? Or should I do a base, hm....Decisions, decisions

[Sharpy]

You need to send a rescue mission! Fun!

Note with experience you'll forfeit all the circularizing and plane matching and you'll be doing your encounters in a single node. But step-by-step it's simply easier, even if it costs a little more delta-V.

Also: "Focus view" on the Mun, and adjust your node precisely to get your Mun periapsis as low as possible (but no lower than 10km, that's how far the highest mountains reach.) Of course you won't get such a nice trajectory after the (imprecise) burn, but then about 1/4 the way between Kerbin and Mun create another node (after performing the burn) to adjust your mun periapsis right this time. It will be a token burn, something like 10m/s or less, but burning retrograde at a low periapsis of Mun saves a lot of delta-V versus trying to get an orbit from a distant flyby. Don't make the corrective burn to match the appointed delta-V, just aim at the node target, open the throttle minimally (don't worry about the time, during the transfer fifteen minutes this or that way is insignificant) and (still with Mun in focus) observe how your actual orbit changes. Cut off when it's where you wanted it.

(remember backspace returns focus to your vehicle afterwards)

[Kryxal]

In an equatorial orbit, you're safe to 7k (and a bit below).

[Snark]

Congratulations on your first Mun landing!

Some tips for landing there (to come in handy for your rescue mission):

Step 1: Munar approach. Sharpy's advice covers this this pretty well. Fine-tuning your orbit for low munar periapsis doesn't require much dV from your rocket if you do it early when you're still a long distance from the Mun. (Reason for wanting the low periapsis: to save fuel, it's an efficient use of dV for the next step.)

Step 2: Orbit Mun. As you approach, set a maneuver node right at periapsis that burns retrograde until you are in a very low circular orbit. Do this burn when you get to it.

(I'm assuming here that your kerbonaut is pretty much on the equator, and you're approaching in the equatorial plane, so that you don't have to do any inclination adjustments on approach-- if that's not the case, you'll have some additional work to do before descending.)

Step 3: F5. This next step is tricky and you may need a few tries.

Step 4: Begin descent. This will be trickier for the rescue than it was for your first mission, since you care about where you land (don't want your poor kerbonaut to have to walk dozens of kilometers or more...) Set your stranded kerbonaut's vessel as your target. Wait until you're maybe 30 longitude degrees west of target, then place a maneuver node around 10 degrees west or so from the target's location. This will be a retrograde burn that puts you on a descending trajectory to impact the Mun near the target. Make it so that the projected impact point is a smidgeon east of your target (i.e. so that you're projected to overshoot slightly, like a km or two).

Step 5: Pre-landing. This is the most critical and tricky part, since it eats up the most dV, and if it's not done "just so", has the most potential for Bad Things (waste lots of fuel, land too far from target, crash). The ideal way to land is called a "suicide burn", and involves waiting until the last possible moment and then starting a hard burn that brings you to a stop right at the surface. That's a hard thing to judge, since if you start your burn too early you waste fuel, and if you wait too long you go splat. Here's a handy way to set it up: Place a maneuver node right precisely at the surface of the Mun, at your projected impact point. Drag the retrograde handle and just hold it there until the projected orbit shrinks to nothing and the prograde/retrograde markers on the node start flipping back and forth. Look at the "estimated burn time" indicator on your nav ball. You'll start your burn when it's a bit less than that time remaining until the node-- for example, if the indicator says that the estimated burn is 20 seconds, you'd wait until you're, say, 16 seconds or so before the manuever to start the burn. When you're burning, keep your craft pointed surface retrograde, and burn until your surface velocity has reduced to something manageable.

Step 6: Landing. At this point, if the tricky and finicky previous step was done just right, you'll be moving pretty slowly and mostly vertically, not very far above the surface. Now just land as you would normally do. Hopefully you've got plenty of fuel left for the return trip.

Happy landings!

[Wemb]

Another tip, if you're not flying with some aids, it can be hard to judge how far the ground is - keep an eyeout for your shadow as you get close to landing. What can also help with this is adding some lights, just like they did in this famous space-movie (at 1.43)

Wemb

Edited July 14, 2015 by Wemb

[soulsource]

For landing, you can also switch to IVA view. There's a radar altimeter in all command capsules. This will give you the current altitude above ground, not above the (arbitrary) zero level of a body.

Now to your original question: The calculation of the phase angle.

Let's assume our ship is in a circular low Kerbin orbit, with no significant inclination with respect to the Mün. Wemb has already described how to adjust inclination in comment #4.

The question we'd like to answer is: "What is the angle traveled by the Mün during the time a Hohmann transfer takes from low Kerbin orbit to the orbit of the Mün?"

I noticed that sometimes my browser doesn't display the formulas in this post correctly. If you see an obviously misplaced or duplicated formula, please reload, or right click and "view image".

Let's first get the time the transfer takes. For this, we'll use Kepler's third law, which can be formulated as: "All orbits with the same semi-major axis have the same orbital period." This allows us to calculate the orbital period of the Hohmann transfer orbit by using a circular orbit which has a radius (we'll call this r) equal to the semi-major axis of the Hohmann transfer. The semi-major axis is simply given by the arithmetic average of the periapsis and apoapsis. For a circular orbit, we know that the angular velocity (omega) is constant, and that the centripetal force needed to stabilize the orbit is given by . As in our case the orbit is stabilized by gravity, this has to be equal to (where GM is the standard gravitational parameter of the parent body - here of Kerbin). This gives us an angular frequency of:

The angular velocity is related to the orbital period by:

Keep in mind, that a Hohmann transfer just takes half of this time, as we only fly from periapsis to apoapsis, and not back.

Now, finding out the angle the Mün is travelling during this time, all we need is to multiply the Mün's angular velocity (which we get by the same formula as above, just this time setting r equal to the Mün's semi-major axis) by T/2. Done.

But now, let's input some numbers:

The Mün has a circular orbit with a radius of 12000000 m, the standard gravitational parameter of Kerbin is 3.5316e12 m^3/s^2. Let's assume we depart from a circular orbit, 100 km above the sea level of Kerbin (which is 600 km from the center of Kerbin).

This means, that the semi-major axis of our Hohmann transfer is given by:

The angular velocity of our equivalent circular orbit would therefore be:

Now, the time our transfer takes is:

The angular velocity of the Mün is given by:

The angle we want to know is now given by the product:

This result tells us, that the ideal moment for a burn would be when the Mün is about 110 degrees ahead of our ship. Nevertheless, this is for a transfer to the center of the Mün, something we probably want to avoid, so I'd either add or subtract a little bit to the apoapsis of the transfer. Or, just play with the maneuver node a little bit, until you get your desired orbit.

Edit 1: The problem with the formulas should now be fixed. I switched from sciweavers to codecogs.

Edit 2: It just hit me: The standard gravitational parameter cancels out. One doesn't need it at all. The phase angle is simply given by:

Edited July 14, 2015 by soulsource
I'm stupid...

[Zambaku]

Many, many thanks for all your suggestions. I managed to get a second crew to the moon, it's going better and better. But I still could not manage landing without a horrible crash so they are now stuck to. My problem is that my landing module is way to long. I did it like that so I could have enough fuel for the landing and then leaving. I'm going for a different approach this time, I'm going to leave modules and do a base.

I came up with this design for the command center as the first part of the base. However I am uncertain about the engines. What do you recommend about dealing with height, weight and engines for these things?

[Wemb]

What do you recommend about dealing with height, weight and engines for these things?

Kerbal Engineer Redux or MechJeb so you can get some numbers in the VAB. You can probably work out what sort of engines are most suitable based on the total weight of your base and looking at tables of the Mun's gravity and doing the maths -

http://wiki.kerbalspaceprogram.com/wiki/Cheat_sheet

For some of the basics - but KER or MJ will give you useful, really useful figure in the VAB about how much dV different engines will produce on different landers/rockets.

Wemb

[soulsource]

You can try the landing legs in the VAB - they can be deployed using the right click menu. By this you can check if they reach down below the engines.

About the lander being to long: Tanks can be surface-attached, so you can build your lander more wide than high. Also, the gravity of the Mün is rather low (acceleration of 1.63 m/s^2). Just multiply this number by the mass of your lander to get the gravitational force and compare it to the sum of the vacuum thrust of all engines of the lander. I'd aim for at least a thrust/weight ratio (TWR) of at least 1.2, but as long as you don't add a significant amount of mass by switching to bigger engines, a higher TWR never hurts (or in other words: the higher the TWR, the more fuel efficient your burns against gravity become).

While I'm a huge fan of doing the math manually, I can also recommend the VOID mod. It offers a nice table in the VAB, listing details for the various stages, including TWR information for the celestial one selects.

My personal landing strategy, which is definitely not the most fuel efficient, is to first go to a low orbit (for the Mün about 10 km), kill all horizontal velocity (switch the navball to "surface" and burn towards the horizon below the retrograde marker, until retrograde shows directly upwards), and then let the craft fall more or less freely (although I tend to decelerate if it goes faster than 100 m/s - just because I tend to be too afraid...), and to make sure that it doesn't move much faster than 60 m/s when the IVA radar altimeter shows less than 3 km. Below 1 km I tend to decelerate even further - around 10 m/s. Of course I always try to keep the retrograde marker pointing directly upwards. Below 300 m radar altitude I usually go below 8 m/s velocity, and meanwhile I even try to get below 2 m/s when landing.

[Wemb]

You can try the landing legs in the VAB - they can be deployed using the right click menu. By this you can check if they reach down below the engines.

Also, looking at your picture, and in case you hadn't tried it - play with the rotate and translate buttons in the VAB - those big-ass landing legs your using go down a long way - you can add more stability by angling them outward and so getting both a wider base and lower CoM when you touchdown - that'll help - but like SourSource says - make sure you don't destroy the engine by bouncing it on the ground when you land. Apollo 15 did that - but the LM didn't have to use the landing engine to ascend.

Wemb