GoSlash27

3a) Elliptical orbits We often have a need to make orbits that are elliptical instead of perfectly circular. Let's take a circular orbit and "squish" it a bit to see what happens... As you can see, our central body will lie at a focal point of the ellipse. This means that our orbit will have a high point and a low point. They are referred to as "Apoapsis" (high like apex) and "Periapsis" (low like a periscope... or Paris Hilton ). They are abbreviated as Ap and Pe, respectively. The orbit will behave like it's average radius as far as period and average velocity are concerned. This "average radius" is called Semi-major axis, or SMA. The first thing to notice about it is that the periapsis is just as far below the semi-major axis as the apoapsis is above it. This holds true for all elliptical orbits and gives us our first set of equations: SMA= (Ap+Pe)/2 Likewise... Ap= 2SMA-Pe and Pe= 2SMA-Ap Now as for the motion... That's a bit more complicated. As you can see, an object in an elliptical orbit moves much faster at Pe than it does at Ap. Because our object sweeps out the same area of the ellipse in the same period of time, our velocity at periapsis divided by average velocity will always equal average velocity divided by velocity at Apoapsis. Vpe/Vavg= Vavg/Vap This gives us some new handy rules: Vavg=sqrt(VapVpe) Vpe=Vavg2/Vap Vap=Vavg2/Vpe Another observation worth noting: Vpe*Pe=Vap*Ap, so Vpe=Vap*Ap/Pe Vap=Vpe*Pe/Ap Pe=Ap*Vap/Vpe Ap=Pe*Vpe/Vap 3b) The Vis-viva equation Putting all of this together and throwing some math at it yields a supremely valuable equation: If we have the u for our system, the SMA for our orbit, and our current radius, this will yield our velocity at the moment. So now to start putting all of this to use...

OhioBob, Thanks, I'll be sure to revise that on my next pass. Best, -Slashy

2) Orbital periods We can derive a simple formula for orbital periods based on radius. This is extremely handy when we start playing with it later. Since we have our radius, our circumference is 2πr. We have already defined our orbital velocity as sqrt(u/r) Our orbital period is the time it takes to complete an orbit, so period (in seconds) = circumference (meters) divided by orbital velocity (m/sec) p=C/Vorb. C= 2πr and Vorb= sqrt(u/r) , so p=2πr/[sqrt(u/r)] Throwing some algebra at it to tidy it up... p=2πr[sqrt(r/u)] p=2π[sqrt(r3/u)] Perhaps we want to know the reverse of this; we need an orbital radius with a specific period. This is just a matter of reorganizing the equation. p=2π[sqrt(r3/u)] p/2π=sqrt(r3/u) (p/2π)2=r3/u up2/4π2=r3 r= cuberoot(up2/4π2)

1a) Gravity Gravity is the force of attraction between two bodies due to their mass and proximity. You can think of it as a bowling ball on a trampoline; the closer a marble is to the bowling ball, the more attraction will be produced. "G" is the universal gravitational constant, and can be thought of as the "looseness" of the trampoline surface. This value is constant both in our universe and KSP itself; G=6.67408x10-11 M is the mass of our bowling ball (or moon/ planet/ sun) in kilograms. r is our distance from the center of the bowling ball in meters. a marble's attraction to the bowling ball is directly proportional to the mass of the bowling ball and inversely proportional to the square of the distance. Our marble's attraction to the bowling ball is therefore: a=GM/r2 Some examples: Jeb in his skivvies in the VAB. Kerbin's mass is 5.292E22. G is always 6.674E-11. Kerbin's sea level radius is 600 kilometers. a=GM/r2 His acceleration towards the planet's core is therefore (5.292E22)*(6.674E-11)/(600E3)2 = 9.811 m/sec2 Standing on the Mun, it's 9.76E20*G/(200E3)2=1.628 m/sec2 2 million meters away from Duna... you get the idea. Now... G and M are best buddies and we never see the one without the other in these problems. To simplify things, we therefore multiply them together and refer to them as "mu". u=GM In other discussions, you may see it referred to as mu or μ. In this tutorial, it will be represented as u. So to summarize, a=GM/r2 u=GM therefore.. a=u/r2 _________________________________________________________________________________________________ 1b) Uniform circular motion To understand a uniform circular orbit, we must first start with centrifugal acceleration. Swinging an object around in a circle will produce an acceleration felt by the body away from the center. This acceleration is directly proportional to the square of the rotational velocity and inversely proportional to the radius. ac=V2/r A circular orbit results when the acceleration of gravity (ag) is counterbalanced by the centrifugal acceleration of orbiting the planet (ac) ag=ac To find the velocity this happens at, we set them as equal, u/r2=V2/r and reorganize to isolate V. u*r/r2=V2*r/r u/r=V2 sqrt(u/r)= sqrt(V2) sqrt(u/r)= Vorb

All, I am setting this thread up for you to post any comments/ questions/ corrections about my tutorial here: Please post all comments in this thread to avoid disrupting that one. Thanks, -Slashy

I will try to explain the math and physics behind orbital mechanics as simply as I can in text and pictures. If I do it right, you should fully understand how to solve these problems in order to plan your missions. I will start with gravity and uniform circular motion, and progress from there to elliptical orbits/ vis-viva, Orbital DV, escape/ interplanetary transfers, gate orbits, etc. This is liable to take some time to complete, so please bear with me. If you have any questions/ corrections/ comments, please post them here: Best, -Slashy

Problem: People don't actually want to live in giant mega tower hives, eating soylent green and drinking each other's recycled urine...

Excellent find! If that's the case, then either it's lost another reaction wheel or it *thinks* it's lost another reaction wheel. Best, -Slashy

It looks like all the news sources are just floating the original press release. http://www.nasa.gov/feature/mission-manager-update-kepler-spacecraft-in-emergency-mode I figure either Charlie Sobeck doesn't know what any of this means himself, or else he forgot that nobody outside of the project would be familiar with "emergency mode". Either way, I guess all we can do is wait for more concrete info.

Same here. They haven't done a good job of explaining what "emergency mode" is or why it would consume fuel. This is kinda central to the whole story.

I'm one of those folks who prefers to do the math myself. In fact, I take it a step further and let the math dictate my design before I even start building. This is how I am able to optimize my designs for weight and cost without resorting to trial and error in the VAB. This is not to say that I think that everyone should be forced to do without a readout (I don't). I'm just saying that I'm very familiar with the process involved and it would be darn near impossible to implement in- game in a way that avoids incorrect answers. As everyone upstream has already said, an in- game DV readout would be tougher to implement than it appears. Best, -Slashy

Yasmy, Now that you mention it, I think that's exactly what it is; Vesc= Vorb*sqrt(2) is true for n- body, but not correct for KSP because it cuts off gravity at the SoI boundary. That would account for the difference.

Kerbin orbits the sun at 9,284.4 m/sec. If you achieve that velocity times the square root of 2 ( 13,127.3 m/sec), you have achieved escape velocity and your probe will never fall back. There's nothing programmed into the game beyond Eeloo, so there's nothing out there but empty space. And the Kraken.... Best, -Slashy

OhioBob, It's always comforting to have this sort of confirmation. If I show up at the party wearing the same dress as you, I must be doing it right Best, -Slashy

Oh, no need to be sorry about your first successful launch being a probe. That's actually the smart way to go about it if you're trying not to kill kerbals. But that is the way KSP works and it's how you develop your skillz... You just set simple goals, achieve them, and build on your success by establishing new goals. Best, -Slashy

Nich, There's no reason to expect a "perfect" gravity turn. I do the same thing you do. My point is that even a bad gravity turn is better than flying straight up to establish Ap and then trying to circularize. JNA, Congratulations! Next step: Get a Kerbal into orbit and recover him (or her) safely back on Kerbin! Best, -Slashy

Yasmy, This is a really cool chart! I'm curious as to why your calculations consistently work out to less DV than mine, even direct from low parent orbit. Best, -Slashy

Teutooni, Hmm... definitely food for thought... Best, -Slashy

I agree 100%. You'll do better in the long run if you don't develop bad habits early. The most efficient and effective way to get to orbit is by using a gravity turn, not "straight up and hang a right". Best, -Slashy

soulsource, Your numbers agree with mine. I thought I had invented something new, but apparently you beat me to it by about 11 hours... Best, -Slashy

JNA, You're not the first to make that mistake KSP is rocket science, so there's a learning curve to it. Thankfully, there's a lot of helpful info available in the tutorial section. Good luck and welcome aboard! -Slashy

This is what we call a "gravity turn" launch. Start tipping it east a little after launch. You'll have to do it a few times to get the hang of it. Best, -Slashy

"Pardon me, Sir... How do I get to Carnegie Hall?" "Practice, my dear boy. Practice" Best, -Slashy

lobe, Remember, we were in a race with the Russians and wanted to beat them to orbit. The Mercury was our best bet to get an astronaut into space with short development time. The X-15 might have been a technically "better" option, but it would've taken too long to field. Best, -Slashy

Gojira1000, I actually have some recommendations for this. I'll start a new thread about it so as not to drag this one further off. Best, -Slashy