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If i were to simulate a lunar module with: $x_0$, $\dot{x}_0$, $y_0$, $\dot{y}_0$. $x$ is horizontal position, and $y$ is vertical position. What would be appropriate values?

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  • $\begingroup$ What exactly are you trying to do? $\endgroup$ – PearsonArtPhoto Nov 7 '16 at 10:52
  • $\begingroup$ I've made a model in matlab, and some controllers. And to make it as realistic as possible(in 2D), I want the initial values to be as close to the real deal as possible. $\endgroup$ – Viktor Nov 7 '16 at 10:55
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    $\begingroup$ For Apollo flights they started in an eccentric orbit, with the lowest altitude a few hundred miles ahead of the landing site. They then used engine braking to reduce velocity (horizontal and vertical) to reach a landing. Do you want to simulate this "real" situation, or just a lander starting from a hover above a flat plane? $\endgroup$ – Andy Nov 7 '16 at 11:17
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    $\begingroup$ Tales from the Lunar Module Guidance computer shows a picture (figure 5) with numbers, in old units (feet per second, miles, etc.) might be good enough to start with. (I guess the angle of travel at the beginning of the powered descent was very shallow, almost horizontal, as they were braking from a stable orbit at that point.) $\endgroup$ – Andy Nov 7 '16 at 14:14
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I fetched the data I think you are interested in from JPL's Horizon application.

Eagle separates from the command module at 6:12 am on the 20'th of July:

CSM-LM separation July 20 06:11:53

At the time of separation, the state vectors for the command module (at the time of separation the lander and command module presumably had the same state vectors, although I'm sure this is a very poor assumption, but at least it gives you something to work with) were as follows:

2440422.758333333 = A.D. 1969-Jul-20 06:12:00.0000 TDB

X: -2.870360413463610E-04 Y: 4.500679223401464E-05 Z: -1.732432604852359E-05 VX: -6.504365861559985E-04 VY: -1.604671519715920E-05 VZ: -5.403321203240985E-05

The origin of the coordinate system is the center of the Moon and the time step 1 minute. Distances are in astronomical units.

The lander conducted several burns after separating from the command module, though, so if you want to model the descent of the lander, you have to take those burns into account.

Have a nice day!

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