# Lunar Mission Simulator

LMS was designed primarily as a mission simulator as opposed to a space flight simulator, as such more emphasis was placed on the simulation of space missions than on the real physics of space flight. With that being said where possible I have endeavered to use as much real physics as possible within the framework of my current knowledge of space flight and mathematical skill. This page documents all the models in use by LMS describing what is more accurate and what is less. As I gain more knowledge into space flight and the related math, I will update the simulator. While my empahsis is on mission simulation, I also would like to keep the physics as real as possible.

#### Coordinate System

The coordinate system in use by this simulator is based upon the Right ascension/declination system, which

#### Earth

The real Earth has a mass of 5.972e+24kg, an equitoral radius of 6,378.1km and a mean radius of 6,371.0km. The modeled Earth in FMS uses the correct mass value, but does not model the oblique spheroid shape of the real Earth. The simulator models a perfectly round Earth using 6,378.1km as the surface radius.

The simulator does not model surface features of the Earth, as far as the simulator is considered the entire world has ground/sea at the same radius. Since this really only effects touch/splashdown I doubt I will do any Earth surface modelling in the future, but I would not rule it out.

The Earth is not modeled in LMS and is at the center of the universe in FMS, being located at cartesian coordinates of 0,0,0. The Earth is not in motion but does rotate, completing one complete rotation in 0.99726968 days.

The Earth's atmosphere is very simply modeled in this simulation. While I do use the real drag formula, which uses air density as one of the components to compute drag, the air density calculation used by the simulator is greatly simplified. The air density calculation is computed as a value between 1.0 (sea level) and 0.0 (in space). The atmosphere is divided into 5 altitude regions and a linear function is used to determine air density within each reagion. This table shows the regions:

Altitude (meters) Density decrease per meter above
100,000 0 0
50,000 0.001 0.00000018
32,000 0.01 0.0000005
16,000 0.1 0.000005625
5,500 0.5 0.000038095
0 1.0 0.0000909

So for example to compute the air density at 27,000 meters. 27,000 meters is 11,000 meters above 16,000, so the decrease above 16,000 would be 11,000 * 0.000005625 or 0.061874, subtracted from the air density at 16,000 meters, 0.1 - 0.061874 equals 0.038125, this would then be used in the drag calculation.

While this model is very simplistic, it does give believable results in the drag experienced during launch or reentry. For example max-q occurs relatively close to the max-q figures published by NASA for their space flights.

The air density calculation is in an isolated function so it would be pretty easy to replace it with something that gives more realistic values in the future. I figured for now, during launch atmospheric flight is usually under 5 minutes and re-entry to splash down is between 10 and 15 minutes, that this time is relatively short compared to a 200+ hour Lunar mission, and therefore not worth of spending too much time on it at present.

Kennedy Space Center is correctly located at a longitude of 80.6077 degrees west and at a latitude of 28.50 degrees north. Upon launch this imparts an eastward velocity of 408.75m/s. The position of KSC is correctly altered by the Earth's rotation in relation to the cartesian coordiantes used by the physics engine.

#### The Moon

The real Moon has a mass of 7.342+e22kg, an equitoral radius of 1738.1km and a mean radius of 1737.1km. The simulator uses the correct mass for the Moon, but like the Earth uses the equitoral radius of 1738.1km for a perfectly spherical Moon. The Moon's surface does not currently model elevation above/below the mean radius, however in the future if I can find the correct data, I would like to model surface elevation for the moon more accurately.

The real Moon orbits the Earth with a perigee ranging from 356,400km to 370,400km and a apogee that ranges from 404,000km to 406,700km. The Moon's inclination is 5.145 degress to the ecliptic. The Moon's declination compared to the Earth's equator changes between 18.5 degrees to as much as 28.5 degrees, changing over an 18.6 year cycle.