## HomeNewton MechanisKeppler System

The purpose of the first project was to simulate the movement of earth around the sun. Since the expected results are well known it is quite easy to compare the computation against the values measured for the earth.

The intial values for the caculation are taken from Wikipedia. Initially the sun (P1) is placed at the location 0,0,0 with a speed of 0.0. The earth (P2) is placed in the X axis with at the semi major axis distance of 149.6E+09 meters. The speed of the earth is then directed perpendicular to this axis with the speed 29.78E+03 $$km s^{-1}$$.

The corresponding lines in the control file of the calculation are shown below:

##              Mass               Pos.: X,Y,Z                 Velocity: Vx,Vy,Vz
P1=0.0,         1.989E+30,          0.0, 0.0, 0.0,              0.0, 0.0, 0.0;
P2=0.0,         5.974E+24,    149.6E+09, 0.0, 0.0,              0.0,29.78E+03,0.0;


The computation has been performed been performed with 0.5 second resultion. The result data has an 12 hour resolution. The calculation yielded the following results:

Computation Actual Values
Perihelion 149,421,000 km 147,098,290 km
Aphelion 149,600,000 km 152,098,232 km
Orbital period 349.00 days 365.256363004 days

The rigth most column contains the real measured values of the earth. The error of the computation is quite considerable specially the different between perihelion and aphelion is exceptional large.

The calculated trajectory is shown in figure 1. The colour of the trajectory indicates different kinetic energies. As expected the picture shows high speeds at the nearest distance and lower velocities at farest distances.

 Fig. 1 - Computation results of the earth solution