EJSS Earth and Moon Model

Description:


The Moon completes its orbit around the Earth in approximately 27.32 days (a sidereal month). In this model, we assume the Moon to orbit about the center of the Earth. By this assumption, the Moon is at a distance of about 385000 km from the center of the Earth, which corresponds to about 60 Earth radii. With a mean orbital velocity of 1.023 km/s,[1] The Moon orbit is modeled to be a perfect circular motion orbit, a close approximation the real Moon's orbit. The model also assume the Moon to move on the Earth's equatorial plane.

The equations of motion are:



δxδt=vx

δyδt=vy

δzδt=vz

δvxδt=GMx(x2+y2+z2)1.5

δvyδt=GMy(x2+y2+z2)1.5

δvzδt=GMz(x2+y2+z2)1.5

The equations of rotation are:

 rotationearth=rotationearth+1δt

 rotationmoon=rotationmoon+1360δt


Equations used to calculate physics quantities are:


 r=x2+y2+z2

 v=v2x+v2y+v2z

 theta=tan1 yx

The model used δt=1, the time taken for Earth to rotate i complete revolution is therefore 
 tday =t360

so after 360 δt steps, 
 tday =1

To calculate period T,  

 omega=vr

therefore, 

 T=2πω

For collision detection, the model assumption used is

 r< rEarth+rMoon

For largely visualization purposes, 
 rEarth=0.637 some what familiar to real data

rMoon=0.1737 not to scale

in order to create realistic simulation, the model used constants to create numeric that corresponds to the real world.

for example in the model versus in the world,
MEarth=0.6=6x1024kg

G=0.667k=6.67x1011m3kg1s2

where k=0.58x104 to achieve comparable period T=27.3 days

r=3.844= 385000km
and velocity of moon is 

vcal=(v)(1x109)k1 where k1=2.4 arbitrarily determined

Credits

The EJSS Earth and Moon Model was developed by Francisco Esquembre, and Loo Kang WEE using the Easy Java Simulations (EJS) version 5.0 authoring and modeling tool.