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=tan−1 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=6.67x10−11m3kg−1s−2
where k=0.58x10−4 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.
