1. Outline
The earth is considered
to be a homogeneous globe of radius R and M in mass.
Universal gravitation F of the earth which acts on the satellite
of m in mass is as follows.
F=G*M*m/r*r
Universal gravitation constant; G=6.67E-11(Nmm/kgkg)
Mass of the earth; M=5.977E24(kg)
Distance between the earth and satellite; ｒ
The equation of motion of the satellite is given by the undermentioned
equation.
m*dv/dt=F
v;velocity
The orbit of the satellite is obtained by solving this equation.
That is, the position of the satellite and the speed only have
to execute the integration of the equation as a function at time.
However,it is extremely difficult to do this solution by using
the personal computer.
Then, the orbit of the satellite was simulated by decomposing
the position of the satellite and the speed into horizontal direction
and the vertical direction, and using the equation of an equal
acceleration movement in each direction.
V=V0+α*t
S=V*t+α*t*t
V;velocity, V0;initial velocity, α;acceleration, t;time,
S;Position
2.. Orbit samples
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Crash on the Earth |
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Circuler Orbit (animation) |
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Elliptical Orbit (animation) |
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Jump to higher Orbit (animation) |
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Voyage to the Space (animation) |
3. Explanation of screen
A green circle
is the earth . A blue
concentric circle shows
the distance from the center of the earth in 100km.
A red mark shows the ignition of the engine .
2nd and 3rd.accelaration are done with the highest point in the
orbit . Moreover, a yellow
circle shows the position
of the satellite of regular intervals.
Kepler's law (The area speed is constant) is plainly recognized
for an elliptical orbit.
