Kepler's third law is illustrated for circular orbits, although the law also applies to elliptical orbits. Click on either of the buttons on the right. The satellite's motion will simulate either the orbit of NASA's space shuttle or that of a satellite in a geosynchronous orbit. A geosynchronous orbit is one with an orbital period equal to the period of the rotation of the Earth. This means that for circular orbits above the Earth's equator, the satellite will always remain above the same point on the Earth.
You can also click on the satellite and drag it to other orbits. The satellite's altitude above the Earth's surface and orbital period are given on the right.
Notice how much slower the satellite moves in a large
orbit, and how much longer it takes to complete an orbit than
when it is closer to the Earth. A mathematical relationship
exists between the orbital period and the size of the orbit,
i.e., the distance between the center of the Earth and the
satellite. The relationship states that the square of the orbital
period is proportional to the cube of the size of the orbit.
Orbit Simulators
The period of twenty-three hours and fifty-six minutes that
you see in the simulation of the geosynchronous orbit on this
page is equal to one sidereal day, that is,
the time taken by the Earth to make one complete rotation (360
degrees) relative to the stars. The standard twenty-four hour
day, known as the solar day, is the time it
takes the Earth to make one complete rotation relative to the
Sun. The difference between the sidereal day and the solar day
arises from the Earth's motion around the Sun. Each day, the
Earth moves a stretch along this orbit. Therefore, it has to
rotate slightly more than 360 degrees so that a given place on
its surface points exactly towards the Sun. This additional daily
rotation amounts to about three minutes and fifty-six seconds.
Comments to: Observatorium
Curator (curator@rspac.ivv.nasa.gov)
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