Synchronous OrbitsAll space orbits obey the laws of Kepler and Newton. As already noted, for circular orbits Kepler's third law may be written T = 5063 seconds R3/2 = 5063 seconds R * SQRT(R) where T is the orbital period, * marks multiplication, R is the orbit's radius in units of Earth radii (= 6371 km) and SQRT(R) is the square root of R.
From this one finds that for T = 86400 sec = 24 hours, R = 6.6 Earth radii. An equatorial satellite at this distance has a period of 24 hours and therefore, as the Earth rotates, it stays above the same point on the Earth's equator. Such an orbit is ideal for a communication satellite, for then a "satellite dish" linked to it need not track it across the sky, but can stay pointed in a fixed direction. It was the British science fiction writer Arthur Clarke who first proposed the use of this "synchronous" orbit, long before the first artificial satellites. Clarke later wrote the book "Fountains of Paradise" (set in Sri Lanka, to which he had moved) in which thin cables linked synchronous satellites to the ground. A material strong enough and light enough for such cables does not exist, and is so far beyond anything known that it is probably impossible; but it makes a good story. About 200 satellites now inhabit synchronous orbit, some owned by governments for their own use, many operated by telecommunication companies. |
Atmospheric Re-entryThe Kepler formula also applies to elliptical motion, provided R is replaced by the semi-major axis a of the orbit. Over time however orbits stray from exact Keplerian ellipses because to additional forces, such as the attraction of the Moon and the Sun. For elongated ellipses, this causes the lowest point in the orbit ("perigee") to move up and down, ultimately reaching the atmosphere and causing satellite to be lost. Atmospheric friction also causes low-altitude satellites to re-enter, sooner or later: all these, as they lose energy, descend deeper and deeper into the atmosphere, and ultimately reach denser regions, where they burn up. That was the fate of the Skylab space station in 1980: NASA had hoped to use the Space Shuttle to boost it into a higher orbit, but the shuttle was not ready on time. Meanwhile the peak of the 11-year sunspot cycle arrived, a more active peak than NASA had hoped for, bringing a greater intensity of solar x-rays and extreme ultra-violet radiation. These radiations are absorbed in the uppermost fringes of the atmosphere, heat them up and make them expand outwards, more at "solar maximum" than at other times. Their expansion increased the air resistance ("drag") to the motion of Skylab and caused its early demise. The Bulge of the EarthIf the Earth were a perfect sphere, orbit calculations could assume that all its mass was concentrated at its center: the force, at least outside the Earth, would have been exactly the same. However, the centrifugal force associated with the Earth's rotation makes it slightly non-spherical, wider across the equator by a few kilometers than from pole to pole. That modifies the orbits of satellites and must be taken into account. When the orbital plane is inclined to the equator, the equatorial bulge slowly rotates it around the Earth: a line perpendicular to the orbit plane gradually traces a cone. Interestingly, there exists a situation where one can take advantage of this rotation. |
Ordinarily, a satellite's orbit is fixed in space, and as the Earth goes around the Sun, its orientation relative to the Sun constantly changes. Take for example the case of a low altitude satellite whose orbit plane contains the axis of the Earth (i.e. it passes right above the north and south poles). If in June that plane happens to be lined up with the dawn-dusk direction, i. e. the division between the sunny side of Earth from the shaded one, then in September it matches the noon-midnight direction, a rotation of 90 degrees. Note that the June orbit enjoys 24-hour sunlight, but the September orbit does not. |
However certain orbits exist, passing just a few degrees from the poles, whose planes are rotated by the bulge of the Earth by exactly one rotation per year. Such "sun synchronous" orbits, can be made to always face the Sun, or always go through midnight. The DMSP satellites have such orbits (the picture here, of the aurora above the Great Lakes, was taken by one of these satellites; note Florida at bottom right), and so did Magsat. Earth observation satellites such as Landsat and SPOT (Satellite Pour l'Observation de la Terre) also prefer sun-synchronous orbits, which ensure that images from different dates are always taken at the same time of the day. Without this, the difference in the shadows may confuse their interpretation. Lagrangian Points |
By Kepler's 3rd law, a spacecraft going around the Sun in a circle smaller than the Earth's orbit will always have a shorter period and will move faster, and if launched from Earth its distance will grow until it and the Earth are well separated. Yet a way exists for keeping the two together. |
Calculation: #34a The Distance to the L1 Point
Next Regular Stop: #35 To the Planets, to the Stars
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