Kepler’s First Law:
The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.
Kepler’s Second Law:
A line joining a planet/comet and the Sun sweeps out equal areas in equal intervals of time
Kepler’s Third Law:
The squares of the periods of the planets are proportional to the cubes of their semimajor axes (P2 = a3)
Sources:
1. http://csep10.phys.utk.edu
2. http://www.windows.ucar.edu
3. http://home.cvc.org
E. Medium Earth Orbit (MEO)
Medium Earth Orbit (MEO), sometimes called Intermediate Circular Orbit (ICO), is the region of space around the Earth above low Earth orbit (2,000 kilometres) and below geostationary orbit (35,786 kilometers).
Medium Earth Orbit enables a satellite provider to cover the earth with fewer satellites than Low Earth Orbit, but requires more satellites to do so that geostationary orbit.
Medium Earth Orbit terrestrial terminals can be of lower power and use smaller antennas than the terrestrial terminals of geostationary orbit satellite systems. However, they cannot be as low power or have as small antennas as Low Earth Orbit terrestrial terminals.
The orbital periods of MEO satellites range from about two to 12 hours. The most common use for satellites in this region is for navigation, such as the GPS (20,200 kilometers), Glonass (19,100 kilometers) and Galileo (23,222 kilometers) constellations. Communications satellites that cover the North and South Pole are also put in MEO.
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F. Geosynchronous Orbit (GEO)
A satellite in geosynchronous orbit circles the earth once each day. The time it takes for a satellite to orbit the earth is called its period. For a satellite’s orbit period to be one sidereal day and is equivalent to 23h 56m 04s of mean solar time, it must be approximately 35,786 kilometers above the earth’s surface. We calculate this height using common geometric formulas. While completed its orbit in the same time it takes the earth to rotate once, it should be obvious that the geosynchronous satellite will move north and south of the equator during its orbit.
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G. Geostationary Orbit (GSO)
A circular geosynchronous orbit in the plane of the Earth’s equator has a radius of approximately 42,164 km (from the center of the Earth). A satellite in such an orbit is at an altitude of approximately 35,786 kilometers above mean sea level. It will maintain the same position relative to the Earth’s surface. If one could see a satellite in geostationary orbit, it would appear to hover at the same point in the sky. This is sometimes called a Clarke orbit. Such orbits are useful for telecommunications satellites.
The advantages of such an orbit are that no tracking is required from the ground station since the satellite appears at a fixed position in the sky. The satellite can also provide continuous operation in the area of visibility of the satellite. Many communications satellites travel in geostationary orbits, including those that relay TV signals into our homes.
However, due to their distance from Earth GEO satellites have a signal delay of around 0.24 seconds for the complete send and receive path. This can be a problem with telephony or data transmission. Also, since they are in an equatorial orbit, the angle of elevation decreases as the latitude or longitude difference increases between the satellite and earth station. Low elevation angles can be a particular problem to mobile communications. Long distance between the satellite and the ground is also a typical problem but with sufficient power or a large enough antenna, though, this limitation can be overcome.
The fact that there is only one geostationary orbit presents a more serious limitation. Just as in putting beads on a loop of string, there are only so many slots into which geostationary satellites can be placed. The primary limitation here is spacing satellites along the geostationary belt so that the limited frequencies allocated to this purpose don’t result in interference between satellites on uplink or downlink. Of course, we also want to make sure the satellites aren’t close enough to run into one another since they will have some small movement.
A perfect stable geostationary orbit is an ideal that can only be approximated. In practice the satellite will drift out of this orbit (because of perturbations such as the solar wind, radiation pressure, variations in the Earth’s gravitational field, and the gravitational effect of the Moon and Sun), and thrusters are used to maintain the orbit in a process known as station-keeping.
Once the satellite has exhausted its fuel, its inclination will begin to grow and it will begin to drift in longitude and may present a threat to other geostationary satellites. Oftentimes, geostationary satellites are boosted into a slightly higher orbit at the end of their planned lifetime to prevent them causing havoc with other geostationary satellites. This final maneuver assumes that no unplanned failure has occurred which would prevent it (such as a power or communications failure).
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H. Highly Elliptical Orbit (HEO)
Highly Elliptical Orbit (HEO) is an elliptic orbit characterized by a relatively low-altitude perigee and an extremely high-altitude apogee. These extremely elongated orbits can have the advantage of long dwell times at a point in the sky during the approach to and descent from apogee. Visibility near apogee can exceed twelve hours of dwell at apogee with a much shorter and faster-moving perigee phase. Bodies moving through the long apogee dwell can appear still in the sky to the ground when the orbit is at the right inclination, where the angular velocity of the orbit in the equatorial plane closely matches the rotation of the surface beneath. This makes these elliptical orbits useful for communications satellites.
Examples of HEO orbits offering visibility over Earth’s Polar Regions, which most geosynchronous satellites lack:
– Molniya orbit, after the Soviet communications satellites which used such an orbit.
– Tundra orbit, also developed for Soviet use, but only used by US Sirius Satellite Radio.
Much of Russia is at high latitude, so geostationary orbit does not provide full coverage of the region. These Soviet HEO orbits include polar coverage.
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I. Molniya Orbit
A Molniya orbit is a type of highly elliptical orbit with an inclination of 63.4 degrees with a high apogee over the northern hemisphere and a low perigee over the southern hemisphere and an orbital period of about 12 hours. Molniya, which means “lightning” in Russian, was the name of the first Russian communications satellites to use it.
The satellite swings low and fast over the southern hemisphere and then slows as it rises toward its apogee in the northern hemisphere, making it appear to “hover” in the sky over northern territories for long periods of time. The primary use of the Molniya orbit was for communications services in the high-latitude areas over Russia and is also used by U.S. intelligence satellites that focus on spying on Russia and Russian missile warning satellites that are observing U.S. ICBM silos.
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J. Tundra Orbit
Tundra orbit is a type of highly elliptical orbit with a high inclination (usually near 63.4°) and an orbital period of one sidereal day (almost 24 hours). A satellite placed in this orbit spends most of its time over a chosen area of the Earth, a phenomenon known as apogee dwell.
These are conceptually similar to Molniya orbits which have the same inclination but half the period (about 12 hours). The only user of Tundra orbits is Sirius Satellite Radio, which operates a constellation of three satellites.
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Sources:
1. http://en.wikipedia.org
2. http://www.centennialofflight.gov
3. http://www.thetech.org
4. http://www.heavens-above.com
5. http://www.satcom.co.uk
6. http://liftoff.msfc.nasa.gov
7. http://celestrak.com
A. Low Earth Orbit (LEO)
A Low Earth Orbit (LEO) is generally defined as an orbit within the locus extending from the Earth’s surface up to an altitude of 2,000 km. Given the rapid orbital decay of objects below approximately 200 km, the commonly accepted definition for LEO is between 160 – 2000 km above the Earth’s surface.
Objects in LEO encounter atmospheric drag in the form of gases in the thermosphere (approximately 80-500 km up) or exosphere (approximately 500 km and up), depending on orbit height. The altitude is usually not less than 300 km because that would be impractical due to the larger atmospheric drag.
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B. Polar Orbit
A polar orbit is a particular type of Low Earth Orbit in which a satellite passes above or nearly above both poles of the planet orbiting (north-south direction) on each revolution. It therefore has an inclination of (or very close to) 90 degrees to the equator. Except in the special case of a polar geosynchronous orbit, a satellite in a polar orbit will pass over the equator at a different longitude on each of its orbits.
Polar orbits are often used for earth-mapping, earth observation and reconnaissance satellites, as well as some weather satellites. During a 12-hour day, a satellite in such an orbit can observe all points on the Earth. The disadvantage to this orbit is that no one spot on the Earth’s surface can be sensed continuously from a satellite in a polar orbit.
To achieve a polar orbit requires more energy, thus more propellant, than does an orbit of low inclination. A polar orbit cannot take advantage of the “free ride” provided by the Earth’s rotation, and thus the launch vehicle must provide all of the energy for attaining orbital speed.
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C. Sun-Synchronous Orbit
A sun-synchronous orbit describes the orbit of a satellite that provides consistent lighting of the Earth-scan view. Like a polar orbit, the satellite travels from the north to the south poles as the Earth turns below it. In a sun-synchronous orbit, though, the satellite passes over the same part of the Earth at roughly the same local time each day. For example, a satellite’s sun-synchronous orbit might cross the equator twelve times a day each time at 3:00 p.m. local time. The orbital plane of a sun-synchronous orbit must also precess (rotate) approximately one degree each day, eastward, to keep pace with the Earth’s revolution around the sun.
Typical Sun-synchronous orbits are about 600-800 km in altitude, with periods in the 96-100 minute range, and inclinations of around 98° (i.e. slightly retrograde compared to the direction of Earth’s rotation: 0° represents an equatorial orbit and 90° represents a polar orbit).
Special cases of the sun-synchronous orbit are the noon/midnight orbit, where the local solar time of passage for equatorial longitudes is around noon or midnight, and the dawn/dusk orbit, where the local solar time of passage for equatorial longitudes is around sunrise or sunset, so that the satellite rides the terminator between day and night. Riding the terminator is useful for active radar satellites as the satellites’ solar panels can always see the Sun, without being shadowed by the Earth. It is also useful for some satellites with passive instruments which need to limit the Sun’s influence on the measurements, as it is possible to always point the instruments towards the night side of the Earth. The dawn/dusk orbit has been used for solar observing scientific satellites such as Yohkoh, TRACE and Hinode, affording them a nearly continuous view of the Sun.
As the satellite’s altitude increases, so does the required inclination, so that the usefulness of the orbit decreases because (for an Earth-observing satellite) the satellite’s photographs are taken from ever farther away, and second because the increasing inclination means the satellite won’t fly over higher latitudes.
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D. Near Equatorial Orbit (NEqO)
A near equatorial orbit is an orbit that lies close to the equatorial plane of the object orbited. This orbit allows for rapid revisit times (for a single orbiting spacecraft) of near equatorial ground sites.
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Sources:
1. http://en.wikipedia.org
2. http://www.centennialofflight.gov
3. http://www.thetech.org
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