Abstract
In this chapter, we discuss the position of the satellite orbit relative to the Earth. There are two distinct parts. The first concerns the position of the satellite ground track relative to the Earth, and the second the altitude of the satellite measured from the terrestrial ellipsoid.
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Notes
- 1.
Eratosthenes of Cyrene (284–192 bc), ὁ ᾿Ερατοσθένης, ους, was a Greek astronomer, mathematician, and geographer. He discovered a systematic method for obtaining the sequence of prime numbers up to any desired value. One writes down the sequence of positive integers, then crosses out the multiples of 2, of 3, of 5, and so on. This method, which sifts the positive integers, keeping only the primes, is known as the sieve of Eratosthenes. His abilities as an astronomer and geographer are revealed by a scientific and relatively accurate measurement of the Earth’s radius, in which he measured the shadow cast by a column in Alexandria at noon on a day when he knew that the Sun’s rays reached the bottom of the wells in ancient Syene (Assouan), the day of the summer solstice at Syene, under the Tropic of Cancer. He determined the obliquity of the ecliptic and estimated at 47∘42′ the arc of the meridian between the two tropics.
- 2.
Such a graph can also be interpreted by identifying the values of \(D_{\mathrm{T}_{\mathrm{o}}}\). Taking for example \(D_{\mathrm{T}_{\mathrm{o}}} = \pm 7\), this value appears for all values of \(C_{\mathrm{T}_{\mathrm{o}}}\) greater than \(2 \times \vert D_{\mathrm{T}_{\mathrm{o}}}\vert = 14\), except for \(C_{\mathrm{T}_{\mathrm{o}}}\) = 21, 28, 35, etc., that is, multiples of 7.
- 3.
It is only when we change from ν to a or h that the type of orbit (inclination, Sun-synchronous or otherwise) becomes relevant. The recurrence module is established without referring to any particular type of satellite and is even independent of the notion of satellite! The only condition is that the phenomenon under consideration should occur uniformly in time.
- 4.
The European mission ERM (Earth Radiation Mission) was supposed to come into operation around 2006, during a minimum of solar activity, thus allowing a very low altitude orbit. Following an agreement between the ESA and JAXA, ERM was merged with the Japanese project ATMOS-B1 to give EarthCARE. The launch date was postponed and the altitude increased, following the heightened solar activity which reached the culmination of its 11 year cycle in 2012. When the launch date was planned after the solar maximum, a lower altitude was chosen.
- 5.
For a quick evaluation, δ can be obtained from an approximate relation for recurrent satellites of altitude h = 900 ± 300 km. For these satellites, the daily orbital frequency ν lies between 13 and 15. We may thus take ν to be equal to 14 and \(N_{\mathrm{T}_{\mathrm{o}}}\) equal to \(14C_{\mathrm{T}_{\mathrm{o}}}\). Expressing δ in degrees, we then find that
$$\displaystyle{\delta \approx \frac{360} {14C_{\mathrm{T}_{\mathrm{o}}}} \;,\quad \mbox{ i.e.,}\quad C_{\mathrm{T}_{\mathrm{o}}}\delta \approx 25\;.}$$We thus see that the product of the grid interval (in degrees) and the recurrence cycle (in days) is roughly equal to 25.
- 6.
The first publications treating the subject of frozen orbits date back to 1965. They concerned satellites in low orbit around the Moon. The term “frozen orbit” was first used to describe Seasat in 1976.
- 7.
For example, for the satellite TOPEX/Poseidon, between 1992 and 2002, we may note the following exceedingly narrow ranges of variation for the orbital elements: e F from 0. 73 × 10−3 to 0. 83 × 10−3, ω F from 264∘ to 270∘, i from 66.037∘ to 66.046∘, a from 7,714.422 to 7,714.436 km.
- 8.
The true values as obtained from the NORAD elements often differ somewhat from the nominal values. In Example 11.1, we note that the true values of the eccentricity of SPOT-5 are well below the nominal values.
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Capderou, M. (2014). Orbit Relative to the Earth: Recurrence and Altitude. In: Handbook of Satellite Orbits. Springer, Cham. https://doi.org/10.1007/978-3-319-03416-4_11
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DOI: https://doi.org/10.1007/978-3-319-03416-4_11
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