lecture05 - Altitude and apogee x perigee specification...

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Unformatted text preview: Altitude and apogee x perigee specification Although we’ll develop a more precise notion of altitude a little later for the purpose of handling ground stations, it is often useful to specify the (nominal) altitude of a satillite above a spher- ical earth, particularly at apogee and perigee. Radius of the earth R ♁ ≈ 6378km. For a given geocentric distance r , the altitude is z = r- R ♁ . Often times (usually informally) an orbit is stated as “perigee altitude x apogee altitude” instead of semimajor axis and eccentricity. For example, 400 × 600km. You should be able to convert these back and forth. Always determine in problems whether a given distance is geocentric r or altitude z ; remember formulas use r . Compute for ISS: its orbit is typically 348 . 6 × 356 . 1 km. L. Healy – ENAE404 – Spring 2007 – Lecture 5 (Feb. 8) 1 Typical Earth orbits Look at circular orbits at various speeds. • At surface of earth, a = 6378km, circular speed is about 7 . 9 km / s , period is about 1 hour 24 minutes. • At an altitude of 500km, speed decreases to about 7 . 6 km / s , period is longer, about 1 hour 34 minutes. • At a semimajor axis of a = 42164km, speed is about 3 . 1 km / s , and orbital period is a few minutes less than 24 hours, a geosyn- chronous orbit . If inclination i = 0, how would this orbit be useful? What are the escape velocities for these orbits? L. Healy – ENAE404 – Spring 2007 – Lecture 5 (Feb. 8) 2 Some popular earth orbits The orbit chosen is strongly governed by what is desired of the spacecraft and the desirable dynamical properties of particular orbits. Astronautics Primer by Jerry Sellers, http:// agi.com/corporate/partners/edu/AstroPrimer/primer1. htm particularly the section “Describing Orbits” → “Satellite Missions”. Technically speaking, a geostationary orbit is a circular orbit with a period of exactly 24 hours and an inclination of exactly 0 degrees. A satellite in a geostationary orbit appears to be stationary to an Earth-based observer. Geosynchronous orbits are slightly inclined orbits with a period of 24 hours. In practice, it is almost impossible to achieve an orbit with exactly a 24-hour period and an inclination of 0 degrees. Thus, the two terms are frequently used interchangeably. Mission- Communications, Early Warning, Nuclear Detection Orbit Type Semimajor Axis (Alt) Period Inclination Other Geostationary 42,158 km (35,780 km) 24 hours ~0 degrees e [IMAGE] 0 A semi-synchronous orbit has a period of 12 hours. Mission- Navigation (GPS) Orbit Type Semimajor Axis (Alt) Period Inclination Other Semi-synchronous 26,610 km (20,232 km) 12 hours 55 degrees e [IMAGE] L. Healy – ENAE404 – Spring 2007 – Lecture 5 (Feb. 8) 3 Some popular earth orbits cont’d....
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lecture05 - Altitude and apogee x perigee specification...

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