## Ellipsoid With Elliptical Cross Section On Equator

SPHEROID DEFINED BY FOURTH ORDER HARMONICS (SEE SECTION 6.2)

GEOID 1° MEAN SEA LEVEL)

TOPOLOGICAL SURFACE |i.e„ REAL SURFACE)

COj LAYER IN ATMOSPHERE

0 AT EQUATOR TO -21.38 km AT POLE

AT EQUATOR. Rmax-Rmin O.tO km (Rmax AT 160°' 3400 EAST LONGITUDE)

0 AT EQUATOR AND POLE TO «.005 km AT 46° LATITUDE

+0.080 km NEAR NEW GUINEA TO ■0.110 km IN INDIAN OCEAN"

~ +40 km AT EQUATOR TO ~ +30 km AT POLE IN WINTER*

* BASED ON EQUATORIAL RADIUS OF 6,378.140 km AND FLATTENING, « - 1/298.267. AS ADOPTED BY THE IAU (TABLE L-3) IN 1976.

** FOR A DETAILED MAP OF THIS DEVIATION. SEE FIG. M.

* BASED ON EQUATORIAL RADIUS OF 6,378.140 km AND FLATTENING, « - 1/298.267. AS ADOPTED BY THE IAU (TABLE L-3) IN 1976.

** FOR A DETAILED MAP OF THIS DEVIATION. SEE FIG. M.

* ACTUAL VALUES DEPEND ON HOW THE LAYER IS SENSED AND LOCAL WEATHER. SEE SECTION 4.2.

* Studies by Phenneger, el al., [1977a, 1977b] for the SEASAT mission indicate 3-o random horizon radiance variations for a percentage-of-peak locator of approximately ±0.1 deg. At the SEASAT altitude of 77S km, this corresponds to a triggering level variation of ±7 km.

series of increasingly complex surfaces. Although a simple spherical model is useful for estimation, it is inadequate for most attitude analysis of real spacecraft data, •j^e basic model for most attitude work is the arbitrarily defined reference spheroid, ^hich is an ellipse rotated about its minor axis to represent the flattening of the Earth. The ellipse is defined by the Earth's equatorial radius, [email protected] «6378.140 km, and the ellipticity or flattening,

where Rj, is the polar radius of the Earth. These numerical values are those adopted by, the International Astronomical Union in 1976 [Muller and Jappel, 1977] and will be;used throughout the book, except in cases such as Vanguard units (Appendix K) or geomagnetic field models (Appendix H) where different values are a part of standard numerical models.

At NASA's Goddard Space Flight Center, a common expression used in attitude work for the radius of the Earth at latitude, K is:

where the terms in /, h, and k account for the flattening, the height of the atmosphere (for IR sensors which trigger on the atmosphere), and seasonal or other latitudinal variations in the atmosphere height

A second more complex surface than the reference spheroid is obtained by expanding the Earth's gravitational potential in spherical harmonics and retaining only terms up to fourth, order! It can be shown that this and a suitably defined reference spheroid are identical up to the second power of the flattening. A much more complex surface is the equipotential surface of the Earth's gravitational field, known as the geoid or mean sea level, which has many local irregularities due to the Earth's nonuniform mass distribution. The difference in elevation between the geoid and a reference spheroid is known as the geoid height and is shown in Fig. S-8. Because of its mathematical simplicity, we will use die reference spheroid of Eq. (4-13) as the shape of the Earth throughout the rest of this section.

The Shape of the Earth as Seen From Space. The Earth's shape as viewed from space is defined by the Earth's horizon as seen from the position of the observer. The horizon is the point where the observer's line of sight is tangent to the Earth's surface or perpendicular to the surface normal. The spheroidal surface of the Earth is expressed in geocentric coordinates by a2 c2

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