# Section 2.1

<Introduction Page, NOAA KLM TOC, Acronyms
Previous Section, Next Section

## 2.1 Navigating the Polar Satellite

Any object in orbit about a more massive body will follow Kepler's three laws of motion:

1. The path of the object will be an ellipse, with the massive body at one focus.

2. A straight line joining the central body and the orbiting body will sweep out equal areas in equal times.

3. The square of the sidereal (relative to the stars) period of the orbiting body is directly proportional to the cube of the semi-major axis of the orbit.

These relations are true for any orbit; a planet orbiting a star, a moon orbiting a planet, or an artificial satellite orbiting the Earth. Discussion here will be confined to the last case.

If the Earth were a perfect sphere and there were no nearby bodies, the orbit into which the satellite was placed initially would remain unchanged. However, the presence of the Sun and Moon will cause the orbit to vary. Since the orbits which are being considered here are close to the Earth, the most important cause of variation in the orbit is the non-sphericity of the Earth; the flattening of the poles and the bulging of the equator resulting from the adjustment of the Earth to its rotation. The equatorial bulge is small, the equatorial radius exceeding the polar radius by only about a third of a percent. Nevertheless, this is sufficient to have a major effect on the behavior of a satellite orbit.

Since a satellite is a rotating body, a torque applied perpendicular to the axis of rotation will result in a precession of the rotation axis. Such a torque is supplied by the attraction of the equatorial bulges. The amount of torque, and hence the amount of precession, is governed by two quantities: the mean distance of the satellite from the Earth center, (a - the semi-major axis of the orbit ellipse), and the inclination of the orbital plane to the Earth's equatorial plane, I, measured through 180 degrees from the east direction (the direction of the Earth's rotation).

This situation permits certain characteristics of the orbit to be controlled. The satellite height is usually specified initially in order to achieve the desired Earth coverage with particular instruments. For NOAA satellites, the inclination is then chosen such that the orbit will precess in the same direction and at the same rate as the Earth revolves about the Sun. This situation is termed "Sun synchronous", and means that the satellite will preserve its angular relationship with the Sun over time. This causes the satellite to view each latitude at the same Local Solar Time (LST) on each orbit.

The NOAA series of satellites have been placed in orbits with a mean height of about 850 kilometers (semi-major axis about 7228 kilometers). In order to be Sun synchronous, the inclination must then be about 99 degrees. This means that the satellite moves in a westward direction, termed a "retrograde" orbit, since the satellite motion is opposite to the Earth rotation direction. Since, by Kepler's third law, the period is related to the semi-major axis, the period must be about 102 minutes. The period usually specified for NOAA series satellites is the nodal period - the time from one ascending node to the next. Since the orbit is precessing, this will be slightly different from the sidereal period - relative to a fixed point on the celestial sphere. A third period which is often given is the anomalistic period - the time from perigee to perigee. Perigee is the point in the orbit which is closest to the Earth center; this also changes with time.

The LST of the ascending node is not constrained by any of these considerations, and is chosen for other reasons, mainly coverage. Power and thermal constraints preclude normal operation within two hours of noon LST. The times usually chosen are either an ascending (northbound) node around 1430 LST or a descending (southbound) node around 0730 LST.

Thus far only the characteristics of the orbit in space have been considered, with no reference to the physical Earth around which the satellite travels (except for the effects of the equatorial bulges). Although the orbital plane is precessing with a period of one year, the Earth is rotating beneath it once per day, causing the satellite to pass over different geographical areas on each pass. The movement is just the amount that the Earth has rotated in one orbital period, and is 25.5 degrees of longitude (in 102 minutes). Since the Earth rotates from west to east, this displacement is westward.