with the various types of years, the month is defined in several ways, depending on the measurement reference. For most purposes, the fundamental intervals are: the sidereal month relative to the fixed stars, about 27.32 days; the synodic month from new moon to new moon, about 29.53 days; and the nodical or draconic month from node to node, about 27.21 days. Other periods are listed in Appendix L. Section 5.5 gives an algebraic approximation which may be used to model the position of the Moon, as seen from the Garth, to within about 0.25 deg.

33 Spacecraft Orbits

Vehicles or objects launched into space are categorized by their orbit. Ballistic missiles and sounding rockets travel in elliptical orbits which intersect the surface of the Garth; this is frequently called a ballistic trajectory because it is also the path of a bullet or cannon shell. The ballistic missile and sounding rocket are distinguished by their function—a missile is used to strike some specific target, whereas a sounding rocket is used to make measurements in or above the Earth's atmosphere. A sounding rocket may either impact the surface, burn up in the atmosphere, or be recovered by parachute.

Any object which travels in an elliptical orbit around a planet is called a satellite of that planet. The semimajor axis of a satellite orbit must be at least as large as the radius of the planet, whereas the semimajor axis for a sounding rocket may be as small as approximately half the radius of the planet.* Because the total energy of a spacecraft depends only on the semimajor axis, the energy of a sounding rocket is normally, though not necessarily, much less than that of an Earth satellite. However, sounding rockets and ballistic missiles frequently reach altitudes well above those of low-Earth satellites because they travel in very elongated elliptical orbits.

If the velocity of an object is greater than the escape velocity of a planet, it will be an interplanetary probe traveling in a hyperbolic trajectory relative to the planet and, after it has left the vicinity of the planet, traveling in an elliptical orbit about the Sun. Finally, if an object attains a velocity greater than the Sun's escape velocity, it will be an interstellar probe. Pioneer 10, swinging past Jupiter in December 1973, gained sufficient energy in the encounter (as described later in this section) to become the first manmade interstellar, probe.

All known satellites or probes are assigned an international designation by the World Warning Agency on behalf of the Committee on Space Research, COSPAR, of the United Nations. These designations are of the form 1983-14D, where the first number is the year of launch, the second number is a sequential numbering of launches in that year, and the letter identifies each of the separate objects launched by a single vehicle. Thus, the docking module for the first Apollo-Soyuz flight, object 1975-66C, was the third component of the 66th launch in 1975.

In addition to the international designation, most satellites are assigned a

•Assume all the mass of the Earth is concentrated at its center and a high platform is built to the former location of New York City. An object dropped from the platform will not go all the way to the former location of Australia, but will swing very rapidly around the central mass (with perigee essentially at the center) and return to apogee at the platform tip. (Use Eq. (3-3) with V=0.) Therefore, the semimqjor axis win be about half the radius of the Earth and the total energy will be a factor of two less than that for a circular orbit at the Earth's surface.

name by the launching agency. For NASA, spacecraft in a series are given a letter designation prior to launch, which is changed to a number after a successful launch. Thus, the second Synchronous Meteorological Satellite was SMS-B prior to launch and SMS-2 after being successfully placed in orbit. Because of launch failures or out-of-sequence launches, the lettering and numbering schemes do not always follow the pattern A = 1, B = 2, etc. For example, in the I nterplanetary Monitoring Platform series, 1MP-B failed on launch, IMP-E was put into a lunar orbit and given another name, and IMP-H and -I were launched in reverse order; thus, 1MP-1 became IMP-6 and IMP-H became 1MP-7. Satellites may also be assigned numbers in different series; IMP-6 was also Explorer-43 and IMP-7 was Explorer-47.

The trajectory of a spacecraft is its path through space. If this path is closed (i.e., elliptical) then the trajectory is an orbit. Thus, correct usage would refer to a satellite in an elliptical orbit or a spacecraft or probe on a hyperbolic trajectory. Although this distinction is maintained at times, orbit and trajectory are often used interchangeably. For satellites it is frequently convenient to number the orbits, so that one may refer to "a maneuver on the sixth orbit." In standard NASA practice, that portion of the orbit preceding the first ascending node is referred to as orbit 0 or revolution 0; orbit 1 or revolution 1 goes from the first ascending node to the second ascending node, etc. Note that revolution refers to one object moving about another in an orbit, whereas rotation refers to an object spinning about an axis;

When spacecraft are launched by a multistage vehicle, the initial stages will be fired and subsequently jettisoned; however, the final stage may remain inactive and attached to the spacecraft during a coasting phase or parking orbit. The final stage is then ignited or reignited to inject or place the spacecraft into its proper orbit-* As defined in Chapter 1, a mission orbit is one in which a satellite will be conducting normal operations. A transfer orbit is one which is used to maneuver a spacecraft from one orbit to another, as in the case of the Apollo transfer orbit to the Moon or the Apollo Command Module transfer orbit back to Earth.

A satellite which revolves about the Earth in the same direction that the planet rotates on its axis is in a prograde or direct orbit; if it revolves in a direction opposite to the rotation, the orbit is retrograde. As shown in Fig. 3-12, the inclination of an Earth-satellite orbit is measured from east toward north; therefore, the inclination of a prograde satellite is less than 90 deg and the inclination of a retrograde satellite is greater than 90 deg. In a polar orbit, i = 90 deg. Most satellites are launched in a prograde direction because the rotational velocity of the Earth provides a part of the orbital velocity. Although this effect is not large (0.46 km/sec for the Earth's rotational velocity at the equator, compared with a circular velocity of 7.91 km/sec), the available energy is typically the limiting feature in a space mission. Thus, all factors which change the energy which must be supplied by rockets are important.

•Only a limited number of upper stages are capable of being reignited. Among these are the'Agena used for unmanned spacecraft and the Service Propulsion System from the Apollo program, both of which use hypergolic fuel which ignites when the two fuel components come in contact. The largest reignitable American rocket currently planned is the Space Shuttle, which has three engines with a total vacuum thrust of about 6Jx 10® N (20% of that of the Saturn V first stage) from a hydrogen/oxygen system.

From Kepler's Third Law, the period, P, of an Earth satellite depends only on the mean altitude (see Eqs. (3-4) and (3-9)); that is,

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