The Complete Book of Spaceflight: From Apollo 1 to Zero Gravity

230 Lagrangian orbit
carries an array of 426 prisms that reflect ground-based
laser beams back to their source. By measuring the time
between the transmission of the beam and the reception of
the reflected signal, stations can measure the distance
between themselves and the satellite to an accuracy of 1 to
3 cm. Long-term data sets can be used to monitor the
motion of Earth’s tectonic plates, measure Earth’s gravitational
field, measure the wobble in Earth’s rotational axis,
and better determine the length of an Earth day. Lageos 1
was developed by NASA and placed into a high inclination
orbit to permit viewing by ground stations around the
world. Lageos 2 was a joint program between NASA and
ASI (the Italian Space Agency), which built the satellite
using Lageos 1 specifications and materials provided by
NASA. Lageos 2’s orbit was chosen to provide more coverage
of seismically active areas, such as the Mediterranean
Sea and California, and to help scientists understand irregularities
noted in the motion of Lageos 1. Lageos 1 contains
a message plaque addressed to humans and other
beings of the far future with maps of Earth from three different
eras—268 million years in the past, the present day,
and 8 million years in the future (the satellite’s estimated
decay date). Both satellites are spherical bodies with an aluminum
shell wrapped around a brass core. The design was
a compromise between numerous factors, including the
need to be as heavy as possible to minimize the effects of
nongravitational forces, to be light enough to be placed in
a high orbit, to accommodate as many retroreflectors as
possible, and to minimize surface area to minimize the
effects of solar pressure. The materials were chosen to
reduce the effects of Earth’s magnetic field on the satellite’s
orbit. (See table, “Lageos Missions.”)
Lagrangian orbit
The orbit of an object located at one of the Lagrangian
points.
Lagrangian point
One of five equilibrium points at which a spacecraft or
some other small object can remain in the same relative
position in the orbital plane of two massive bodies, such as
the Earth and the Sun, or the Earth and the Moon.
Lagrangian points are named after the Italian-born French
mathematician Joseph Louis de Lagrange (1736–1813),
Lageos Missions
who first demonstrated their existence mathematically. Two
of these points, known as L4 and L5, are said to be stable
because an object placed at one of them will, if slightly displaced,
return to the point rather than move farther away.
The L5 point of the Earth-Moon system, located 60°
behind the Moon in its orbit (as seen from Earth), has been
proposed as an ideal site for a space colony. However, to
date, all practical spaceflight applications have focused on
unstable Lagrangian points—L1, L2, and L3—so called
because the slightest disturbance to any object located at
one of them will cause the object to drift away permanently
unless it makes a correction (a station-keeping maneuver)
using an onboard propulsion system. The L1 and L2 points
have proven particularly useful and are being used increasingly
by a variety of scientific satellites. The L1 point of the
Sun-Earth system—about 1.5 million km directly Sunward
of Earth—affords a good spot for monitoring the solar wind,
which reaches it about one hour before reaching Earth.
Beginning in 1978, ISEE-3 carried out solar wind observations
from the L1 region for several years. More recently,
Wind, SOHO, ACE, and Genesis have studied the Sun
and its particle emissions from the same celestial perch. The
preferred position is actually some distance to the side of
L1, for if the spacecraft is right on the Sun-Earth line, the
antennas that track it from Earth are also aimed at the Sun,
which is an intense source of interfering radio waves. At the
Spacecraft Date
Launch
Vehicle Site Orbit Mass (kg)
Lageos 1 May 4, 1976 Delta 2914 Vandenberg 5,837 × 5,945 km × 109.8° 411
Lageos 2 Oct. 22, 1992 Shuttle STS-52 Cape Canaveral 5,615 × 5,952 km × 52.6° 400
L3
Sun
L4
L5
L1 L2
Earth
Lagrangian point The five Lagrangian points in the Sun-
Earth system.