4.17 Artificial Satellites

Introduction

A satellite is an object that orbits a larger celestial body, held in its path by the force of gravity. Satellites can be categorized as either natural or artificial.

• Natural satellites are celestial bodies that formed naturally (e.g., the Moon orbiting Earth, or Jupiter's moons: Io, Europa, Ganymede, and Callisto).
• Artificial satellites are human-made objects intentionally placed into orbit. Since the launch of Sputnik 1 in 1957, thousands have been launched for communication, navigation, weather monitoring, and scientific research.

Orbital Mechanics

For a satellite in circular orbit, the gravitational force provides the centripetal force:

$\frac{GMm}{r^2}=\frac{m{v}^2}{r}$

Solving for orbital velocity:

$v_o=\sqrt{\frac{GM}{r}}$

For a satellite orbiting close to Earth's surface ($r\approx R$), using $g=\frac{GM}{R^2}$:

$v_o=\sqrt{gR}\approx 7.9\text{ km/s}$

Note that orbital velocity is independent of the satellite's mass — only the central body's mass $M$ and orbital radius $r$ matter.

Types and Applications of Artificial Satellites

Communication Satellites

Communication satellites relay telephone, television, radio, and internet signals between locations on Earth.

Geostationary Orbit (GEO): Many communication satellites are placed in a geostationary orbit at an altitude of approximately 35,786 km above the equator (orbital radius $\approx 4.22\times 10^7$ m from Earth's center). In this orbit:

• The satellite's orbital period equals Earth's rotation period (24 hours).
• The satellite appears stationary over a fixed point on the equator.
• A fixed ground antenna can always point at the satellite.
• A minimum of 3 geostationary satellites can provide near-global coverage.

INTELSAT (International Telecommunications Satellite Organization, founded 1964) was one of the first providers of global satellite coverage.

Navigation Satellites

Navigation satellites provide precise geo-spatial positioning. A receiver picks up signals from at least 4 satellites and uses trilateration to determine its 3D position (latitude, longitude, altitude).

GPS (Global Positioning System): Developed by the US Department of Defense, it consists of ~30 satellites in Medium Earth Orbit (MEO) and is used for personal navigation, military operations, and precision agriculture.

Weightlessness in Orbiting Satellites

Astronauts in an orbiting satellite experience weightlessness. This is not because gravity is absent — gravity still acts on the satellite (it provides the centripetal force). Instead, weightlessness occurs because:

$W_{apparent}=m(g-g)=0$

Artificial Gravity

Prolonged weightlessness causes muscle atrophy, bone density loss, and cardiovascular problems. To counter these effects during long-duration missions, artificial gravity can be created by rotating the spacecraft around its axis.

The centripetal acceleration experienced by occupants acts as a substitute for gravity:

$a_c={\omega }^{2}R=(2\pi f{)}^{2}R$

To simulate Earth's gravity, set $a_c=g$:

$g=(2\pi f{)}^{2}R⟹f=\frac{1}{2\pi }\sqrt{\frac{g}{R}}$

where $R$ is the radius of the rotating section and $f$ is the rotation frequency. A larger radius requires a smaller rotation frequency to produce the same artificial gravity.