A satellite is any object which is orbiting the earth,
sun or other massive body. Satellites can be categorized as
natural satellites or
man-made satellites. The
moon, the planets and comets are examples of natural
satellites. Accompanying the orbit of natural satellites are
a host of satellites launched from earth for purposes of
communication, scientific research, weather forecasting,
intelligence, etc. Whether a moon, a planet, or some
man-made satellite, every satellite's motion is governed by
the same physics principles and described by the same
mathematical equations.

The fundamental principle to be understood
concerning satellites is that a satellite is a projectile.
That is to say, a satellite is an object upon which the only
force is gravity. Once launched into orbit, the only
force
governing the motion of a satellite is the force of gravity.
Newton was the first to theorize that a projectile launched
with sufficient speed would actually orbit the earth.
Consider a projectile launched horizontally from the top of
the legendary Newton's Mountain - at a location high
above the influence of air drag. As the projectile moves
horizontally in a direction tangent to the earth, the force
of gravity would pull it downward. And as mentioned in
Lesson 3, if the launch speed
was too small, it would eventually fall to earth. The
diagram at the right resembles that found in Newton's
original writings. Paths A and B illustrate the path of a
projectile with insufficient launch speed for orbital
motion. But if launched with sufficient speed, the
projectile would fall towards the earth at the same rate
that the earth curves. This would cause the projectile to
stay the same height above the earth and to orbit in a
circular path (such as path
C). And at even greater launch speeds, a
cannonball would once more orbit the earth, but now in an
elliptical path (as in path
D). At every point along its trajectory, a
satellite is falling toward the earth. Yet because the earth
curves, it never reaches the earth.

So what launch speed does a satellite need
in order to orbit the earth? The answer emerges from a basic
fact about the curvature of the earth. For every 8000 meters
measured along the horizon of the earth, the earth's surface
curves downward by approximately 5 meters. So if you were to
look out horizontally along the horizon of the Earth for
8000 meters, you would observe that the Earth curves
downwards below this straight-line path a distance of 5
meters. For a projectile to orbit the earth, it must travel
horizontally a distance of 8000 meters for every 5
meters of vertical fall. It so happens that the vertical
distance which a horizontally launched projectile would fall
in its first second is approximately 5 meters
(0.5*g*t^{2}). For this reason, a projectile
launched horizontally with a speed of about 8000 m/s will be
capable of orbiting the earth in a circular path. This
assumes that it is launched above the surface of the earth
and encounters negligible atmospheric drag. As the
projectile travels tangentially a distance of 8000 meters in
1 second, it will drop approximately 5 meters towards the
earth. Yet, the projectile will remain the same distance
above the earth due to the fact that the earth curves at the
same rate that the projectile falls. If shot with a speed
greater than 8000 m/s, it would orbit the earth in an
elliptical path.

Velocity,
Acceleration and Force Vectors

The motion of an orbiting satellite can be described by
the same motion characteristics as any object in circular
motion. The velocity of the
satellite would be directed tangent to the circle at every
point along its path. The acceleration
of the satellite would be directed towards the center of the
circle - towards the central body which it is orbiting. And
this acceleration is caused by a net
force which is directed inwards in the same direction as
the acceleration.

This centripetal force is supplied by
gravity - the force which
universally acts at a distance between any two objects
which have mass. Were it not for this force, the satellite
in motion would continue in motion at the same speed and in
the same direction. It would follow its inertial,
straight-line path. Like any projectile, gravity alone
influences the satellite's trajectory such that it always
falls below its straight-line, inertial
path. This is depicted in the diagram below. Observe
that the inward net force pushes (or pulls) the satellite
(denoted by blue circle) inwards relative to its
straight-line path tangent to the circle. As a result, after
the first interval of time, the satellite is positioned at
position 1 rather than position 1'. In the next interval of
time, the same satellite would travel tangent to the circle
in the absence of gravity and be at position 2'; but because
of the inward force the satellite has moved to position 2
instead. In the next interval of time, the same satellite
has moved inward to position 3 instead of tangentially to
position 3'. This same reasoning can be repeated to explain
how the inward force causes the satellite to fall towards
the earth without actually falling into it.

Elliptical Orbits
of Satellites

Occasionally satellites will orbit in paths which can be
described as ellipses. In such
cases, the central body is located at one of the foci of the
ellipse. Similar motion characteristics apply for satellites
moving in elliptical paths. The velocity of the satellite is
directed tangent to the ellipse. The acceleration of the
satellite is directed towards the focus of the ellipse. And
in accord with Newton's
second law of motion, the net force acting upon the
satellite is directed in the same direction as the
acceleration - towards the focus of the ellipse. Once more,
this net force is supplied by the force of gravitational
attraction between the central body and the orbiting
satellite. In the case of elliptical paths, there is a
component of force in the same direction as (or opposite
direction as) the motion of the object. As discussed in
Lesson 1, such a
component of force can cause the satellite to either speed
up or slow down in addition to changing directions. So
unlike uniform circular motion, the elliptical motion of
satellites is not characterized by a constant speed.

In summary, satellites are projectiles
which orbit around a central massive body instead of falling
into it. Being projectiles, they are acted upon by the force
of gravity - a universal force which acts over even large
distances between any two masses. The motion of satellites,
like any projectile, are governed by Newton's laws of
motion. For this reason, the mathematics of these satellites
emerges from an application of Newton's universal law of
gravitation to the mathematics of circular motion. The
mathematical equations governing the motion of satellites
will be discussed in the next part of
Lesson 4.

Check
Your Understanding

1. The fact that satellites can maintain their motion and
their distance above the Earth is fascinating to many. How
can it be? What keeps a satellite up?

2. If there is an inward force acting upon an earth
orbitting satellite, then why doesn't the satellite collide
into the Earth?