Planetary and Satellite Motion
Student Extras
Need to see it? View the Satellite Motion animation from the Multimedia Physics Studios.
PhET: Gravity and OrbitsExplore satellite motion with this interactive Java applet from PhET. View the orbit of moons and planets or both simultaneously.
Flickr PhysicsVisit The Physics Classroom's Flickr Galleries and enjoy a visual tour of the topic of gravitation.
Shockwave StudiosManipulate, watch and interact with the Orbital Motion activity from the Shockwave Studios.
PhET Simulation: My Solar System
Now here's a chance of a lifetime - build your own solar system with this interactive Java applet from PhET. Total cosmic phun.
Teacher's Guide
This problem-based learning unit targets concepts of universal gravitation and satellite motion.
Newton’s Mountain Model
Re-create the Newton's Mountain thought experiment with this interactive EJS simulation from Open Source Physics (OSP).
PhET: Gravity and OrbitsThis interactive Java applet from PhET allows the user to explore the orbits of satellites, moons and planets. Includes force and velocity displays.
Shockwave StudiosOrbital Motion from the Shockwave Studios is an excellent accompanying activity to this page.
Curriculum CornerPractice makes perfect with this computational activity from The Curriculum Corner.
PhET Simulation: My Solar System
This interactive Java applet from PhET allows students to build their own solar system with up to four bodies. Preset solar systems can also be studied.
Circular Motion Principles for Satellites
A satellite is any object that 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 that a horizontally launched projectile would fall
in its first second is approximately 5 meters
(0.5*g*t2). 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 that it is orbiting. And this acceleration is caused by a net force that is directed inwards in the same direction as the acceleration.
This centripetal force is supplied by gravity - the force that universally acts at a distance between any two objects that 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 that 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 that 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 that acts over even large distances between any two masses. The motion of satellites, like any projectile, is 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 orbiting satellite, then why doesn't the satellite collide into the Earth?