Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Orbital Path Shapes
Name: John
Status: educator
Grade: N/A
Location: Md
Country: N/A
Date: 12/25/2004

My question is about orbital paths and projectile motion. A diagram in my Astronomy text (Astronomy Today, Chaisson & McMillan, 4th edition) shows the elliptical shape of all orbits, including those that are "interrupted" by the Earth's surface. From this diagram, one would conclude that projectile motion should take an elliptical path, contrary to what we see in every physics text. Further, the diagram shows that objects that achieve escape velocity have hyperbolic paths. Shouldn't a parabolic curve be possible for speeds in between ellipses and hyperbolas? Is the diagram wrong?

The various conic sections taken by a projectile depends upon whether the kinetic energy of the projectile is less than that accounted for by gravity (a parabola), equal to i.e. in "free fall" (an ellipse), or greater than (a hyperbola).

gives a more quantitative algebraic treatment. For those wanting even more details and are willing to navigate a large physics web site try:

Vince Calder

Click here to return to the Astronomy Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (, or at Argonne's Educational Programs

Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory