The Energy and Geometry of Orbits

  • Douglas W. MacDougal
Part of the Undergraduate Lecture Notes in Physics book series (ULNP)


The velocities we found for the elliptical orbit were at the apsides, the places where the comet, or the orbiting planet, moon, star or spacecraft is nearest or farthest from one focus of the ellipse. These again are the perihelion and aphelion distances (when referring to the Sun), perigee and apogee (the Earth), perastron and apastron (stars), or more generally for any object, periapsis and apoapsis. These two points in the orbit are important to know, but it is usually essential as well to be able to calculate the precise orbital velocities at other points of the elliptical orbit. How fast will the comet be moving against the stars when it travels past the Earth? Is it on its predicted path, or has its speed been altered by the gravitational influences of another planet during its trip? In another context, it can be critically important to know at each moment the velocity of a vehicle destined for a rendezvous with a moon, planet, comet or asteroid. We want to compare actual with predicted velocity of the vehicle to see if it is on course for the interception. In the Apollo Moon program days, it was vital to know the speed of the returning spacecraft to predict whether it would have a successful “insertion” at just the right spot on reentry, or fly past the Earth and be lost in space. The many smaller probes sent into the corners of our solar system have relied on accurate knowledge of velocity at any point in the orbit. Velocity corrections are commonplace in space vehicles, with short bursts of rocket thrust, to keep them on course.


Circular Orbit Elliptical Orbit Astronomical Unit Gravitational Potential Energy Escape Velocity 
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    Marsden BG, Williams GV (2008) Catalogue of cometary orbits, 17th edn. Central Bureau for Astronomical Telegrams & Minor Planet Center, Smithsonian Astrophysical Observatory, Cambridge, MAGoogle Scholar
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    Clerke AM (2003) A popular history of astronomy during the 18th century. Sattre Press, Decorah, pp 358–359, first printed in 1902Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Douglas W. MacDougal
    • 1
  1. 1.PortlandUSA

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