What is it about?
Given two points relative to a central body, what are the possible orbits that connect them? These includes ellipses, a parabola, and hyperbolas. I use the orbits' "half-widths" (amusingly called the semi-latus rectum) to parameterise these paths. If one knows the time interval between the two positions, the connecting orbit becomes uniquely specified - there is only one possibility, and I show how to find that with a straightforward numerical search.
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Photo by NASA Hubble Space Telescope on Unsplash
Why is it important?
Orbit determination from 2 observations is relevant for newly discovered asteroids - will their orbits intersect Earth's? Also for mission planning, one wants to find the most fuel-efficient orbit that results in interception or rendezvous. In the supplement I even mention targeted re-entry, such as may be required with Star Trek escape pods!
Perspectives
The treatment of these topics in advanced textbooks is needlessly complicated, involving parameters that have no or obscure physical meaning. I try to break the problem down into easy steps that are transparent and interesting to teachers and students of physics and aerospace engineering. I am most proud of the MS Excel spreadsheet orbit plotter/solver that I provide in the supplementary materials. With it, one can solve many problems in the real world as well as problems posed in advanced textbooks. (Look up the "Lambert Problem") - all in a few easy steps.
Dr. Philip Blanco
Grossmont College
Read the Original
This page is a summary of: Connect the dots… finding all possible orbits between two points, European Journal of Physics, July 2025, Institute of Physics Publishing,
DOI: 10.1088/1361-6404/ade37d.
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