Astronomy & space · University
Kepler orbits and gravitational scaling · revision notes
Keplerian orbits approximate isolated Newtonian two-body motion. Real trajectories can include perturbations, drag or relativistic corrections.
Key ideas and conditions
Two-body model
Keplerian orbits approximate isolated Newtonian two-body motion. Real trajectories can include perturbations, drag or relativistic corrections.
Period law
P²=4π²a³/[G(M+m)]. For a negligible planet mass orbiting one solar mass, years and AU give the familiar approximate P²=a³.
Circular motion
Circular speed is sqrt(μ/r), with μ=GM for a dominant central mass. Orbiting bodies are in continuous free fall rather than outside gravity.
Escape
Escape speed from radius r in the isolated Newtonian model is sqrt(2μ/r). This is not a propulsion budget including drag or powered trajectory details.
Explain without looking
- At fixed μ, circular-orbit radius quadruples. Find new speed divided by old speed.
- Name two limitations of an isolated two-body orbit model.
Further reading and review references
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