01 · The speed that makes an orbit
At the same starting radius, how does speed change an orbit?
Predict the path below and above circular speed.
- Pause and set speed to 0.8 times circular speed.
- Run, then reset and compare ratios 1.0 and 1.2.
- Record closest and farthest distances.
Measurement
Compare radius r, speed v, elapsed time and energy error.
Circular motion requires gravity to provide exactly the inward acceleration needed. Other launch speeds produce eccentric paths, collisions or escape, depending on energy and the planet’s radius.
μ=GM in m³/s²; centre distance r in m; v_c in m/s; T in s.
Worked example 1
With μ=3.986×10¹⁴ m³/s² and r=7×10⁶ m, v_c=7546 m/s.
Worked example 2
At that radius T=5829 s≈97.1 min. Doubling r multiplies T by 2√2.
What radius factor doubles a circular orbital period?
Assumptions
Newtonian two-body model with fixed central mass. No drag, third bodies, oblateness or relativity. Visual sizes are illustrative; initial conditions are fictional, not live ephemerides.
University Physics Volume 1, 13.4 Satellite Orbits and Energy