A small burn. A different orbit.

The question. Seeing Jupiter’s moons through my great-grandfather’s telescope made me want to see how orbits change over time. Here is one experiment from the sandbox: what happens when a spacecraft in a circular orbit gains 100 m/s?

A circular orbit. Start 400 km above Earth. At 7.669 km/s, the two-body model gives a circular orbit with a 92.56 minute period. Speed and distance are linked by v = √(μ/r).

Change velocity. At mission time 0, execute a 100 m/s transverse burn in the direction of motion. Position stays fixed. The added velocity increases orbital energy and changes the path to an ellipse.

Check the result. The burn point stays at 400 km altitude. Apoapsis rises to 765.5 km. A separate vis-viva calculation predicts 765.5 km. The spacecraft slows as it climbs toward apoapsis.

Test the model. These results assume one spherical central body and an instantaneous burn. Earth’s equatorial bulge changes the gravity field. How long does the simpler prediction remain close enough? Compare both models using the same initial state and a stated distance threshold.

Predicted and simulated apoapsis differ by 2.73e-12 km. That agreement checks this two-body calculation; it does not validate a complete real-world force model.