02 · Falling without landing
How can a satellite keep falling without reaching the ground?
Without gravity, would it move radially outward or along the tangent?
- Start a circular orbit and show vectors.
- Pause and advance one step at a time.
- Compare how velocity and acceleration turn.
Measurement
Compare x, y, v_x, v_y and |a| at two positions.
Velocity carries the body along a tangent while gravity bends its path inward. Apparent weightlessness is shared free fall, not the absence of gravity. In circular motion acceleration changes direction without changing speed.
r is position vector in m; a in m/s²; v in m/s.
Worked example 1
At r=7×10⁶ m, acceleration is 8.13 m/s², far from zero.
Worked example 2
In 1 s the small inward fall is approximately aΔt²/2=4.07 m while tangential travel is about 7.55 km.
Use a dot product to check perpendicular velocity and acceleration.
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, 13.2 Gravitation Near Earth’s Surface
University Physics Volume 1, 13.4 Satellite Orbits and Energy