Circular Orbits

Wrong Speed-Square Does Not Close

A wrong speed-square renders as a rejected circular ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The wrong candidate still renders as a checked ledger

Try speed-square 3 at the same radius 4.

v2=3v^{2}=3
Wrong speed-square candidateThe diagram is valid but marked rejected by arithmetic.mu=16 m^3/s^2radius=4 mradiusSquared=16 m^2field=1 m/s^2speedSquared=3 m^2/s^2centripetalAcceleration=3/4 m/s^2acceptedBit=0 bit

Three over four does not equal the field one

The candidate acceleration is 3 over 4, not the checked field 1.

v2r=34≠1\frac{v^{2}}{r}=\frac{3}{4}\ne 1
Rejected circular closureThe accepted bit is zero because acceleration does not equal field.mu=16 m^3/s^2radius=4 mradiusSquared=16 m^2field=1 m/s^2speedSquared=3 m^2/s^2centripetalAcceleration=3/4 m/s^2acceptedBit=0 bit