CLS-27

Circular period

Kepler circular orbit.

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GoverningCircular period

Governing equation

T=2\pi\sqrt{r^3/GM}

where

r: r (km)
M: M (Mearth)
T: Circular period (min)

Lecture brief

Historical brief

Newtonian mechanics (1687) plus energy, angular momentum, Kepler and the ballistic parabola remain the first language of motion. Every sheet here is a closed-form orbit, throw, spin or oscillator. This sheet (CLS-27 — Circular period) is the form associated with Circular period. Working symbols: $r$ , $M$ $\rightarrow$ $T$ . Kepler circular orbit. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

T

from

r

M

in Classical mechanics via

T=2\pi\sqrt{r^3/GM}

Kepler circular orbit. Use it when a real classical mechanics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

r = 7000.000\,\mathrm{km}

M = 1.000\,\mathrm{Mearth}

, the governing relation

T=2\pi\sqrt{r^3/GM}

yields

T = 97.145\,\mathrm{min}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

r r7000 kmM M1 Mearth

Outputs

Circular period T97.145 min

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Kepler circular orbit. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube