CLS-22

Newton gravity

Inverse-square point masses.

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GoverningNewton gravity

Governing equation

F=G m_1 m_2/r^2

$r \in \left[0.05, 4\right]$

where

m1: m1 (kg)
m2: m2 (kg)
r: r (m)
F: Newton gravity (nN)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

F=G m_1 m_2/r^2

$r \in \left[0.05, 4\right]$

$r = 0.05$ $F = 1067.8$

Along the curve

②

Domain of the variable — blue

r_{\min} = 0.05,\quad r_{\max} = 4

$r \in \left[0.05, 4\right]$

$r = 0.05$ $r = 0.05$

Along the curve

③

Response curve — green

F=G m_1 m_2/r^2

$r \in \left[0.05, 4\right]$

$r = 0.05$ $F = 1067.8$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}F}{\mathrm{d}r}

$r \in \left[0.05, 4\right]$

$r = 0.075$ $F^{\prime} = -16085$

Along the curve

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-22 — Newton gravity) is the form associated with Newton gravity. Working symbols: $m1$ , $m2$ , $r$ $\rightarrow$ $F$ . Inverse-square point masses. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

F

from

m1

m2

r

in Classical mechanics via

F=G m_1 m_2/r^2

Inverse-square point masses. 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

m1 = 5.000\,\mathrm{kg}

m2 = 8.000\,\mathrm{kg}

r = 0.400\,\mathrm{m}

, the governing relation

F=G m_1 m_2/r^2

yields

F = 16.685\,\mathrm{nN}

. 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

m1 m15 kgm2 m28 kgr r0.4 m

Outputs

Newton gravity F16.685 nN

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Narration of this film

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

Inverse-square point masses. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube