Universal Gravitation

1687 · Mechanics · The companion to Plate I

The Moon test Newton published in his Principia in 1687, worked out step by step.

A Demonstration is a plate’s companion print: the reasoning behind the discovery, worked out on a sheet of its own.

Paper ground, a warm cream, on Hahnemühle Photo Rag, 308 gsm cotton

The plate it accompanies

Plate I, Universal Gravitation: An orbit is a fall that never lands. See it

What it shows

In his Principia of 1687, Newton set out to show that the force holding the Moon in its orbit is the same gravity that makes an apple fall. The Moon is about sixty times farther from the Earth’s centre than an apple on a tree. If gravity weakens with the square of the distance, the Moon should drop below its straight course in a minute as far as the apple falls in the first second after it starts falling.

With today’s figures for the Moon’s distance and the length of the month, the Moon’s drop in a minute comes to 4.9 metres, the same distance the apple falls in one second. The two agree to about one per cent, and most of the difference comes from treating the Earth as fixed, as Newton did.

The sheet sets Newton’s own figures beside today’s. He found that the Moon drops 15 1/12 Paris feet in a minute, or 4.90 metres, and that a body near the ground falls the same distance in one second. The Paris foot was a common unit in the science of the day.

Close up, at about the size it prints at Medium

Step 3 of the sheet: the Moon’s circle, with the right triangle that finds how far it drops in a minute. — Step 3. In one minute the Moon drops 4.9 metres below the straight line it would otherwise follow. Pythagoras’s theorem gives the distance.

Step 7: a square comparing the predicted and measured falls, with a magnified corner. — Step 7. The square compares the drop the law predicts with the drop measured, and its magnified corner shows the gap of about one per cent.

A table of today’s measurements beside Newton’s figures of 1687. — Newton’s figures from 1687 beside today’s. He has the Moon dropping 15 1/12 Paris feet in a minute, which is 4.90 metres.

Hang them together

Plate I

Demonstration I

Demonstration I is the companion to Plate I, Universal Gravitation, which shows the law at work. Hung side by side in the same size and frame, the two cost 10% less bought together.

Plate I and Demonstration I, Medium, 42 × 59 cm each, in black frames.

The sheet

Newton’s Moon test (Principia, 1687, Book III, Proposition IV), with today’s measurements

1The Moon’s distance and its month, as measured
2Its speed along the orbit
3How far it falls in a minute
4Why the fall grows as the square of the time
5An apple’s fall in one second
6The two falls compared
7The inverse square, put to the test
†And a question to take further: the month, predicted from the apple

Sizes and prices

Size	Unframed	Framed	Print
Medium42 × 59 cm	£95$145	£225$295	420 × 594 mm
Large59 × 84 cm	£160$215	£390$515	594 × 841 mm
Extra large84 × 119 cm	£285$385	Unframed only	841 × 1189 mm

Paper: Hahnemühle Photo Rag, 308 gsm cotton, printed as a giclée by theprintspace.
Printed in: London for the UK, Brooklyn for the US. Unframed prints travel rolled in a tube.
Framed medium: A2 frame, glazed with 3 mm acrylic.
Framed large: A1 frame, glazed with 3 mm acrylic.
Extra large: unframed only. A0 is a standard frame size.
Frames: solid wood, finished in black, white or oak veneer, made in Germany. Each comes ready to hang.
Edition: open, with a certificate. File version v1.