IndexGaya & MedanMug

Keplora

Kepler’s Third Law Physics

\[T^{2} = \frac{4\pi^{2}}{GM}\,a^{3}\]
$21.99 USD
$21.99 USD
Obral Habis
Size

Why is a year on Neptune 165 Earth years? Keplora counts the laps. Kepler’s third law, T² = (4π²/GM)a³, ties a planet’s orbital period to its average distance from the Sun. Farther out, the orbit is longer and the planet moves slower. Pixel-art black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingBy destination

Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

The square of a planet's orbital period is proportional to the cube of its orbit's size. Newton showed the constant depends only on the central mass, so periods and distances can be used to weigh the Sun.

Keplora counts the laps, and the outer ones take longest.

Johannes Kepler, working from Tycho Brahe's observations, announced his third law in 1618: the square of a planet's orbital period is proportional to the cube of its average distance from the Sun. Decades later Newton showed it follows from his law of gravity, which supplies the constant on this mug.

Neptune is about 30 times farther from the Sun than Earth. Thirty cubed, square-rooted, is about 165, and Neptune's year is about 165 Earth years. FARTHER OUT. LONGER YEAR. An outer planet has a longer path and also moves more slowly along it.

The formula as written uses the Sun's mass alone. Strictly it should be the Sun plus the planet, which matters for binary stars and moons but barely at all for planets. The same law lets astronomers weigh stars from the orbits of their planets.

Keplora never rushes. Her year is set by how far out she runs.

Equations

\[T^{2} = \frac{4\pi^{2}}{GM}\,a^{3}\]
SymbolMeaningUnit
\(T\) orbital period \(\mathrm{s}\)
\(a\) semi-major axis of the orbit (average of the closest and farthest distances) \(\mathrm{m}\)
\(G\) Newtonian constant of gravitation \(\mathrm{m³·kg⁻¹·s⁻²}\)
\(M\) mass of the Sun (central body); the planet's mass is neglected \(\mathrm{kg}\)

Sources

  1. HyperPhysics — Kepler's Laws
  2. Encyclopaedia Britannica — Kepler’s laws of planetary motion
  3. NASA Science — Neptune Facts
  4. NASA NSSDCA — Neptune Fact Sheet (semimajor axis, orbital period)

Source Kepler, J. (1619). Harmonices Mundi, Book V. Linz: J. Planck.

Field notes

Lihat semua
1 3
Lihat semua