Vol. Science · Astronomy · The year
A larger orbit takes longer, and the classroom form of that fact is short. For a circular orbit around the Sun — one solar mass, nothing else pulling — when the semi-major axis a is in astronomical units and the period P is in years, P² = a³. The predicted year is P = a3/2. NASA’s Basics of Space Flight states the law in words: the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. NASA Science writes the same relation as p² = a³. That page also rounds three periods — Mercury 88 days, Earth 365 days, Saturn 10,759 days. This desk does not use those rounds. The presets use each NSSDCA fact sheet’s line labeled Semimajor axis (AU), in the Mean Orbital Elements (J2000) block, and that sheet’s sidereal orbit period in days. Earth’s sheet prints 1.00000011 AU and 365.256 days. Divide the days by 365.256 and the fact-sheet year is 1.000. The solar map is where those worlds sit. The pull that makes the law true is the gravity desk. Passing and lining up are retrograde and opposition.
Classroom schematic — top-down, from the north, so the orbit runs counterclockwise. One circle. Its radius tracks the slider on a log scale from 0.30 AU to 40 AU, so Mercury and Neptune share the disk. The planet mark is a dot, not a world drawn to size. Real orbits are slightly eccentric: the fact sheets list 0.0068 for Venus and 0.2056 for Mercury, and the path is an ellipse with the Sun at one focus. In the one-sun law the year still comes from a, not from that eccentricity, so the sheet and a3/2 disagree only a little — rounded means, other planets tugging, and a J2000 element set beside a mean period. The remainder is a classroom comparison. It is not an ephemeris error bar. Play is a time-lapse, not a clock: a 1-year circle laps in about 8 seconds, and a longer period is stretched by that period to the power 0.35, so an outer planet still moves. Not a live position. Not spacecraft trajectory design. Not astrology.
From the north · log radius · Play is a time-lapse
Literacy · the law in solar units
Sources · public NASA pages
Classroom picture of one law: P² = a³ in years and AU, for a circular orbit around one solar mass. Not an ephemeris, not a live sky, and not a trajectory. The AU presets are the fact sheets’ Mean Orbital Elements (J2000). The sidereal periods are the orbital-parameter tables. Fact-sheet years are those days ÷ 365.256. The radius is log-compressed. Play is a time-lapse. Earthrise preview: NASA / Bill Anders (public domain).
Keep going
Neighborhood
Where the eight planets sit. Day and local time, still a schematic, still not this law drawn as a clock.
The pull
The force Kepler did not have. The year on this page is what that pull schedules.
Lineup
Earth between the Sun and an outer planet. A geometry, not a period.
Passing
Earth laps Mars on a faster inner orbit. The loop is the line of sight.
A classroom Sun and one circle, viewed from the north. The radius is log-compressed. The law is P² = a³ in years and AU. Nothing here is tonight’s sky, a finder chart, or a spacecraft path.
| Semi-major axis | The slider. It runs from 0.30 AU to 40 AU on a log scale, a little inside Mercury and a little past Neptune. The live readout is in AU. A free position is the slider, not a fact-sheet figure. |
|---|---|
| Play | The planet mark walks counterclockwise. A 1-year orbit laps in about 8 seconds. Longer orbits take longer by the period to the power 0.35, so Neptune still moves. Pause keeps the place. Play is a time-lapse, not a year and not a mission clock. |
| Mercury through Neptune | Each button snaps a to that planet’s fact-sheet Semimajor axis (AU), the Mean Orbital Elements (J2000) line. The sidereal period from the same sheet appears beside the prediction. Dragging the slider clears the preset. |
|---|---|
| Earth | 1.00000011 AU and 365.256 days, as the Earth Fact Sheet prints them. Fact-sheet years are 365.256 ÷ 365.256 = 1.000. |
| Sun | The center. One solar mass, by the classroom rule. Not a drawing of the photosphere. |
|---|---|
| Slider orbit | The bright circle. Its radius is the slider, log-compressed between 0.30 and 40 AU. A true scale would hide Mercury. |
| Planet mark | A dot on that circle. Size is a mark, not a diameter. It moves only while Play is on. |
| Fact-sheet distances | Eight faint circles at the preset AU values, on the same log scale. They are rulers, not a second solar system in motion. |
| N | North, the view. The orbit runs counterclockwise, the same sense as the other top-down desks. |
| a | Semi-major axis in AU. A preset shows the printed fact-sheet digits. A free slider shows the slider’s AU. |
|---|---|
| Predicted P | a3/2 in years, and the same interval in days: years × 365.256. That 365.256 is Earth’s sidereal orbit period on these sheets. |
| Fact-sheet sidereal | Shown when a preset is on. Days as printed, and years = days ÷ 365.256. Off a preset, the law still predicts a period. There is no sheet to compare. |
| Remainder | Predicted days minus the fact-sheet days. A little, on purpose. Not an uncertainty. |
| a³ and P² | Predicted P² equals a³ by the classroom law. Fact-sheet P² is the sheet’s year, squared. The two sit near each other. They are not forced to match. |