Sections · Light time

Vol. Science · Astronomy · The delay

Light time
across the system

Pick a date and two bodies. The distance between them is divided by the speed of light. One way is that quotient. The round trip, the wait for a radio answer, is twice it. c = 299,792,458 m/s exactly, the SI defining constant. One astronomical unit is 149,597,870,700 m exactly, the IAU 2012 value, so 1 AU of light time is 499.005 seconds, 8.317 minutes, about 8.3 minutes. Planet places are the JPL approximate Keplerian elements of Standish and Williams, Table 1, valid 1800–2050. The Moon is held at the fact-sheet mean, 384,400 km, and the perigee 363,300 km and apogee 405,500 km are labeled, not solved. A Mars rover cannot be joysticked live: Earth–Mars runs roughly 3 to 22 light-minutes. The Moon’s mean round trip is about 2.5 seconds. The year of a circular solar orbit is the Kepler desk. The milliseconds of a station overhead are the satellites desk.

Educational schematic. Not a JPL Horizons ephemeris. Earth on this page is the Earth–Moon barycenter from Table 1. The date is read as 12:00 UTC. The delay is the straight-line distance at that instant divided by c. The bodies are not moved forward by the flight time, and there is no Shapiro delay. Published heliocentric distance tolerances for 1800–2050 run from 1 × 1000 km (Mercury) to 1,500 × 1000 km (Saturn). Mars is 25 × 1000 km. Jupiter is 600 × 1000 km. A separation can miss by more than either figure. Pluto is a historical row the current table no longer prints, and the page gives it no fake tolerance. Spacecraft ranges are not stored here.

What this means

Literacy · c, the au, and the fit

Speed of light

c = 299,792,458 m/s exactly. The metre is defined by fixing that number. A radio signal in vacuum and a pulse of light take the same time. The satellites desk uses the same c for a hop straight down to the ground, which is milliseconds.

Astronomical unit

1 au = 149,597,870,700 m exactly, IAU 2012 Resolution B2. It is a defined length, not this year’s measured Earth–Sun distance. Light crosses it in 499.005 seconds, 8.317 minutes. The Kepler desk measures orbits in this unit.

One way and round trip

One way is the geometric distance divided by c. The round trip is twice that, the wait if a signal goes out and the answer comes straight back along the same line. A tracking pass is not always that straight line. This page draws the straight line.

Table 1

Six Keplerian elements and their rates per century, for 1800–2050, from Standish and Williams via JPL. Mean anomaly, then Kepler’s equation, then a rotation into the J2000 ecliptic. Table 2, and the extra terms that belong to it, are not used. Outside 1800–2050 the slider stops.

The Moon’s circle

Semimajor axis 384,400 km, sidereal period 27.3217 days, inclination 5.145° to the ecliptic. The node is held fixed, as on the solar map. That is a direction for the diagram. The Earth–Moon distance on the card does not change with the date. Perigee and apogee are the fact sheet.

What the number leaves out

Light-time iteration, aberration, the Shapiro delay, and the few thousand kilometres between Earth’s center and the Earth–Moon barycenter. The barycenter is what Table 1 calls Earth. Pluto is the historical row the solar map already uses, semimajor axis 39.482 AU, and the current JPL page publishes no Pluto error. A spacecraft distance is a link, not a stored figure.

Tolerances · JPL Table 1, 1800–2050

Sources · public pages

Classroom picture of a straight-line delay. c is the SI constant. The astronomical unit is IAU 2012 Resolution B2. Planet positions are JPL Table 1. The Moon is a mean-distance circle with the fact-sheet range labeled. Pluto is the historical row, flagged as such. Not a JPL Horizons ephemeris. Earthrise preview: NASA / Bill Anders (public domain).

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