Hold a finger out and blink from eye to eye. The finger seems to jump against the far wall. The finger stayed put. Your eyes moved. A nearby star does that as Earth goes around the Sun: it seems to shift against the distant stars. That shift is parallax. It is the line-of-sight change from Earth’s orbit, not the star sliding sideways on its own. The short side of the triangle is the baseline, 1 AU. The half-angle at the star, for that baseline, is the annual parallax p. Distance in parsecs is 1 divided by p in arcseconds. One parsec is the distance where p is one arcsecond. The nearest stars desk is the neighborhood this yardstick measures. The solar map is the same orbit, drawn for the planets.
Classroom schematic — a circular orbit, flattened into one plane with the star, disks and the nearby star enlarged so a phone can see the triangle. The Earth Fact Sheet lists orbit eccentricity 0.0167; this circle leaves that out. The slider is a 365-day classroom year, not that sheet’s 365.256-day sidereal period. That count is the orbit. One spin against the stars is the shorter sidereal day. The arcseconds in the panel are the teaching figures cited below, run through d(pc) = 1 / p(″). The wedge on the canvas is drawn large. Not a precision ephemeris, not Gaia catalog precision, not a finder chart, and not astrology. It does not point Proxima or Sirius.
Interactive · Earth, Sun, and a nearby star
Drag Earth · or slide the day · star drawn far too close · baseline = 1 AU
Against the background · shift exaggerated · not a chart
Sun
Earth · drag
Nearby star
Background
Baseline · 1 AU
Apr 2
Literacy · words for the yardstick
Annual parallax
The yearly shift of a nearby star against more distant stars, caused by Earth’s orbit. ESA’s Gaia parallax page puts it as the finger trick: blink from eye to eye and the finger moves against the background, and every six months Earth gives a new vantage point. A NASA Hubble caption says the same thing in one line: stars appear to slightly shift against very distant stars over the course of a year. The star in this drawing is held still.
Arcsecond
A small angle. ESA’s cosmic-distances page divides a circle into 360 degrees, a degree into 60 arcminutes, and an arcminute into 60 arcseconds. An arcsecond is 1/3600 of a degree, which is also how the stellar-distances page puts it. A milliarcsecond is one thousandth of an arcsecond. The panel’s milliarcseconds are that conversion of the arcsecond figure, not a separate measurement.
Parsec
The distance at which the parallax is one arcsecond. NASA’s Hubble caption says one parsec is the distance creating a parallax of one arcsecond, equal to 3.26 light-years. ESA’s stellar-distances page derives the name the same way — “parallax of one arcsecond” — and prints 1 parsec = 3.26 light years = 206 265 AU. Then d(pc) = 1 / p(″). An archival NASA GSFC lesson says no star is that close. The “1 parsec” button is the definition, drawn so the formula reads 1.
Light-year
The distance light travels in one year. ESA’s cosmic-distances page calls it about 9.5 million million kilometres. The same page, and the NASA caption, and the ESA stellar-distances page, all put 1 parsec at 3.26 light-years. Light-years on this desk are the parsec figure times 3.26. Proxima’s 4.22 and Sirius’s 8.6 are the products ESA already prints.
Baseline · 1 AU
The Sun–Earth side of the triangle. The Earth Fact Sheet lists the semimajor axis as 149.598 × 106 km, and the J2000 elements list it as 1.00000011 AU. This circle calls that scale 1 AU and ignores the sheet’s eccentricity 0.0167. NASA’s Hubble note uses the diameter, 186 million miles, when the baseline runs from one side of the year to the other. The label on the canvas is the radius.
Sources · public NASA and ESA
Cited, not invented
NASA NSSDCA — Earth Fact Sheet — semimajor axis 149.598 × 106 km; J2000 semimajor axis 1.00000011 AU; orbit eccentricity 0.0167; sidereal orbit period 365.256 days. The baseline label is 1 AU. The circle does not use the eccentricity. The slider counts 365 days.
NASA Science — Hubble image of ESO 300-16 — the motion of Earth around the Sun makes stars appear to slightly shift against very distant stars over a year. That shift is parallax. One parsec is the distance creating a parallax of one arcsecond, equal to 3.26 light-years or 30.9 trillion kilometers (19.2 trillion miles). The closest star to the Sun is Proxima Centauri, at 1.3 parsecs. Image credit on that page: ESA/Hubble & NASA, R. Tully. One divided by 1.3 is about 0.77 arcseconds, about 770 milliarcseconds. That reciprocal is a classroom reading of NASA’s rounded 1.3 parsecs. It is not a catalog parallax, and the Proxima button does not use it.
ESA Science & Technology — Stellar distances — parallax is the apparent movement of a nearer object against distant ones. The parsec is “the distance at which an object has a parallax of one arcsecond.” An arcsecond is 1/3600 of a degree. 1 parsec = 3.26 light years = 3.09 × 1013 km = 206 265 AU. The parallax is the angular radius of Earth’s orbit as seen from the star, and d(parsec) = 1 / p(arcsecond). The table lists Proxima Centauri, the closest star to the Sun, at 1.294 parsec and 4.22 light years (also 3.99 × 1013 km and 2.67 × 105 AU). The Proxima button’s p is 1 / 1.294, so the distance reads that table back. Sirius (α Canis Major) is the worked example: parallax 0.37921 arcseconds, distance 1 / 0.37921 = 2.637 parsecs, times 3.26 is 8.6 light-years.
ESA — Gaia, Parallax — even the nearest star is 40 trillion kilometres away. Every six months Earth is a new vantage point, and the star seems to move against more distant stars. For the nearest stars that apparent movement is less than one arcsecond. Gaia measured positions of one billion stars to microarcsecond accuracies. This page does not reprint a Gaia catalog.
ESA — Gaia, Cosmic distances — a light-year is the distance light travels in one year, about 9.5 million million kilometres. A parsec is 3.26 light-years, or nearly 31 trillion kilometres, the distance for a parallax angle of one arcsecond. An arcminute is 1/60 of a degree. An arcsecond is 1/60 of an arcminute. A milliarcsecond is one thousandth of an arcsecond. A microarcsecond is one millionth.
NASA Science — Hubble stretches the stellar tape measure — the reliable distance method is geometry, using the 186-million-mile diameter of Earth’s orbit as the baseline of a triangle. A close enough star zigzags through the year as a reflection of Earth’s orbit. That is parallax. It works for stars within a few hundred light-years. Alpha Centauri, the nearest star system, varies by only one arc second over the year on that page, the apparent width of a dime seen from two miles away. Farther stars make a smaller angle. The one-arc-second line is that page’s example. It is not the p on these buttons.
NASA GSFC — Parallax (archival ISTP lesson) — a parsec is the distance to a star whose yearly parallax is 1″, one second of arc. One parsec equals 3.26 light years, and no star is that close. The page gives Alpha Centauri a distance of 4.3 years and a parallax of 0.75″. It also calls the biggest baseline the diameter of Earth’s orbit, 300,000,000 kilometers, the separation of two positions half a year apart. The page is kept online for archival use and is no longer updated. This slider does not use the 0.75″ figure.
Classroom picture of an angle becoming a distance. Proxima’s parallax on the button is the reciprocal of ESA’s 1.294 parsec, not a Gaia measurement. Sirius’s 0.37921″ is the parallax ESA prints, and the parsecs and light-years are that page’s arithmetic. The 1 parsec button is the definition: p = 1″, d = 1 pc, 3.26 light-years. Today’s angle is p times the sine of Earth’s angle from the star, so it equals p when the baseline is broadside. The six-month swing on the lower strip is that angle from one side of the orbit to the other, drawn huge. Not an ephemeris, not a catalog, not a pointing aid. Earthrise preview: NASA / Bill Anders (public domain).