Space

The Solar System on the day you were born

Where every planet was on your birth date, how far each one was from Earth, which were in the evening sky, what the Moon looked like, and when each planet comes back to the spot it held that day. The positions come from an N-body integration started from NASA JPL’s own state vectors, and further down each kind of result is checked against JPL, the US Naval Observatory or the textbook it comes from. Nothing you type leaves your browser.

Your birth date

Any date from 1800 to 2199 works. The time of day matters most for the Moon, which moves about 13° a day against the stars, and then for Mercury, up to 6.3° a day; the outer planets barely move. Leave the time blank and noon is used. The page opens on 15 June 1990 at midnight UTC, the worked example below, so the first numbers you see are ones you can check against JPL yourself.

Date of birth Time of birth (optional: noon if left blank) Time zone at the birthplace on that date (UTC offset)

What it assumes. Positions are heliocentric and geometric — where each planet was at that instant, not where its light seemed to come from — measured around the ecliptic from the equinox of J2000, a direction fixed against the stars, so 0° points the same way on every date. Earth means Earth’s centre. Your clock time becomes the integration’s time scale through NASA’s ΔT polynomials, 57 seconds in 1990. The maps look down from the north side of Earth’s orbit, where every planet travels anticlockwise; the Moon is drawn as seen from the Northern Hemisphere, and is mirrored left to right from the Southern. “Evening” means east of the Sun, setting after it; within 10° of the Sun, or of the point opposite it, east and west stop meaning much, and the table says so instead. How far each number can be trusted is measured below.

How the positions are calculated

The starting point is JPL’s own answer for one instant: the position and velocity of each of the eight planets — each counted with its moons, as one body at their common centre of mass — at JD 2451545.0, noon TDB on 1 January 2000, from the DE441 ephemeris behind NASA’s Horizons system. From there the page integrates Newton’s law of gravity for the Sun and the eight planets, one day at a time, forward or backward to your date. It is the same integrator and the same starting vectors that drive this site’s 3D universe simulator.

The method is a Wisdom–Holman map in the democratic heliocentric coordinates of Duncan, Levison and Lee (1998): positions measured from the Sun, velocities from the centre of mass of the whole system. Each one-day step is five exact pieces:

1. kick v_i += (h/2) · Σ_j≠i G m_j (Q_j − Q_i) / |Q_j − Q_i|³ 2. drift Q_i += (h/2) · Σ_j (m_j/M_Sun) v_j 3. Kepler every planet follows its exact two-body orbit about the Sun for h 4. drift as 2 5. kick as 1 Q_i = planet i’s position from the Sun · v_i = its velocity relative to the centre of mass · m_j = planet masses, M_Sun = the Sun’s · h = 1 day. Step 1 is the planets pulling on each other; step 2 is the Sun’s own recoil; step 3 solves Kepler’s equation for the change in eccentric anomaly and moves each planet with the f and g functions.

A map built this way is symplectic: its energy error stays bounded instead of drifting. Measured at every day for 200 years in each direction from 2000, the relative energy error never exceeds 3 × 10⁻⁹. The step length matters more than that suggests, because Mercury goes round in 88 days. Against JPL at 3,000 random instants from 1800 to 2199, a one-day step keeps Mercury within 0.022°; a two-day step lets it wander 0.21°, and a four-day step 0.99°. So the step is one day.

From the positions on your date, everything in the table is geometry:

longitude around the Sun L = atan2(y, x) from the Sun r = |Q_p| from Earth Δ = |Q_p − Q_E| angle from the Sun cos ψ = (Q_p − Q_E) · (−Q_E) / (Δ · |Q_E|) x, y, z = heliocentric position in the J2000 ecliptic frame, x toward the equinox · Q_E = Earth’s centre. The planet is east of the Sun, in the evening sky, when the z-component of (−Q_E) × (Q_p − Q_E) is positive.

One correction is not in the simulator. Its “Earth” is the centre of mass of Earth and Moon, which Earth’s own centre circles once a month; at 3,000 random instants from 1800 to 2199 the gap reached 4,942 km. The page moves Earth to its centre, 0.012150584 of the Earth–Moon distance on the far side from the Moon — the ratio read from Horizons’ own Earth, Moon and barycentre vectors — with the Moon placed by the leading terms of Meeus’s lunar tables: the first 13 rows of his Table 45.A for longitude and distance, and the four largest terms of Table 45.B for latitude. At those same 3,000 instants this correction matched the offset between Horizons’ Earth and its Earth–Moon barycentre to within 16 km.

Checked against JPL: 15 June 1990

At 00:00 UT on 15 June 1990 (TDB 57.2 seconds later) this is what the calculator returns, beside the heliocentric vectors JPL Horizons gives for the same instant, in the same frame:

Planet	This page: longitude, distance from the Sun	JPL Horizons	Gap
Mercury	358.0358°, 0.357486 AU	358.0348°, 0.357485 AU	929 km
Venus	354.0348°, 0.726911 AU	354.0349°, 0.726911 AU	176 km
Earth	263.7876°, 1.015716 AU	263.7874°, 1.015716 AU	426 km
Mars	326.1835°, 1.383047 AU	326.1837°, 1.383047 AU	526 km
Jupiter	110.1301°, 5.210656 AU	110.1301°, 5.210656 AU	7 km
Saturn	291.2455°, 10.013233 AU	291.2455°, 10.013233 AU	16 km
Uranus	277.5584°, 19.409503 AU	277.5584°, 19.409503 AU	12 km
Neptune	283.1940°, 30.206652 AU	283.1940°, 30.206652 AU	10 km

That morning Mars was 1.2819 AU from Earth and 73° west of the Sun, in the morning sky; Jupiter was the only planet east of the Sun. One trap if you check this yourself: Horizons’ observer tables list Mars’s heliocentric longitude at that moment as 326.1790°, not 326.1837°. Those tables give the position at the instant the light left the planet, 10.7 minutes earlier at that distance. The vector table gives the instantaneous position, which is what this page computes.

A textbook check, independent of JPL: Jean Meeus’s Example 31.a puts Venus on 1992 December 20 at 0h dynamical time at L = 26.11428°, B = −2.62070°, R = 0.724603 AU, from the VSOP87 planetary theory, measured from the equinox of that date rather than J2000. The integration gives 26.21230° from the J2000 equinox; carried to the equinox of the date with Meeus’s rigorous precession formulas (chapter 20), that becomes 26.11402°, −2.62060°, 0.724602 AU — within one arcsecond of the book.

One date proves little, so the calculator was also run on 3,000 random birth dates, times and time zones from 1800 to 2199, and every answer was compared with Horizons’ vectors for the same instant. The worst errors among them:

Planet	Worst longitude error, 1800–2199	Worst position error
Mercury	0.022°	26,351 km
Venus	0.0020°	3,687 km
Earth (its centre)	0.0035°	9,252 km
Mars	0.0031°	11,102 km
Jupiter	0.00002°	284 km
Saturn	0.00002°	394 km
Uranus	0.00002°	1,158 km
Neptune	0.00004°	2,847 km

The errors grow with distance from 2000 in both directions, and Mercury’s is the largest. The integration is Newtonian, while DE441 is integrated with the relativistic (post-Newtonian) equations of motion (Park and others, 2021), and the difference shows most in Mercury, the planet closest to the Sun: in the integration its perihelion falls behind JPL’s by 43.0 arcseconds a century, and a test copy with the Sun’s relativistic term added closes that gap to 0.2. At the one decimal place the calculator shows, Mercury’s longitude comes out one digit different from JPL’s rounded value on about one date in ten, Venus’s, Earth’s and Mars’s on one in fifty or fewer, and the outer planets’ almost never. At the same 3,000 instants every distance from Earth was within 0.00015 AU of JPL’s and every angle from the Sun within 0.019°. Horizons’ observer tables, which give where each planet appeared rather than where it was, agree on the angle from the Sun to within 0.024°, and on the evening-or-morning call in all 17,105 cases where the planet was more than 10° from the Sun and from the point opposite it.

The Moon

How much of the Moon is lit depends on the phase angle i, the angle between the Sun and Earth as seen from the Moon. Jean Meeus gives the lit fraction from it, and finds i from where the Sun and the Moon are (Astronomical Algorithms, 1991, formulas 46.1 to 46.3). The page does the same with vectors: the Sun’s position from the integration, the Moon’s from the leading terms of Meeus’s lunar tables, the same ones that place Earth’s centre above.

k = (1 + cos i) / 2 cos i = (S − M) · (−M) / (|S − M| · |M|) k = fraction of the disc lit · M = the Moon’s position from Earth’s centre · S = the Sun’s, so S − M points from the Moon to the Sun and −M from the Moon to Earth

Meeus’s Example 46.a, the Moon on 1992 April 12 at 0h dynamical time, finds i = 69.0756° and k = 0.6786 from the positions of his Example 45.a. The page gets i = 69.095° and k = 0.6784. Across the same 3,000 random instants the page’s k was within 0.00054 of the value from Horizons’ own Sun and Moon vectors, 0.00015 root mean square, and the whole percent it shows differed from Horizons’ by one point at 33 of the 3,000. Meeus also gives a shortcut that needs no positions, his formula 46.4; tested the same way it is off by up to 0.0036, enough to change the percent shown about one time in twelve, so the page does not use it. For the worked example the page says 63% lit, waning gibbous; Horizons says 62.99%.

The New Moon, Full Moon and quarters around your date come from Meeus’s chapter 47: a mean lunation of 29.530588853 days, plus about 25 periodic corrections for each kind of phase and 14 small planetary terms. It reproduces his Example 47.a, the New Moon of 1977 February 18 at 3h37m41s dynamical time, to the second, and Example 47.b, the Last Quarter of 2044 January 21 at 23h48m15s. Against the US Naval Observatory’s published times for all 1,832 phases in 37 sample years from 1800 to 2100, the typical difference is half a minute; the worst is 2.1 minutes, in 2099, and before 2060 none is more than 0.93 minutes. USNO rounds to the minute. The phase is named New, First Quarter, Full or Last Quarter when that instant falls within 12 hours of your time, and crescent or gibbous, waxing or waning, otherwise.

Planet birthdays

A planet’s birthday here is the moment its longitude around the Sun comes back to exactly where it was when you were born: one full orbit measured against the stars, the sidereal period. The page does not divide your age by an average period. It follows the integration forward, finds the day in which the longitude passes the target, and splits that day in half 26 times.

That matters because real orbits are not clocks. Run forward 210 years from the start of 2000, the integration brings Mars back to its starting longitude every 686.94 to 687.04 days, against NASA’s mean sidereal period of 686.980, and Jupiter every 4,331.5 to 4,334.8 days, against 4,332.589; JPL’s own positions give the same ranges. Saturn’s first three returns took 10,761.1, 10,746.9 and 10,762.5 days, either side of NASA’s 10,755.699-day mean. The difference is Jupiter’s doing: run the same integration with Jupiter’s mass set to zero and all three take 10,788 days, to within half a day of each other.

Your Earth return is not your birthday either. NASA gives Earth’s sidereal year as 365.256 days and its tropical year, the one the seasons and the calendar follow, as 365.242; the Gregorian calendar averages 365.2425. So the moment Earth is back where it was against the stars slips about 20 minutes later each year relative to your calendar birthday, stepped around by leap days. Born at midnight UTC on 15 June 1990, you turn 37 at midnight on 15 June 2027, and the calculator puts Earth back at its birth position at 11:33 UT that day; JPL’s positions give 11:32.

The return times were checked against Horizons’ own vectors: at each moment the page gives, how far the planet still was from its birth longitude, divided by how fast it was moving. For the 1990 example every return lands within 1.4 minutes of JPL’s, except Neptune’s in 2155, 4.7 minutes early. Across the 3,000 random births the worst were Neptune’s 13.2 minutes, Mercury’s 12.8, Mars’s 8.0, Earth’s 6.0, Uranus’s 3.9, Venus’s 2.0, Saturn’s 0.8 and Jupiter’s 0.4, all for births before 1840. A return more than 50 years ahead is shown as a date without a time.

Where it stops being right

1800 to 2199 only. That is the range the checks above cover. The integrator itself runs further, and its errors keep growing as it does.
The time zone is yours to choose. “This device’s time zone” applies the rules your browser holds for that date, which is right only if you were born under the same zone. Otherwise pick the UTC offset that was in force at the birthplace, daylight saving included.
Future clock times are estimates. For dates still to come, converting between the integration’s time and clock time depends on a forecast of ΔT, and Earth’s rotation cannot be forecast exactly.
Where, not where it looked. No light-time or aberration: the page gives each planet’s true position at that instant. Against Horizons’ apparent angles from the Sun the difference stayed under 0.025°.
Newtonian. No general relativity and no asteroids. Mercury, the planet relativity moves most, is the one that ends up furthest from JPL’s position: 0.022° at the ends of the range.
This is astronomy, not a horoscope. Longitudes are measured from the Sun in a frame fixed to the stars. Astrological charts use positions seen from Earth, measured from the moving equinox, so the numbers here will not match one.

See the same day in 3D

The site’s universe simulator runs this integrator from these same JPL vectors and draws the Solar System in 3D, with sunspots that follow the real 11-year cycle, the real stars behind it, and the orbits compressed so that Mercury and Neptune fit on one screen. The “Open this date in 3D” button under the calculator opens it paused on the date you entered. It is free and runs in your browser.

Open the universe simulator → · More free calculators

Sources

NASA JPL Horizons (DE441) — the starting state vectors, and most of the checks on this page: heliocentric vectors, observer tables, the Moon’s lit fraction, the planet-return crossings and the Earth–Moon barycentre ratio.
R. S. Park and others, “The JPL Planetary and Lunar Ephemerides DE440 and DE441”, AJ 161, 105 (2021) — the ephemeris behind Horizons, and its post-Newtonian equations of motion.
Jean Meeus, Astronomical Algorithms, Willmann-Bell, 1991 — chapter 45 (the Moon’s arguments and leading lunar terms), 46 (lit fraction, formulas 46.1 to 46.4 and Example 46.a), 47 (phase times, Examples 47.a and 47.b) and 20 (precession of ecliptic coordinates, formula 20.6); chapter 31, Example 31.a (Venus by VSOP87).
Espenak and Meeus, Polynomial Expressions for Delta T, NASA Goddard.
US Naval Observatory, Phases of the Moon — the published phase times used as the check.
NASA Planetary Fact Sheets — mean sidereal orbit periods, and Earth’s sidereal and tropical years.
D. M. Hernandez, “Fast and reliable symplectic integration for planetary system N-body problems”, MNRAS 458, 4285 (2016) — for the Wisdom–Holman map and the democratic heliocentric coordinates of Duncan, Levison and Lee (1998, AJ 116, 2067).