https://www.cyclecalcs.com/2026-07-10monthly1.0 https://www.cyclecalcs.com/calculators.html2026-06-18monthly0.9 https://www.cyclecalcs.com/sky.html2026-07-02weekly0.9 https://www.cyclecalcs.com/sky-map.html2026-07-04monthly0.9 https://www.cyclecalcs.com/voyage.html2026-07-04monthly0.8 https://www.cyclecalcs.com/date-calculator.html2026-06-16monthly0.9 https://www.cyclecalcs.com/synodic-period-calculator.html2026-06-16monthly0.9 https://www.cyclecalcs.com/planetary-alignment-calculator.html2026-06-18monthly0.9 https://www.cyclecalcs.com/celestial-return-calculator.html2026-06-19monthly0.9 https://www.cyclecalcs.com/telescope-calculator.html2026-06-20monthly0.9 https://www.cyclecalcs.com/sunrise-sunset-calculator.html2026-06-20monthly0.9 https://www.cyclecalcs.com/eclipse-explorer.html2026-06-30monthly0.9 https://www.cyclecalcs.com/conjunctions/2026-06-19monthly0.8 https://www.cyclecalcs.com/conjunctions/venus-jupiter.html2026-06-19monthly0.7 https://www.cyclecalcs.com/conjunctions/jupiter-saturn.html2026-06-19monthly0.7 https://www.cyclecalcs.com/conjunctions/venus-mars.html2026-06-19monthly0.7 https://www.cyclecalcs.com/conjunctions/venus-saturn.html2026-06-19monthly0.7 https://www.cyclecalcs.com/conjunctions/mars-jupiter.html2026-06-19monthly0.7 https://www.cyclecalcs.com/conjunctions/mars-saturn.html2026-06-19monthly0.7 https://www.cyclecalcs.com/conjunctions/uranus-neptune.html2026-06-19monthly0.7 https://www.cyclecalcs.com/planet-parade/2026-06-18weekly0.9 https://www.cyclecalcs.com/orrery.html2026-06-18monthly0.9 https://www.cyclecalcs.com/today.html2026-07-02daily0.9 https://www.cyclecalcs.com/moon-phase-calendar.html2026-07-08daily0.9 https://www.cyclecalcs.com/constellations.html2026-07-02monthly0.9 https://www.cyclecalcs.com/nautical-almanac.html2026-06-28monthly0.8 https://www.cyclecalcs.com/celestial-navigation.html2026-06-28monthly0.7 https://www.cyclecalcs.com/pythagorean-numerology-calculator.html2026-06-16monthly0.9 https://www.cyclecalcs.com/cycles.html2026-07-08monthly0.9 https://www.cyclecalcs.com/cosmic-position.html2026-07-10daily0.7 https://www.cyclecalcs.com/grand-cycle-timeline.html2026-06-19monthly0.7 https://www.cyclecalcs.com/cycle-convergence.html2026-06-30monthly0.7 https://www.cyclecalcs.com/cycles/synodic-month.html2026-07-11monthly0.7 https://www.cyclecalcs.com/assets/figures/cycles-synodic-phases.svgThe phases come from viewing angle, not from Earth's shadow. The Sun always lights the half of the Moon that faces it (here, the right). As the Moon circles Earth once every synodic month, we see that lit half from a changing angle: none of it at new moon, all of it at full. New moon to new moon is 29.530589 days. https://www.cyclecalcs.com/assets/figures/synodic-sidereal-lunar-27-degree-catchup.svgWhy the synodic month is longer. In the 27.32 days the Moon takes to lap the stars, Earth moves about 27 degrees along its own orbit, so the Moon must travel that much further to catch the Sun's new direction and become new again. Closing that gap stretches the 27.32-day orbit into the 29.53-day cycle of phases. https://www.cyclecalcs.com/cycles/sidereal-month.html2026-07-11monthly0.7 https://www.cyclecalcs.com/assets/figures/cycles-sidereal-return.svgThe sidereal month is the Moon's true orbit: the time to return to the same position against the fixed stars, 27.321661 days. It is measured against a star, not the Sun, which is why it is about 2.2 days shorter than the 29.53-day cycle of phases. https://www.cyclecalcs.com/assets/figures/moon-phases-synodic-vs-sidereal.svgThe sidereal month (against the stars) beside the synodic month (against the Sun). The Moon returns to the same star in 27.32 days, but because Earth has moved along its orbit meanwhile, the Moon needs about 2.2 more days to return to the same phase, a synodic month of 29.53 days. https://www.cyclecalcs.com/cycles/anomalistic-month.html2026-07-11monthly0.7 https://www.cyclecalcs.com/assets/figures/cycles-anomalistic-ellipse.svgThe Moon's orbit is an ellipse, so its distance swings from about 363,300 km at perigee to 405,500 km at apogee. Perigee to perigee is the anomalistic month, 27.554550 days. It is longer than the star orbit because the ellipse itself slowly turns, one full circuit in 8.85 years. A perigee near a full moon gives a supermoon. https://www.cyclecalcs.com/assets/figures/apsidal-precession-anomalistic-month.svgThe Moon's orbit slowly turns in its own plane, one full circuit in 8.85 years, so the point of perigee advances. The Moon must travel a little past one full orbit to reach perigee again, which is why the anomalistic month of 27.55 days is longer than the star orbit. https://www.cyclecalcs.com/cycles/eclipse-year.html2026-07-11monthly0.7 https://www.cyclecalcs.com/assets/figures/cycles-eclipse-seasons.svgEclipses can only happen when the Sun is near one of the two points where the Moon's tilted orbit crosses the ecliptic, the nodes. The Sun passes a node every 173 days, opening an eclipse season, and returns to the same node every 346.620 days, the eclipse year, about 18.6 days shorter than a calendar year because the nodes drift. https://www.cyclecalcs.com/assets/figures/eclipses-seasons-line-of-nodes.svgEclipses cluster into seasons twice a year, when the Sun lines up with the line of nodes where the Moon's orbit crosses the ecliptic. The Sun returns to the same node every 346.62 days, the eclipse year, shorter than a calendar year because the nodes slowly regress. https://www.cyclecalcs.com/cycles/saros.html2026-07-11monthly0.7 https://www.cyclecalcs.com/assets/figures/cycles-saros-shift.svgWhy the same eclipse repeats. After one Saros of 18 years 11 days the Sun, Moon and node realign and a near-twin eclipse occurs, but the extra third of a day has turned Earth so the shadow falls about 120 degrees of longitude further west. Three Saroses, about 54 years, shift it a full turn back to nearly the same place, an interval called the exeligmos. https://www.cyclecalcs.com/assets/figures/synodic-sidereal-saros-three-months.svgThe Saros works because three different lunar months come back into step at once: 223 synodic, 242 draconic and 239 anomalistic months all fill almost exactly the same 6,585-day span. When phase, node and distance realign together, a near-twin eclipse repeats. https://www.cyclecalcs.com/cycles/metonic-cycle.html2026-07-11monthly0.7 https://www.cyclecalcs.com/assets/figures/cycles-metonic-return.svgNineteen tropical years (6,939.60 days) are almost exactly 235 synodic months (6,939.69 days), agreeing within about two hours. So the Moon's phases fall on nearly the same calendar dates every 19 years. A year's place in this cycle is its golden number, from 1 to 19; it underlies lunisolar calendars. https://www.cyclecalcs.com/assets/figures/metonic-cycle-235-months-19-years-comb.svgThe Metonic identity as a comb: 235 synodic months (6,939.69 days) lie almost exactly over 19 tropical years (6,939.60 days). The two scales agree within about two hours, so the Moon's phases return to the same calendar dates every 19 years. https://www.cyclecalcs.com/cycles/lunar-nodal-cycle.html2026-07-11monthly0.7 https://www.cyclecalcs.com/assets/figures/cycles-nodal-regression.svgThe Moon's orbit is tilted about 5 degrees to the ecliptic and crosses it at two nodes. Those nodes creep westward, about 19.3 degrees a year, all the way around in 18.61 years. When the nodes line up with the solstices the Moon reaches its widest monthly swing in the sky, a major lunar standstill; a minor standstill follows 9.3 years later. https://www.cyclecalcs.com/assets/figures/lunar-nodes-standstill-tilt-stack.svgAs the nodes swing around over 18.61 years, the tilt of the Moon's path against the celestial equator grows and shrinks. At a major lunar standstill the Moon rides highest and lowest each month; at a minor standstill, 9.3 years later, its monthly range is smallest. https://www.cyclecalcs.com/cycles/tropical-year.html2026-07-11monthly0.7 https://www.cyclecalcs.com/assets/figures/cycles-tropical-seasons.svgThe seasons come from the fixed 23.4-degree tilt of Earth's axis, not from distance. As Earth circles the Sun the axis keeps pointing the same way in space, so the north pole leans toward the Sun in June and away in December. One turn of the seasons, equinox to equinox, is the tropical year of 365.2422 days. https://www.cyclecalcs.com/assets/figures/seasons-sunlight-angle-concentration.svgThe seasons are set by the angle of sunlight, not distance. When a hemisphere tilts toward the Sun the light strikes more directly and is concentrated over less ground, warming it. The tropical year is one full turn of this cycle, equinox to equinox, 365.2422 days. https://www.cyclecalcs.com/cycles/sidereal-year.html2026-07-11monthly0.7 https://www.cyclecalcs.com/assets/figures/cycles-sidereal-vs-tropical.svgThe sidereal year, 365.25636 days, is Earth's true orbit measured against the fixed stars. The tropical year of the seasons is measured against the equinox, which drifts slowly westward from precession, so the Sun reaches it about 20 minutes before it returns to the same star. That 20-minute gap is the whole difference between the two years. https://www.cyclecalcs.com/assets/figures/precession-equinox-drift-zodiac-ages.svgThe equinox slowly drifts westward through the zodiac, one full circuit in 25,920 years. That drift is exactly why the tropical year, measured equinox to equinox, runs about 20 minutes shorter than the sidereal year, measured star to star. https://www.cyclecalcs.com/cycles/great-conjunction.html2026-07-11monthly0.7 https://www.cyclecalcs.com/assets/figures/cycles-great-conjunction-trigon.svgJupiter and Saturn line up in our sky about every 19.86 years, the great conjunction. Each meeting lands about 117 degrees further around the zodiac than the last, so three of them, close to 60 years, nearly return to the same region and trace a slowly turning triangle called the trigon. Two Saturn orbits nearly equal five Jupiter orbits, a 5:2 near-commensurability, not a resonance. https://www.cyclecalcs.com/assets/figures/synodic-sidereal-planets-synodic-vs-orbit-curve.svgA conjunction cycle is a lapping problem: how often the faster body catches the slower. Jupiter and Saturn's two long orbits give a synodic period of 19.86 years, the beat between one great conjunction and the next. https://www.cyclecalcs.com/cycles/venus-pentagram.html2026-07-11monthly0.7 https://www.cyclecalcs.com/assets/figures/cycles-venus-rose.svgThe rose of Venus. Over eight years, the path of Venus seen from Earth traces a five-petalled flower, with Earth at the centre. Each of the five gold points is an inferior conjunction, when Venus swings closest to us between Earth and the Sun. The five-fold shape comes from the 13:8 near-commensurability, thirteen Venus years in almost exactly eight Earth years. Because it is not exact, the rose drifts about 2.4 days each cycle and never quite closes. https://www.cyclecalcs.com/assets/figures/venus-cycle-8-year-13-8-clock.svgWhy the pattern nearly repeats every eight years. Eight Earth orbits (2,922 days), thirteen Venus orbits (2,921 days), and five Sun-Earth-Venus synodic periods (2,920 days) almost coincide. The near miss of roughly 2.4 days is why the rose of Venus does not close perfectly and instead drifts about 2.4 degrees each cycle, taking some 1,200 years to come full circle. https://www.cyclecalcs.com/cycles/sunspot-cycle.html2026-07-11monthly0.7 https://www.cyclecalcs.com/assets/figures/cycles-sunspot-curve.svgThe number of sunspots rises and falls on a roughly 11-year rhythm, the Schwabe cycle, though individual cycles run from about 9 to 14 years. We are in Solar Cycle 25, past its 2024-2025 maximum and heading toward a minimum around 2030. The Sun's magnetic polarity flips each cycle, so the full magnetic Hale cycle is about 22 years. These figures come from the SILSO sunspot record; future cycles are estimates. https://www.cyclecalcs.com/assets/figures/sunspot-cycle-hale-polarity-flip.svgThe Sun's magnetic field reverses at each sunspot maximum, so the poles that lead in one 11-year cycle trail in the next. Only after two cycles, about 22 years, does the magnetic pattern return: the Hale cycle. https://www.cyclecalcs.com/cycles/axial-precession.html2026-07-11monthly0.7 https://www.cyclecalcs.com/assets/figures/cycles-precession-top.svgEarth's axis stays tilted 23.4 degrees but slowly wobbles like a spinning top, so the north celestial pole traces a great circle among the stars. One full turn, the Great Year, takes about 25,920 years, cycling the pole star from Thuban to Polaris today and on to Vega. The same wobble drags the equinox westward about one zodiac sign every 2,160 years. https://www.cyclecalcs.com/assets/figures/precession-torque-equatorial-bulge.svgPrecession has a cause: Earth is not a perfect sphere but bulges at the equator, and the gravity of the Sun and Moon tugs on that bulge. On a spinning body that pull becomes a slow wobble of the axis, one full turn every 25,920 years. https://www.cyclecalcs.com/planets/2026-07-10monthly0.8 https://www.cyclecalcs.com/the-moon.html2026-07-10monthly0.8https://www.cyclecalcs.com/assets/img/objects/moon.webpSpace photo of the Moon. Credit: NASA. https://www.cyclecalcs.com/the-sun.html2026-07-10monthly0.8https://www.cyclecalcs.com/assets/img/objects/sun.webpSpace photo of the Sun. Credit: NASA. https://www.cyclecalcs.com/planets/mercury.html2026-07-10monthly0.8https://www.cyclecalcs.com/assets/img/objects/mercury.webpSpace photo of Mercury. Credit: NASA/Johns Hopkins APL/Carnegie Institution of Washington. https://www.cyclecalcs.com/planets/venus.html2026-07-10monthly0.8https://www.cyclecalcs.com/assets/img/objects/venus.webpSpace photo of Venus. Credit: NASA/JPL. https://www.cyclecalcs.com/planets/mars.html2026-07-10monthly0.8https://www.cyclecalcs.com/assets/img/objects/mars.webpSpace photo of Mars. Credit: NASA/JPL/STScI. https://www.cyclecalcs.com/planets/jupiter.html2026-07-10monthly0.8https://www.cyclecalcs.com/assets/img/objects/jupiter.webpSpace photo of Jupiter. Credit: NASA/JPL-Caltech/SwRI/MSSS/Kevin M. Gill. https://www.cyclecalcs.com/planets/saturn.html2026-07-10monthly0.8https://www.cyclecalcs.com/assets/img/objects/saturn.webpSpace photo of Saturn. Credit: NASA/JPL/STScI. https://www.cyclecalcs.com/planets/uranus.html2026-07-10monthly0.8https://www.cyclecalcs.com/assets/img/objects/uranus.webpSpace photo of Uranus. Credit: NASA/JPL-Caltech. https://www.cyclecalcs.com/planets/neptune.html2026-07-10monthly0.8https://www.cyclecalcs.com/assets/img/objects/neptune.webpSpace photo of Neptune. Credit: NASA/JPL-Caltech. https://www.cyclecalcs.com/planets/pluto.html2026-07-10monthly0.8https://www.cyclecalcs.com/assets/img/objects/pluto.webpSpace photo of Pluto. Credit: NASA/Johns Hopkins APL/SwRI. https://www.cyclecalcs.com/learn/2026-07-08monthly0.8 https://www.cyclecalcs.com/learn/moon-phases.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/moon-phases-not-earths-shadow.svgThe dark part of a crescent or quarter Moon is just its own night side, the half turned away from the Sun, with no shadow involved. Earth's shadow points straight away from the Sun, so it misses the Moon at every phase except full, and even then it usually passes just above or below because the Moon's orbit is tilted about five degrees. Only when the alignment is nearly perfect does the shadow fall on the Moon, giving a lunar eclipse. Distances are not to scale. https://www.cyclecalcs.com/assets/figures/moon-phases-synodic-vs-sidereal.svgIn one sidereal month of 27.32 days the Moon completes a full orbit and again points the same way among the stars, but Earth has carried about a thirteenth of the way around the Sun. The Moon then needs roughly two more days to catch the shifted Sun-Earth line, which is why the synodic cycle of phases runs about 29.53 days. The Moon's orbit is drawn far larger than scale relative to the Sun's distance. https://www.cyclecalcs.com/assets/figures/moon-phases-rise-set-clock.svgThe same orbital position that sets a phase also sets when you can see it. A first quarter Moon rides high at sunset, a full Moon rises as the Sun goes down and shines all night, and a last quarter Moon is highest just before dawn, while a new Moon is up with the Sun and lost in its glare. Body sizes and the Earth-to-Moon distance are not to scale. https://www.cyclecalcs.com/learn/tides.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/tidal-force-differential-gravity.svgTidal force in two steps: differential gravity stretches Earth's ocean into two bulges. https://www.cyclecalcs.com/assets/figures/spring-tides-neap-tides-geometry.svgSpring tides versus neap tides: how the alignment of the Sun and Moon sets the tidal range. https://www.cyclecalcs.com/learn/tidal-locking.html2026-07-09monthly0.7 https://www.cyclecalcs.com/assets/figures/tidal-locking-synchronous-vs-nonrotating.svgWhy the Moon keeps one face toward Earth. A Moon that did not rotate would show us every side as it went around; the real Moon turns exactly once per orbit, so the same near side stays pointed at Earth. That one-spin-per-orbit lock is synchronous rotation, the end state of billions of years of tidal friction. https://www.cyclecalcs.com/assets/figures/tidal-locking-libration-longitude-latitude.svgThe two main librations. Libration in longitude: the Moon's steady spin runs ahead of and behind its varying elliptical-orbit speed, rocking the face east and west by up to about 7.9 degrees. Libration in latitude: the Moon's axis is tilted about 6.7 degrees to its orbit, so we look alternately over its north and south poles. https://www.cyclecalcs.com/assets/figures/tidal-locking-59-percent-coverage.svgAbout 59 percent of the Moon over time. The near side we see at any moment is half the sphere; libration adds a rim of about 9 percent all the way around, bringing the total ever visible from Earth to about 59 percent and leaving roughly 41 percent, the far side, that can only be seen from space. https://www.cyclecalcs.com/learn/keplers-laws.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/keplers-first-law-ellipse-foci.svgKepler's first law: an orbit is an ellipse with the Sun at one focus, built with two pins and a string. https://www.cyclecalcs.com/assets/figures/keplers-second-law-equal-areas.svgKepler's second law: the Sun-planet line sweeps equal areas in equal times, fast at perihelion and slow at aphelion. https://www.cyclecalcs.com/learn/meteor-showers.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/meteor-shower-radiant-perspective.svgA meteor shower's radiant is perspective: parallel meteor paths seem to fan out from one point on the sky. https://www.cyclecalcs.com/assets/figures/meteor-shower-after-midnight-windshield.svgWhy meteor rates rise after midnight: your side of Earth turns into the oncoming stream like a windshield into rain. https://www.cyclecalcs.com/learn/eclipses.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/eclipses-total-vs-annular.svgWhether a central solar eclipse turns out total or annular is decided by distance. Near its closest point (perigee) the Moon looks a little larger than the Sun, about 33.5 arcminutes across against the Sun's roughly 32, so it blots out the disk completely and the corona appears. Near its farthest point (apogee) the Moon shrinks to about 29.4 arcminutes, just too small, and a brilliant ring of sunlight is left all the way around it. The two disks are drawn to their true relative sizes. https://www.cyclecalcs.com/assets/figures/eclipses-seasons-line-of-nodes.svgEclipses are possible only when the line of nodes, where the Moon's tilted orbit crosses the ecliptic, points toward the Sun. That alignment happens at just two opposite points in Earth's yearly orbit, so eclipses arrive in two seasons rather than every month. The gap is about 173 days, not a full six months, because the nodes slowly swing backward, roughly 19.3 degrees a year and a complete turn in 18.6 years, which also makes each eclipse season fall about 20 days earlier than the year before. Sizes are not to scale. https://www.cyclecalcs.com/assets/figures/eclipses-shadow-footprint-track-vs-nightside.svgThe two eclipses differ in reach because their shadows differ in size. The Moon's umbra paints a track at most about 270 kilometers wide across a 12,742 kilometer Earth, so a total solar eclipse is visible only from that thin strip as it sweeps by. Earth's shadow at the Moon's distance is far larger, roughly 2.6 times the Moon's diameter, so the whole Moon slips inside it and a lunar eclipse can be watched from the entire night side of Earth at once. Sizes and distances are schematic, not to scale. https://www.cyclecalcs.com/learn/metonic-cycle.html2026-07-09monthly0.7 https://www.cyclecalcs.com/assets/figures/metonic-cycle-235-months-19-years-comb.svgWhy the Moon's phases repeat every 19 years. Nineteen tropical years total 6,939.60 days and 235 synodic months total 6,939.69 days, so the two counts land within a whisker of each other. A magnified inset reveals the tiny 0.09-day gap, about 2 hours, which is why the pattern drifts a full day only about every 219 years. https://www.cyclecalcs.com/assets/figures/metonic-cycle-golden-number-leap-months.svgHow 235 months fit into 19 years. Twelve years get 12 lunar months and seven get a thirteenth leap month, because 12 times 12 plus 7 times 13 equals 235. The seven leap years keep a lunar calendar in step with the seasons, and each year's Golden Number, the year modulo 19 plus 1, is still used to find the date of Easter. https://www.cyclecalcs.com/assets/figures/metonic-cycle-vs-saros-callippic.svgThree lunar cycles compared. The Metonic cycle of 235 synodic months, about 19 years, returns the Moon's phases to the same dates. The Saros of 223 months, about 18 years 11 days, returns eclipses because it also realigns the node and distance. The Callippic cycle of 940 months, about 76 years, is a tighter refinement of the phase cycle. https://www.cyclecalcs.com/learn/lunar-nodes.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/lunar-nodes-draconic-vs-sidereal-month.svgEach month the line of nodes slips westward by about 1.4 degrees, toward the oncoming Moon. So the Moon meets the node after turning a little less than a full circle, and the draconic month of 27.21 days runs about 0.11 days shorter than the 27.32-day sidereal month, the time to return to the same star. The tilt is exaggerated for clarity. https://www.cyclecalcs.com/assets/figures/lunar-nodes-standstill-tilt-stack.svgAt a major standstill the Moon's roughly 5-degree orbital tilt adds to Earth's 23.4-degree axial tilt, so the Moon swings about 28.6 degrees north and south of the celestial equator each month. About 9.3 years later the tilts partly cancel and the swing shrinks to a minor standstill of about 18.3 degrees. The live clock above tracks where in this cycle the Moon stands now. https://www.cyclecalcs.com/assets/figures/lunar-nodes-eclipse-alignment.svgA new moon casts its shadow onto Earth only when it lands at or near a node, where the tilted orbit crosses the ecliptic. A new moon away from a node rides up to about 5 degrees off the Sun's path, so its shadow sweeps above or below Earth and no eclipse occurs. Sizes and distances are not to scale, and the tilt is exaggerated for clarity. https://www.cyclecalcs.com/learn/seasons.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/seasons-perihelion-not-distance.svgEarth reaches perihelion, its closest approach to the Sun, in early January, right in the depth of northern winter, and aphelion in early July. The whole difference is only about 5 million km, roughly 3.4 percent, far too small to make the seasons. The orbit is drawn close to its true shape, which is very nearly a perfect circle. https://www.cyclecalcs.com/assets/figures/seasons-sunlight-angle-concentration.svgThe same bundle of sunlight strikes the ground steeply at the June solstice but at a shallow angle at the December solstice. At 40 degrees north the noon Sun stands about 73 degrees high in summer and only about 27 degrees high in winter, so the winter beam is spread over roughly twice as much ground and each patch receives about half the energy. https://www.cyclecalcs.com/assets/figures/seasons-sun-path-sky-dome.svgFrom 40 degrees north the Sun climbs high and traces a long arc for a summer day of nearly 15 hours, but stays low and short for a winter day of only about 9 hours. At the equinoxes it rises due east, sets due west, and daylight lasts 12 hours. Notice how the sunrise point itself slides north and south along the horizon through the year. https://www.cyclecalcs.com/learn/precession.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/precession-equinox-drift-zodiac-ages.svgThe same wobble drags the spring equinox, the spot where the Sun crosses the equator, backward along the ecliptic at about one degree every 72 years. Crossing a whole 30-degree sign takes roughly 2,160 years, one astrological age, which is why the equinox has slipped from Aries into Pisces and is now edging toward Aquarius. The signs are shown as equal 30-degree slices; real constellation boundaries are uneven, so the age dates are only approximate. https://www.cyclecalcs.com/assets/figures/precession-torque-equatorial-bulge.svgPrecession's cause. Earth bulges at the equator, and because the spin axis leans 23.4 degrees, the Sun and Moon pull a little harder on the near side of that bulge than the far side. In a spinning world the tug does not tip the axis upright; it swings the axis slowly sideways, so it sweeps a full cone every 25,920 years. The bulge and the Sun and Moon are exaggerated for clarity and are not to scale. https://www.cyclecalcs.com/assets/figures/precession-nutation-lunar-node-cause.svgNutation and the lunar nodes are one cycle. The Moon's orbit tilts about 5.1 degrees to the ecliptic, and its line of nodes swings all the way around every 18.6 years. As that tilted plane turns, the Moon's pull on Earth's bulge waxes and wanes on the same beat, nodding the axis by about 9.2 arcseconds, roughly one 390th of a degree. The tilt and the nod are exaggerated here so the geometry is visible. https://www.cyclecalcs.com/learn/apsidal-precession.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/apsidal-precession-mercury-43-arcseconds.svgMercury's perihelion advances about 574 arcseconds per century against the stars. The pull of the other planets accounts for about 531 of them, and the small 43-arcsecond remainder is just what Einstein's general relativity predicted in 1915. The bar is drawn to scale, so you can see the relativistic slice is only about one part in thirteen. https://www.cyclecalcs.com/assets/figures/apsidal-precession-anomalistic-month.svgThe Moon's perigee creeps forward about 3 degrees a month, in the same direction the Moon travels. So after one 27.32-day sidereal circuit the Moon has not quite reached perigee again; it needs about five and a half hours more, which is why the anomalistic month runs to 27.55 days. https://www.cyclecalcs.com/learn/venus-cycle.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/venus-cycle-8-year-13-8-clock.svgWhy the pattern nearly repeats every eight years. Eight Earth orbits (2,922 days), thirteen Venus orbits (2,921 days), and five Sun-Earth-Venus synodic periods (2,920 days) almost coincide. The near miss of roughly 2.4 days is why the rose of Venus does not close perfectly and instead drifts about 2.4 degrees each cycle, taking some 1,200 years to come full circle. https://www.cyclecalcs.com/assets/figures/venus-cycle-phase-and-apparent-size.svgVenus's phase and apparent size change together, in opposite directions. Near superior conjunction, on the far side of the Sun at 1.72 AU, Venus is almost fully lit but tiny. Near inferior conjunction, closest to us at 0.28 AU, it is a large thin crescent, about six times wider. At greatest elongation it is exactly half lit. This full-to-crescent march is the evidence Galileo saw in 1610 that Venus circles the Sun. The disks are to scale with one another but hugely enlarged against the real sky. https://www.cyclecalcs.com/assets/figures/venus-cycle-greatest-elongation-geometry.svgVenus's greatest elongation is fixed by geometry. The line of sight from Earth that just grazes Venus's orbit meets the Sun direction at an angle equal to the arcsine of 0.72, about 46 degrees, and the true maximum reaches roughly 47 degrees. The right angle sits at Venus. Mercury, on a smaller 0.39 AU orbit, is held to only about 23 degrees, which is why it is harder to catch. The orbit sizes are to scale; the planets are enlarged so you can see them. https://www.cyclecalcs.com/learn/retrograde.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/retrograde-opposition-inferior-conjunction.svgRetrograde begins at the moment of closest passing. For an outer planet like Mars that is opposition, when Earth slides directly between the Sun and the planet and it shines opposite the Sun, closest and brightest. For an inner planet like Venus it is inferior conjunction, when the planet passes between us and the Sun and is lost in the glare. Orbit sizes are close to scale (Sun to Earth 1.0, to Mars 1.52, to Venus 0.72 astronomical units); the planets themselves are enlarged to be visible. https://www.cyclecalcs.com/assets/figures/retrograde-orbit-tilt-loop-vs-line.svgWhy the path is a loop and not a straight back-and-forth. If every orbit lay in one flat plane (left), the planet would simply retrace a single line. Because each orbit is tilted a little from Earth's, about 1.85 degrees for Mars and 3.39 degrees for Venus, the planet also drifts slightly north or south during the pass, opening the reversal into the S-shaped loop (right). The vertical spread here is exaggerated to make the drift visible; the real loop is long and shallow. https://www.cyclecalcs.com/assets/figures/retrograde-epicycle-vs-heliocentric.svgThe same loop, explained two ways. In Ptolemy's Earth-centered sky (left) each planet had to ride a small circle, an epicycle, turning on top of its main orbit purely to reproduce the backward loops. Once Copernicus let the Sun sit at the center and Earth move (right), the epicycles were unnecessary: the loop is simply the view from a faster Earth overtaking the planet. The epicycle path is schematic and not to scale. https://www.cyclecalcs.com/learn/synodic-sidereal.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/synodic-sidereal-saros-three-months.svgAn eclipse needs three lunar clocks at once: the Moon new or full (synodic), close to a node (draconic), and its distance, which sets how total it looks (anomalistic). After about 6,585 days, one Saros of 18 years and 11 days, the 223 synodic, 242 draconic, and 239 anomalistic months have each run almost exactly the same span and fall back into step, so a near-twin eclipse returns. https://www.cyclecalcs.com/assets/figures/synodic-sidereal-lunar-27-degree-catchup.svgOne sidereal month (27.32 days) brings the Moon back to the same star, shown by the parallel sightlines, but Earth has meanwhile carried the Sun's direction about 27 degrees further along its orbit. The Moon must swing that extra 27 degrees, roughly 2.2 more days, to sit between Earth and Sun again at new moon, which is why the synodic month stretches to 29.53 days. The Moon's distance from Earth is enlarged for clarity; the angles are true. https://www.cyclecalcs.com/assets/figures/synodic-sidereal-planets-synodic-vs-orbit-curve.svgPlotting each body's synodic period against its true orbital period shows why the two differ in either direction. A planet orbiting near Earth's own year would almost never lap us, so the curve spikes there. Far beyond it, a planet moves so slowly that Earth laps it about once a year, so Jupiter's synodic period of 399 days sits just above one year even though its orbit lasts nearly twelve. Points above the dashed diagonal have a synodic period longer than their orbit, points below have a shorter one. https://www.cyclecalcs.com/learn/sidereal-solar-day.html2026-07-09monthly0.7 https://www.cyclecalcs.com/assets/figures/sidereal-solar-day-extra-degree.svgWhy a solar day runs longer than a sidereal day. At position 1 the surface marker faces both the Sun and a distant star, local noon. One sidereal day later Earth has spun a full 360 degrees and the marker points at the star again, but Earth has moved along its orbit, so the Sun now sits about 1 degree to the side. Earth must turn that extra degree, roughly 4 minutes, to reach the next noon. The daily orbital step is drawn far larger than its real value of about 1 degree. https://www.cyclecalcs.com/assets/figures/sidereal-solar-day-yearly-extra-turn.svgOne extra turn every year. Even if Earth never spun relative to the stars, orbiting the Sun once would still carry the Sun once around the sky, giving one solar day per orbit. Earth actually spins 366.24 times against the stars in a year, but because the orbit itself accounts for one of those turns as seen from the Sun, we count only 365.24 solar days. The one extra rotation is exactly the single trip around the Sun. https://www.cyclecalcs.com/assets/figures/sidereal-solar-day-nightly-star-drift.svgWhy the stars rise about 4 minutes earlier each night. Checked at the same clock time on successive nights, a star sits a little higher in the eastern sky each time, having risen about 4 minutes earlier, because a sidereal day is about 4 minutes shorter than the 24-hour solar day the clock keeps. Four minutes a night adds up to about half an hour a week, two hours a month, and a full 24 hours, one complete circuit of the sky, over a year. That is why the evening constellations change with the seasons. https://www.cyclecalcs.com/learn/sunspot-cycle.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/sunspot-cycle-hale-polarity-flip.svgWhy the full cycle takes 22 years. Sunspots emerge in pairs of opposite magnetic polarity, and the leading polarity in the north is the mirror image of the south. From one 11-year cycle to the next every polarity flips, so the Sun's magnetism only returns to its starting arrangement after two cycles, about 22 years. That doubled rhythm is the Hale cycle. https://www.cyclecalcs.com/assets/figures/sunspot-cycle-planetary-tide-strength.svgCan the planets' pull do the job? The tide the planets raise on the Sun is less than a millimeter high on a star nearly 1.4 million kilometers across, far too small to draw to scale here, so the bulge is exaggerated. At the depth where the Sun builds its magnetism, Jupiter's tug is about ten thousand times weaker than the churning gas already stirring there. This is the strength test the planetary idea fails, separate from the timing test in the chart above. https://www.cyclecalcs.com/assets/figures/sunspot-cycle-anatomy-umbra-penumbra.svgAnatomy of a sunspot. The dark core, the umbra, is where the magnetic field is strongest and the gas is coolest, near 3,700 degrees, against roughly 5,800 degrees for the bright surface around it. A lighter, feathery penumbra rings the core. Earth is drawn to the same scale to show that a large sunspot group can be wider than our entire planet. https://www.cyclecalcs.com/learn/galactic-year.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/galactic-year-vertical-bob.svgThe carousel bob. Besides going around the galaxy, the Sun rides gently up and down through the disk, crossing the midplane and sinking back roughly every 60 to 70 million years. That is about three to four bobs in one 230-million-year lap. The real up-and-down swing is tiny next to the 26,000-light-year orbit, so the vertical scale here is exaggerated to make the wave visible; the Sun always stays within the thin disk. https://www.cyclecalcs.com/assets/figures/galactic-year-vs-ordinary-year.svgTwo kinds of year. On the left the Earth takes one ordinary year to circle the Sun. On the right the Sun takes about 230 million years, one galactic year, to circle the center of the Milky Way from its place roughly 26,000 light-years out. The two panels are not drawn to the same scale: the Sun's galactic orbit is more than a billion times wider than Earth's orbit around the Sun, and one galactic year is about 230 million ordinary years. https://www.cyclecalcs.com/assets/figures/galactic-year-twenty-laps.svgAbout twenty laps in a lifetime. Dividing the Sun's 4.6-billion-year age by a 230-million-year lap gives roughly twenty galactic years. Each lap retraces nearly the same circle about 26,000 light-years out, so this is twenty trips around one orbit, not a widening spiral. The whole ride in the animation above is only the last of the twenty, and a single 80-year human life is about one third of a millionth of one lap, far too thin to draw. https://www.cyclecalcs.com/learn/milankovitch.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/milankovitch-cool-summer-ice-mechanism.svgWhat grows an ice sheet is not the year's total sunlight but the summer sunlight over the high northern latitudes, near 65 degrees north, where the great northern landmasses lie. Even at midsummer the noon Sun there climbs only to about 48 degrees, so when low axial tilt, summer near aphelion, and a stretched-enough orbit combine into a cool summer, the previous winter's snow survives the season and piles up year on year into ice. A warmer summer melts it back. The ice extents shown here are schematic. https://www.cyclecalcs.com/assets/figures/milankovitch-precession-season-at-perihelion.svgPrecession slowly moves which season falls nearest the Sun. Today northern midsummer happens near aphelion, Earth's farthest point, so northern summers receive a little less sunlight and run milder. About 11,000 years to either side of now, half of the climatic precession cycle, northern midsummer instead falls near perihelion, the closest point, making northern summers more intense. The eccentricity of the orbit sets how large this swing can be. The orbit shape is exaggerated here so the near and far points read clearly. https://www.cyclecalcs.com/assets/figures/milankovitch-eccentricity-true-scale.svgDrawn to true scale, Earth's orbit at today's eccentricity of 0.0167 is very nearly a perfect circle. The only visible sign of its eccentricity is that the Sun sits a little off center, about 1.67 percent of the way from the middle to the edge, so Earth is roughly 3.4 percent farther from the Sun at aphelion than at perihelion. Even at the rare 0.058 extreme the shape is barely an oval, which is why the animation above exaggerates it about nine times so it can be seen at all. https://www.cyclecalcs.com/learn/equation-of-time.html2026-07-08monthly0.7 https://www.cyclecalcs.com/assets/figures/equation-of-time-apparent-vs-mean-sun-meridian.svgAt clock noon in early November the real Sun has already crossed the meridian, sitting about four degrees, roughly eight Sun-widths, to the west of due south. That gap is the equation of time for the day, here about sixteen minutes ahead, because one degree of the sky equals four minutes of time. The pale Sun marks where the steady clock Sun would be. The offset is drawn to scale. https://www.cyclecalcs.com/assets/figures/equation-of-time-eccentricity-orbit-equal-areas.svgEarth's orbit is a slightly flattened ellipse with the Sun at one focus, so Earth swings fastest at perihelion near January 3 and slowest at aphelion near July 4. By Kepler's second law the two shaded wedges cover equal area in equal time, which is why the January wedge spans a wider angle. That faster January motion makes the real Sun appear to race ahead of the steady clock Sun. The orbit's shape is exaggerated here; the true orbit is only about 1.7 percent from a circle. https://www.cyclecalcs.com/assets/figures/equation-of-time-obliquity-ecliptic-equator-projection.svgThe Sun moves at a nearly even pace along the tilted ecliptic, but our clocks measure its eastward progress along the celestial equator. Where the ecliptic crosses the equator at the equinoxes, the steep 23.4 degree slant shortens each day's progress by about eight percent, so the Sun falls behind. Near the solstices the path runs almost parallel and each step counts for about nine percent more, so the Sun runs ahead. 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