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Ephemeris:04/02/2026 – Determining the date of Easter

April 2, 2026 Leave a comment

This is Ephemeris for Thursday, April 2nd. Today the Sun will be up for 12 hours and 50 minutes, setting at 8:11, and it will rise tomorrow at 7:19. The Moon, 1 day past full, will rise at 9:14 this evening.

Easter will be celebrated by Western Christian churches this Sunday. Easter is a movable feast in that it falls on a different date each year following the first full moon of spring. It was an attempt to follow the Jewish Passover, which starts on the 15th of the month of Nisan. The Jewish calendar being a lunar calendar, the 15th generally begins at sundown on the night of the full moon. And since the Last Supper was a Seder, according to at least one Gospel, the Christian church wanted to link Easter with Passover as closely as possible using the Roman solar based (Julian) calendar. That’s not always the case, especially with our current Gregorian Calendar. Passover this year began last night at sunset, so this year it is nearly in agreement with the Gospel narrative.

The astronomical event times given in this blog are for the Traverse City/Interlochen area of Michigan (Lat 44.7° N, Long 85.7° W; EST, UT – 5 hours) unless stated otherwise. Times will be different for other locations.

Addendum

Calendar pages showing the relationship of the first full moon after the vernal equinox and Easter, the following Sunday.
This calendar shows the relationship between Easter, the first full moon of spring, and vernal equinox, the first day of spring. In the calculation of Easter, March 21st is considered the date of the vernal equinox, no matter when it actually falls. This year it fell on the 20th,* even in Europe, and the Holy Land. The full moon date is also what I would call a tabular value. The Moon’s orbit is elliptical so a tabular date may not be the exact date of a full moon. So it may be a day off from the actual full moon date.

*Our Gregorian Calendar will correct for this by making the year 2100, normally a leap year of 366 days, an ordinary year of 365 days. The rule is that century years not divisible by 400 get clipped.

Categories: Concepts, Ephemeris Program Tags:

Ephemeris: 03/17/2026 – It’s also an equilux day

March 17, 2026 Comments off

This is Bob Moler with Ephemeris for St. Patrick’s Day, Tuesday, March 17th. Today the Sun will be up for 12 hours and to the minute, setting at 7:51, and it will rise tomorrow at 7:49. The Moon, 1 day before new, will rise at 7:33 tomorrow morning. |  This upcoming Saturday will be the vernal equinox, the first day of spring. Equinox means equal night, meaning that day and night are equal. Geometrically that’s correct, but, that’s not actually true. Today is the day when the sun is up for 12 hours and of course set for 12 hours. The name for this day has come to be called equilux day. Lux being the Latin for light. The difference is, because the Earth has an atmosphere, plus we have a different definition of sunrise and sunset that puts the sun a little bit below the horizon at the rise and set moment. So enjoy a few extra minutes of sunlight before the official equinox date. Think of it as a St Patrick’s Day bonus.

The astronomical event times given in this blog are for the Traverse City/Interlochen area of Michigan (Lat 44.7° N, Long 85.7° W; EST, UT – 5 hours) unless stated otherwise. Times will be different for other locations.

Addendum

Atmospheric Refraction
How the atmosphere bends the light of the Sun or Moon rising or setting to appear higher than it actually is. S is the actual position of the Sun, S’ is the apparent position of the Sun. The blue line is the observer O’s horizon extended into space. The gray line is the actual, though much exaggerated, light path bent or refracted by the Earth’s atmosphere. The black line is the apparent sight line to the Sun. Credit Francisco Javier Blanco González, 2017.

A note: This is equilux day for folks a 45 degrees north latitude. The actual date may vary by a day or so depending on one’s latitude, which affects the angle the Sun appears to cross the horizon.

Categories: Astronomical Event, Concepts, Ephemeris Program Tags: ,

Ephemeris: 03/13/2026 – Precession of the equinoxes

March 13, 2026 Comments off

This is Ephemeris for Friday, March 13th. Today the Sun will be up for 11 hours and 47 minutes, setting at 7:46, and it will rise tomorrow at 7:56. The Moon, 2 days past last quarter, will rise at 6:01 tomorrow morning.

Yesterday I talked about the fact that the constellation of Cancer the crab is no longer the northernmost constellation of the zodiac, where the Sun is positioned on the first day of summer. There’s been a slow change in the position of the earth’s axis, in that it wobbles slowly in a period of nearly 26,000 years. The inclination of the Earth’s axis to its orbit is around 23 1/2 degrees, and the gravitational pull of the Moon and the Sun on the Earth’s equatorial bulge, wants to straighten it up. But because the Earth is spinning, it wobbles instead, slowly sliding the actual zodiacal constellations eastward about one constellation in 2,150 years. So the actual constellations are off one constellation from the astrological signs.

The astronomical event times given in this blog are for the Traverse City/Interlochen area of Michigan (Lat 44.7° N, Long 85.7° W; EST, UT – 5 hours) unless stated otherwise. Times will be different for other locations.

Addendum

An animation of the precession of the equinoxes.
An animation of the precession of the equinoxes. The blue horizontal line is the celestial equator. The orange line is the ecliptic, the apparent annual path of the Sun against the stars. Where the two lines cross is the vernal equinox where the Sun is on the first day of spring, which on our calendar is trending to be March 20th. The slippage of the stars eastward (to the left) along the ecliptic is about the apparent width of the Sun or Moon, or half a degree, in 36 years. We’re looking at two different years 150 CE, the time of Ptolemy, and our time. To tell which is which, the one from our time has Saturn at the lower right. Jupiter happens to be in both of them, but it’s obviously been around lots of times between then and now. Created using Stellarium and GIMP.
The force causing precession
The Moon and Sun’s gravitational force act on the Earth’s equatorial bulge attempting to cause the earth to straighten up and fly right. Because the Earth is spinning, it acts like a gyroscope and the torque to straighten it up causes it to be applied 90 degrees away in the direction of the rotation causing the procession. Credit: Open Course: Astronomy.
Precession circle
The path of the north pole of the sky (celestial sphere) over time. The celestial north pole is still approaching Polaris. In the past the Big Dipper was closer to the north pole of the sky than it is now. Polaris will be it closest to the north pole around the year 2110. Source: taichifuture.com/cosmology.html.
Categories: Concepts, Zodiac Tags:

Ephemeris: 03/12/2026 – Cancer the crab used to welcome summer

March 12, 2026 Comments off

This is Ephemeris for Thursday, March 12th. Today the Sun will be up for 11 hours and 44 minutes, setting at 7:45, and it will rise tomorrow at 7:58. The Moon, 1 day past last quarter, will rise at 5:25 tomorrow morning.

There’s a line on some globes and maps at approximately 23 1/2° north latitude called the Tropic of Cancer. It’s related to the constellation Cancer the crab. However, Cancer no longer fits that role that it was named to a couple of thousand years ago, when the sun entered the constellation of Cancer on the first day of summer. That’s the latitude on the Earth where the Sun was directly overhead on the first day of summer. Now that an honor goes to Gemini. The way we draw the figure of that constellation, the Sun is right near Castor’s big toe on the first day of summer. But I don’t think they’re going to change the name anytime soon. The reason for the change is that the Earth’s axis slowly wobbles like a top or gyroscope as they slow down. The effect is called precession.

The astronomical event times given in this blog are for the Traverse City/Interlochen area of Michigan (Lat 44.7° N, Long 85.7° W; EST, UT – 5 hours) unless stated otherwise. Times will be different for other locations.

Addendum

Comparison of the position of the Sun against the constellations on the summer solstice from 150 CE to now due to the precession of the equinoxes.
Comparison of the position of the Sun against the constellations on the summer solstice from 150 CE to now due to the precession of the equinoxes. The reason I chose 150 CE, is that it was the approximate date of Ptolemy’s Almagast, the standard work on astronomy until Copernicus in the 16th century or later. Created using Stellarium, LibreOffice Draw and GIMP.
How the tropics of Cancer and Capricorn line up with the Sun on the solstices.
How the tropics of Cancer and Capricorn line up with the Sun on the solstices. From an animation in Wikipedia, in the Public Domain.

The Greek letter epsilon in the image above represents the tilt of the Earth’s axis of around 23.5°. Astronomers call it the obliquity of the ecliptic, the angle between the ecliptic and the celestial equator as seen in the illustration below.

An animation of the precession of the equinoxes.
An animation of the precession of the equinoxes. The blue horizontal line is the celestial equator. The orange line is the ecliptic, the apparent annual path of the Sun against the stars. Where the two lines cross is the vernal equinox where the Sun is on the first day of spring, which on our calendar is trending to be March 20th. The slippage of the stars eastward (to the left) along the ecliptic is about the apparent width of the Sun or Moon, or half a degree, in 36 years. We’re looking at two different years 150 CE, the time of Ptolemy, and our time. To tell which is which, the one from our time has Saturn at the lower right. Jupiter happens to be in both of them, but it’s obviously been around lots of times between then and now. Created using Stellarium and GIMP.
Precesion animation
The 25,700-year cycle of precession as seen from near the Earth. The current North Pole star is Polaris (top). In about 8,000 years it will be the bright star Deneb (left), and in about 12,000 years, Vega (left center). The Earth’s rotation is not depicted to scale – in this span of time, it would actually rotate over 9 million times. Credit image Tfrooo, caption Wikipedia.
Categories: Concepts, Constellations, Ephemeris Program, Seasons, Uncategorized Tags:

Ephemeris: 02/17/2026 – There’s an annular solar eclipse today… if you’re a penguin

February 17, 2026 Comments off

This is Ephemeris for Fat Tuesday, February 17th. Today the Sun will be up for 10 hours and 34 minutes, setting at 6:14, and it will rise tomorrow at 7:38. The Moon is new today, and won’t be visible.

This morning there is an annular solar eclipse occurring. Don’t run outside to see it, especially if you’re here in northern Michigan. The eclipse is only visible in the Southern Ocean and Antarctica. However, this eclipse marks the beginning of an eclipse season, and we will have an eclipse that will be visible for our location in two weeks: a total lunar eclipse, which will be visible before sunrise on Tuesday morning, March 3rd. There are two periods were eclipses will occur in a year, with at least one of the sun and the moon. These periods are separated by a little less than six months, and last about 35 days. That’s about 5 1/2 days longer than a lunar month, so it is possible to squeeze in another eclipse, though not this time.

The astronomical event times given in this blog are for the Traverse City/Interlochen area of Michigan (Lat 44.7° N, Long 85.7° W; EST, UT – 5 hours) unless stated otherwise. Times will be different for other locations.

Addendum

An adaption of the NASA eclipse map for the annular solar eclipse of February 17th 2026. The path of angularity is almost completely on Antarctica and a bit of the Southern Ocean.
An adaption of the NASA eclipse map for the annular solar eclipse of February 17th 2026. The path of angularity is almost completely on Antarctica and a bit of the Southern Ocean. The area of partial eclipse will extend from southern Africa along the eastern African coast and Madagascar. They will see a very slight partial eclipse. The eclipse season started about February 11th and will extend for 35 days. It will include a lunar eclipse which will be visible for us on the morning of March 3rd. Map by Fred Espenak. The original map is located at https://eclipse.gsfc.nasa.gov/SEplot/SEplot2001/SE2026Feb17A.GIF
This is a diagram showing how eclipse seasons occur, due to the motions of the sun the moon and the wobbling of the moon’s orbit. The nodes which are the crossing points of the planes of the moons and the earth’s orbit around the sun shift westward over a period of 18.6 years. This causes the eclipse seasons to move earlier and earlier in the year over 18.6 years. Eclipses can occur when the sun is within 17° of the ascending or the descending nodes which is why eclipses eclipse seasons occur every six months and the season is long enough to squeeze in at least two eclipses, one each of the sun and the moon, and possibly a third if one occurs at the very beginning of the eclipse season.
Categories: Concepts, Eclipses, Ephemeris Program Tags: , ,

Ephemeris: 02/13/2026 – The real cause of a planet’s retrograde motion

February 13, 2026 Comments off

This is Ephemeris for Friday, February 13th. Today the Sun will be up for 10 hours and 22 minutes, setting at 6:08, and it will rise tomorrow at 7:44. The Moon, halfway from last quarter to new, will rise at 6:30 tomorrow morning.

So what is the real reason that Jupiter is currently moving westward for a while in retrograde motion? Retrograde motion occurs in outer planets because the Earth is actually passing them. A simple analogy would be, if you were in a car that was passing another, the car you are passing would seem to move backwards compared to you. And that is exactly what’s happening. The Earth moves faster than the outer planets. Since the solar system is like a racetrack, and we get to lap these outer planets repeatedly when they are closest to us. For the inner planet it’s opposite. They go retrograde or backwards when they are passing us. This is a much simpler answer than all these circles upon circles the ancients invented.

The astronomical event times given in this blog are for the Traverse City/Interlochen area of Michigan (Lat 44.7° N, Long 85.7° W; EST, UT – 5 hours) unless stated otherwise. Times will be different for other locations.

Addendum

A diagram showing the Earth and Jupiter and above, the appearance of Jupiter in our sky and the retrograde motion as the Earth in essence passes Jupiter in our orbital motions around the Sun.
A diagram showing the Earth and Jupiter and above, the appearance of Jupiter in our sky and the retrograde motion as the Earth in essence passes Jupiter in our orbital motions around the Sun. When the sight lines from earth to Jupiter are trending counterclockwise, moving to the left, the planet appears to be moving eastward in its normal motion. As we pass Jupiter, at our closest point to it, the sight lines tend to rotate in the clockwise direction, which causes the appearance of retrograde motion of Jupiter in our sky. The plotting intervals on the top diagram is 10 days, 20 days on the bottom one. The diagram on the bottom was created using my LookingUp app, the upper diagram was created using Stellarium. Annotations added in LibreOffice Draw, all put together with GIMP.
Categories: Concepts, Ephemeris Program, Planets Tags: ,

Ephemeris: 02/12/2026 – Why do planets stop and move backward for a time? Part 1

February 12, 2026 Comments off

This is Ephemeris for Darwin Day, Thursday, February 12th. Today the Sun will be up for 10 hours and 19 minutes, setting at 6:07, and it will rise tomorrow at 7:45. The Moon, 3 days past last quarter, will rise at 5:49 tomorrow morning.

For the last month or so I’ve been talking about Jupiter in its retrograde or westward motion against the stars of Gemini. This motion isn’t due to just Jupiter itself. Jupiter orbits smoothly around the sun in one direction, in a little less than 12 years. The ancients thought that the earth was stationary, and everything in the sky orbited the earth. They thought that the planets orbited the earth in the same time that the planet orbits the sun, however every year and depending on where the planet was in the sky it would stop, reverse itself for a while and then resume its eastward motion through the sky. They thought that the planet moved on a small circle called an epicycle that rode on the larger circle called the deferent.

The astronomical event times given in this blog are for the Traverse City/Interlochen area of Michigan (Lat 44.7° N, Long 85.7° W; EST, UT – 5 hours) unless stated otherwise. Times will be different for other locations.

Addendum

A geocentric chart of the solar system.
The geocentric universe as imagined by the ancients with the Earth in the center. The outer ring is the celestial sphere of the stars. The other concentric circles around the Earth are deferents for each of the planets. Note that the line from the deferent to the planet on the epicycle is parallel to the line of the earth to the sun. One would think that screams the fact that somehow the Earth was in motion. But only the Greek astronomer Aristarchus figured it out. Then that idea was discarded until Copernicus in the 15th century of the modern era resurrected the idea.

Tomorrow, we’ll find out what’s really going on.

Categories: Concepts, Ephemeris Program, Planets Tags: ,

Ephemeris: 01/05/2026 – We just passed perihelion… Can’t you feel the warmth?

January 5, 2026 Comments off

This is Ephemeris for Monday, January 5th. Today the Sun will be up for 8 hours and 57 minutes, setting at 5:16, and it will rise tomorrow at 8:19. The Moon, 2 days past full, will rise at 8:10 this evening.

While we were busy with other matters, several astronomical events happened over the weekend. First, on Friday we had our latest sunrise, so our lengthening days are beginning to show up in the morning now. On Saturday the Earth passed perihelion, that is its closest point in its orbit to the Sun. That doesn’t make things any warmer, but it does make winter the shortest season by about four days shorter than summer. Not that you could tell in Northern Michigan. The distance of the Earth from the Sun is still hanging around 91.4 million miles. The earth is moving faster so we move through winter quicker. Also, there was a meteor shower, the Quadrantids, which peaked on Saturday, but was pretty much wiped out by the full moon.

The astronomical event times given in this blog are for the Traverse City/Interlochen area of Michigan (Lat 44.7° N, Long 85.7° W; EST, UT – 5 hours) unless stated otherwise. Times will be different for other locations.

Addendum

This is a diagram of the true shape of the Earth’s orbit
This is a diagram of the true shape of the Earth’s orbit and position of the Sun showing aphelion and perihelion for the year 2024. The dates do vary by up to a couple of days each year as do the distances a little bit, but it’s lost in rounding. The date difference is a bit more than the date change of the solstices and equinoxes year to year. For 2026 the perihelion date was January 3rd, and the aphelion date will be July 6th. Created using my LookingUp app, LibreOffice Draw for captions, and GIMP.
Categories: Concepts, Earth, Ephemeris Program, Seasons Tags:

Ephemeris: 12/26/2025 – Conjunctions, eclipses, transits and occultations, oh my!

December 26, 2025 Comments off

This is Ephemeris for Friday, December 26th. Today the Sun will be up for 8 hours and 49 minutes, setting at 5:08, and it will rise tomorrow at 8:19. The Moon, 1 day before first quarter, will set at 12:13 tomorrow morning.

Tonight the Moon will pass north of the planet Saturn. That will mean in that location in the southwestern sky, the planet will appear just below and left of the Moon. When two solar system objects appear to pass each other, it’s called a conjunction. To astronomers, it’s no big deal unless one passes directly in front of the other. If a smaller appearing one crosses the disc of a larger one, it’s called a transit, If one is completely hidden by another it’s an occultation. Occultations and transits of Jupiter and its satellites are common. Also, Jupiter’s satellites are eclipsed by passing through the planet’s shadow. We are in a period now when Jupiter’s moons occult and eclipse each other occasionally.

The astronomical event times given in this blog are for the Traverse City/Interlochen area of Michigan (Lat 44.7° N, Long 85.7° W; EST, UT – 5 hours) unless stated otherwise. Times will be different for other locations.

Addendum

The conjunction of Saturn and the Moon at 8 PM tonight, December 26th from Northern Michigan.
The conjunction of Saturn and the Moon at 8 PM tonight, December 26th from Northern Michigan. The position of the moon in relation to Saturn will change for your 8 PM depending on where you are because the Moon moves its own diameter in about an hour against the stars, and of course Saturn, If you are east of my location 8 PM comes earlier so the Moon would be farther to the lower right than this image. If you are east of me, it will be to the upper left. The farther you are away east or west, the farther the Moon will be from this, based on your time zone and location. Created using Stellarium.
Categories: Concepts, Ephemeris Program Tags:

Ephemeris: 12/19/2025 – Winter begins Sunday

December 19, 2025 Comments off

This is Ephemeris for Friday, December 19th. Today the Sun will be up for 8 hours and 48 minutes, setting at 5:04, and it will rise tomorrow at 8:16. The Moon is new today, and won’t be visible.
The thermometer and snowfall tell us that winter ought to be here. Well, it will be at 10:03 Sunday morning. At that point, the winter solstice, the Sun will be directly over the Tropic of Capricorn at 23 ½ degrees south latitude. It’s an odd name because 2,000 years ago the Sun was in indeed entering Capricornus. Now it will be entering Sagittarius, right above the spout of the teapot asterism we know so well in summer. From then on the Sun will be climbing up the sky each noon until June 21st next year when summer will start. To which I say: Go Sun Go! The Sun will almost make it up to 22 degrees above the southern horizon at local noon, which is 12:40 pm, in Interlochen and be out for only 8 hours and 48 minutes. If it stayed that low all year, we’d be in a deep freeze, possibly colder than Antarctica.

The astronomical event times given in this blog are for the Traverse City/Interlochen area of Michigan (Lat 44.7° N, Long 85.7° W; EST, UT – 5 hours) unless stated otherwise. Times will be different for other locations.

Addendum

Comparing the Sun's path in the sky for winter and summer solstices
Comparing the sun’s path at the summer and winter solstices. This is a stereographic representation of the whole sky which distorts the sky and magnifies the size of the sun’s path near the horizon.
December solstice
The Earth and its axis on the first day of winter, the winter solstice. From my Sun and the Earth talk slides.
A comparison of the solar heating effect of the Sun at local noon on winter and summer solstices at 45° north latitude. Winter, 37% and summer, 93% of the Sun at the zenith.
A comparison of the solar heating effect of the Sun at local noon on winter and summer solstices at 45° north latitude. This ignored the effect of the thickening atmosphere as the altitude decreases, making the difference even greater. Also, near the summer solstice the Sun is out higher and longer. Created using LibreOffice Draw and GIMP.
Categories: Concepts, Seasons Tags: