Archive

Archive for the ‘Concepts’ Category

Ephemeris: 06/29/2026 – Red stars large and small

June 29, 2026 Leave a comment

This is Ephemeris for Monday, June 29th. Today the Sun will be up for 15 hours and 32 minutes, setting at 9:32, and it will rise tomorrow at 6:00. The Moon, at full today, will rise at 9:53 this evening.

There are two kinds of red stars very bright ones and very dim ones. The bright red ones are very few. One of them in the evening sky now is Antares in the heart of Scorpius the scorpion. Another one is in the winter sky and the most famous red giant of all, Betelgeuse in the shoulder of Orion the hunter. These are giant stars have exhausted the hydrogen in their cores to produce helium and are working on helium or even heavier elements fusing them to still heavier elements at even higher temperatures to keep them alive, but since they are working on the ash of the previous reaction, they won’t last very long, and the star dies, possibly cataclysmically. The higher internal heat bloats the star to be, huge, making its outer layers are actually cooler.

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; EDT, UT – 4 hours) unless stated otherwise. Times will be different for other locations.

Addendum

Size comparison between the Sun and two famous red giant stars.
Size comparison between the Sun and two famous red giant stars. However, believe the numbers, not the image size comparisons, which are not to scale and actually too small.
Graphic of the Sun and Barnard's Star.
Graphic of the Sun and Barnard’s Star. Until we found a planet in the habitable zone of Proxima Centauri, the nearest star to the Sun, Barnard’s Star was the most famous red dwarf star. Bernard’s star’s claim to fame that is it has the fastest proper motion of any known star, mainly because it’s only 6 light years away. Proper motion is the apparent star’s motion against more distant stars. In 1916 E. E. Barnard discovered it above the right shoulder of the constellation Ophiuchus the serpent bearer. It moves at a rate of 10.3 arcseconds per year that is 10.3/3600ths of a degree. It can only be seen in a telescope.

Categories: Concepts, Ephemeris Program, Stars Tags: ,

Ephemeris: 06/26/2026 – How do we know so much about those points of lights in the sky?

June 26, 2026 Comments off

This is Ephemeris for Friday, June 26th. Today the Sun will be up for 15 hours and 33 minutes, setting at 9:32, and it will rise tomorrow at 5:59. The Moon, 3 days before full, will set at 3:37 tomorrow morning.

All but a handful of stars are mere points in even our largest telescopes. How do we know so much about them then? The reason is the science of spectroscopy, breaking down light into its constituent colors where color equals frequency or the energy of the light. Isaac Newton was the first to discover that by passing white light through a prism it turned into a rainbow of colors that the colors were actually combined within the white light. Passing sunlight through a vertical slit and smearing the light horizontally with the prism into its constituent colors, many dark vertical lines within that spectrum of colors appear. They turned out to be the fingerprints of the elements within the atmospheres of the stars, and that is just the beginning.

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; EDT, UT – 4 hours) unless stated otherwise. Times will be different for other locations.

Addendum

The visible solar spectrum. In 1814 Joseph von Fraunhofer observed the spectrum and labeled the dark lines on it.
This is the visible solar spectrum. In 1814 Joseph von Fraunhofer observed the spectrum and labeled these lines with the letters that you see on top . These lines are the most prominent lines of the solar spectrum. There are many more for all the elements in the sun’s atmosphere. These elements absorb light of specific wavelengths coming to us and remit it in all directions, so we have a net loss. The lines are actually the images of the slit that the light went through, or in this case didn’t go through so they imprint on the spectrum as a line. The bottom scale is the wavelength in nanometers (billionths of a meter).

Categories: Concepts, Ephemeris Program, Stars Tags: ,

Ephemeris: 06/25/2026 – The color of stars

June 25, 2026 Comments off

This is Ephemeris for Thursday, June 25th. Today the Sun will be up for 15 hours and 34 minutes, setting at 9:32, and it will rise tomorrow at 5:58. The Moon, halfway from first quarter to full, will set at 3:03 tomorrow morning.

Looking out at the night sky casually, the first impression is that the stars all appear to be white. Closer inspection shows that some appear with tinges of red or orange or maybe yellow while other stars have a bluish cast to them. The color of stars is due to their surface temperature which physicists call black body radiation. A rainbow is a spectrum of colors from red through orange yellow green blue and violet. These colors represent the different wavelengths of light. The peak wavelength determines the star’s surface temperature. The Sun’s in the green in the middle of our visual field. Cooler stars have their peak in the red, while hotter stars have their peak output to the blue end of the spectrum.

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; EDT, UT – 4 hours) unless stated otherwise. Times will be different for other locations.

Addendum

The curved lines are the black body emission curves of these three particular stars the blue one the yellow one and the red one. The peak of each moves farther into the blue as the surface temperature of the star increases.
The curved lines are the black body emission curves of these three particular stars the blue one the yellow one and the red one. The peak of each moves farther into the blue as the surface temperature of the star increases. The temperature is in Kelvins. Think Celsius. Multiply by 2 (1.9 if you’re picky) to get the approximate temperature in Fahrenheit.
The spectral class of the star is determined by its surface temperature which is shown by its color.
The spectral class of the star is determined by its surface temperature which is shown by its color. The alphabetical classes used to be in alphabetical order by the strength of the hydrogen absorption lines in their spectrum. This turned out to be not useful. So about to turn it the last century Annie Jump Cannon, a Harvard College Observatory human “computer”, and an expert in determining spectral classes of stars, had them rearranged in this particular order by color. She even made-up a mnemonic to remember the order. It was “Oh Be A Fine Girl, Kiss Me”. Of course nowadays you could substitute guy for girl.
Annie Jump Cannon (1863-1941)
Annie Jump Cannon (1863-1941)

Categories: Concepts, Ephemeris Program, Stars Tags: ,

Ephemeris: 04/28/2026 – Stars spend most of their lives fueled by hydrogen

April 28, 2026 Comments off

This is Ephemeris for Tuesday, April 28th. Today the Sun will be up for 14 hours and 7 minutes, setting at 8:44, and it will rise tomorrow at 6:35. The Moon, 3 days before full, will set at 5:24 tomorrow morning.

A star is a gaseous ball made mostly of hydrogen, which due to its mass crushes down in its core to create heat in the millions of degrees. Under those temperatures and pressures hydrogen nuclei, stripped of their electrons can collide to convert into helium and in doing so lose a tiny bit of mass that turns into energy which is used to sustain the star’s light and keep it stable. This hydrogen burning, so to speak, takes place during the longest period of a star’s life. And stars have a characteristic color based on their mass. Stars with little mass are cooler and appear a dim red. We call them red dwarfs. The nearest star to our solar system is a red dwarf called Proxima Centauri. It’s so dim that it’d be difficult to find with a pair of binoculars. And it’s only four light years away.

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; EDT, UT – 4 hours) unless stated otherwise. Times will be different for other locations.

Addendum

H-R diagram
The Hertzsprung-Russell (H-R) diagram of star luminosity vs. surface temperature. Credit: European Southern Observatory (ESO).

The HR diagram above shows the various types and brightness of stars. The relatively thin line of stars from upper left to lower right, called the main sequence, are stars that are running primarily on hydrogen as a fuel. At the bottom end of the main sequence small stars with a fraction of the sun’s mass. All these stars are near the sun. It doesn’t mean that we live in a bad neighborhood, but that the most numerous stars are red dwarfs, and we just can’t see them when they’re farther away. All the other stars are not using as hydrogen as their main fuel source. Stars the upper right are using heavier elements to produce energy from the fusion products of lighter elements, after having run out of hydrogen in their cores. The white dwarf stars in the lower part of the diagram no longer have active thermonuclear reactions in their cores and are cooling down and collapsing. A star with the mass of the sun, when it becomes a white dwarf, will shrink down to about the size of the earth.

Categories: Concepts, Ephemeris Program, Stars Tags: , ,

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

April 2, 2026 Comments off

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: ,