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04/14/2022 – Ephemeris – The Moon appears to wobble

April 14, 2022 Comments off

This is Bob Moler with Ephemeris for Thursday, April 14th. Today the Sun will be up for 13 hours and 26 minutes, setting at 8:26, and it will rise tomorrow at 6:58. The Moon, 2 days before full, will set at 6:43 tomorrow morning.

Tonight’s Moon is nearly full, only two days to go. In the evening, the little dark sea on the Moon called Mare Crisium or Sea of Crises is near the top of the Moon. Now it’s real close to the top edge of the Moon, what astronomers call the limb. Ten days ago, when the Moon was a crescent, Mare Crisium was farther from the limb. This wobbling motion over the lunar month is called libration. This occurs because the Moon has an elliptical orbit of the Earth and speeds up when it’s closer and slows when it’s farther away. However, the Moon’s rotation is constant due to its angular momentum. The period of the revolution of the Moon around the Earth exactly matches its rotation. When the Moon is farthest, its rotation gets a bit ahead of its revolution around the Earth. When closest, the rotation lags a bit. So it appears to wobble over the lunar month.

The astronomical event times given are for the Traverse City/Interlochen area of Michigan (EDT, UT – 4 hours). They may be different for your location.

Addendum

The Moon as it should appear at 10 pm tonight

The Moon as it should appear at 10 pm tonight, April 14, 2022. Note the position, relative to the Moon’s limb, of the small lunar sea called Mare Crisium near the top of the Moon. Mare Crisium means Sea of Crises. It is quite close to the limb tonight. In the animation below, shown without the phase, the orientation of the Moon is not changed by the position in the sky or the latitude of the observer. Created using Stellarium.

Demonstration of libration via animation

A demonstration of libration by viewing the position of Mare Crisium. Also note that there is also a libration in the Moon’s latitude, causing a north-south nodding. Another good indicator of libration is the dark floored crater called Grimaldi on the left side of the Moon, which is not visible tonight in the image at the top. But it will appear in sunlight tomorrow night. Created using Virtual Moon Atlas.

03/17/2022 – Ephemeris – We have 12 hours of daylight and night today, three days early

March 17, 2022 Comments off

This is Ephemeris for St. Patrick’s Day, Thursday, March 17th. Today the Sun will be up for 12 hours even, setting at 7:51, and it will rise tomorrow at 7:49. The Moon, 1 day before full, will set at 8:20 tomorrow morning.

Why is this the day of equal day and night, when the vernal equinox, which means “equal night” is still three days away? The difference is due to our atmosphere and our definition of sunrise and sunset. Our atmosphere makes objects near the horizon appear higher than they actually are, which hastens sunrise and retards sunset. Also, the instant of sunrise and sunset is when the top of the sun appears to touch the horizon, rather than when the Sun bisects the horizon. Plus, it’s moving about a degree a day (twice its diameter) against the stars. So by the time of the equinox, on Sunday the 20th, the time between sunrise and sunset will have progressed to 12 hours and 9 minutes. But it was close enough for the ancients who coined the term.

The astronomical event times given are for the Traverse City/Interlochen area of Michigan (EDT, UT – 4 hours). They may be different for your location.

Addendum

This works for the Interlochen area. It may be a different by a day for other locations, but for the northern latitudes, it will be before the true equinox day, March 20th here.

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. 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

03/14/2022 – Ephemeris – It’s Pi Day!

March 14, 2022 Comments off

This is Ephemeris for Pi Day, Monday, March 14th. Today the Sun will be up for 11 hours and 50 minutes, setting at 7:47, and it will rise tomorrow at 7:55. The Moon, 4 days before full, will set at 7:10 tomorrow morning.

Mathematicians and scientists, both professional and amateur, celebrate Pi day to bake and eat pies. Actually, the Pi we’re talking about is the Greek letter π that signifies the ratio of the circumference of a circle to its diameter. March 14th can be written 3.14, π to two decimal places. Of course, if you wait until 4 pm to have your pie, you can have π to 4 decimal places, since 4 pm is the 16th hour of the day in military time. This gives 3.1416. The digits go on forever, never repeating a pattern. Some mathematicians prefer Tau Day, June 28th or 2 times π which is the more useful mathematical ratio of the circumference of a circle to its radius, which is 6.28 or 6.2832. However you slice it, π is a very useful number.

The astronomical event times given are for the Traverse City/Interlochen area of Michigan (EDT, UT – 4 hours). They may be different for your location.

Addendum

Have a slice of Pi Day pie

Here’s a link to NASA’s Pi Day Challenge: https://www.jpl.nasa.gov/edu/nasapidaychallenge/. The link also has a link for educators for STEM related challenges.

Since recording this program, I learned about another Pi day some celebrate. A well-known approximation of pi is the fraction 22/7ths. Europeans and others write dates in day/month order, so July 22nd is also a Pi Day: 22/7.

09/23/2021 – Ephemeris – The Earth’s axial tilt gives us our seasons

September 23, 2021 Comments off

This is Bob Moler with Ephemeris for Thursday, September 23rd. Today the Sun will be up for 12 hours and 6 minutes, setting at 7:37, and it will rise tomorrow at 7:32. The Moon, 3 days past full, will rise at 9:03 this evening.

The Earth has an axial tilt* of about 23 and a half degrees, which gives us our seasons. Because the Earth rotates on its axis, it has a slight equatorial bulge. Earth’s polar diameter is 7,900 miles (12,714 kilometers) while its equatorial diameter is 7,926 miles (12,756 kilometers), a difference of 26 miles (42 kilometers). The gravitational tug on that equatorial bulge by the Moon and Sun actually keeps the tilt stable, but does cause the Earth’s axis to precess like a top slowing down. It’s why Polaris will no longer be our North Pole star in centuries to come, just as it wasn’t in centuries past. It’s also why the constellations of the zodiac no longer align with the astrological signs of Ptolemy’s zodiac of the second century AD.

The astronomical event times given are for the Traverse City/Interlochen area of Michigan (EDT, UT-4 hours). They may be different for your location.

* Astronomers call axial tilt “obliquity” or “obliquity of the ecliptic”.

Addendum

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. Image credit: Open Course: Astronomy.

Precesssion of a spinning top

Precession of a spinning top: the spin axis traces the surface of a cone. The axis, in the case of the Earth, traces a circle of radius 23.5 degrees on the sky. Credit NASA.

Precesion animation

The 25,700-year cycle of precession traced on the sky 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: Tfr000, caption: Wikipedia.

08/24/2021 – Ephemeris – The Harvest Moon is coming next full moon

August 24, 2021 Comments off

This is Bob Moler with Ephemeris for Tuesday, August 24th. Today the Sun will be up for 13 hours and 36 minutes, setting at 8:33, and it will rise tomorrow at 6:57. The Moon, 2 days past full, will rise at 10:00 this evening.

We are at that time of year when the advance in Moon rising times from night to night is shorter than the average 50 minutes per night. Tonight the Moon will rise only 21 minutes later than it did last night, and tomorrow’s Moon will rise 20 minutes later than it will tonight. It’s what I call the harvest moon effect, though Harvest Moon will be next month. I find the effect lasts for three full moons, centered on the start of autumn. That’s because the angle of the Moon’s and also the Sun’s paths in the sky called the ecliptic intersect the horizon at a shallow angle near sunset. It’s also the reason Venus will stay close to the western horizon for its evening appearance this year. The planets also hang around the ecliptic, where the zodiacal constellations are.

The astronomical event times given are for the Traverse City/Interlochen area of Michigan (EDT, UT – 4 hr). They may be different for your location.

Addendum

Autumn vs spring sunset ecliptic

The autumn vs spring sunset ecliptic (orange line). I’m using the autumnal equinox 2021 and vernal equinox 2022 as examples. At the autumnal equinox sunset, the ecliptic runs low in the south, and the ecliptic meets the horizon at a low angle. At the vernal equinox in March, the ecliptic runs very high in the south. It meets the horizon at a steep angle. Click on the image to enlarge it. Created using Stellarium and GIMP.

Near the autumnal equinox, the ecliptic appears low in the south at sunset. Planets near the Sun like Venus are seen low in the west and set soon after sunset. At the opposite end of the sky, a rising Moon near full will rise at less than the 50 minutes later each night average.

08/20/2021 – Ephemeris – The Moon will pass Saturn tonight

August 20, 2021 Comments off

This is Bob Moler with Ephemeris for Friday, August 20th. Today the Sun will be up for 13 hours and 48 minutes, setting at 8:39, and it will rise tomorrow at 6:52. The Moon, 2 days before full, will set at 5:26 tomorrow morning.

The Moon is passing Saturn this evening. Saturn will be directly above the Moon by about 10 moon-widths or five degrees at 10 pm tonight. Tomorrow night the Moon will have moved toward Jupiter, which at the same time of night, the planet will appear to the upper left of our satellite. The sky appears to us to be a dome over us, which is useful for imagining the constellations, navigation, and pointing telescopes. However, that is an illusion. The night sky is impossibly and wonderfully deep. The Moon is a quarter of a million miles away, Jupiter and Saturn are hundreds of million miles away. The nearest nighttime stars are trillions of miles away, and so on as far as our eyes and instruments can see.

The astronomical event times given are for the Traverse City/Interlochen area of Michigan (EDT, UT – 4 hr). They may be different for your location.

Addendum

Moon passing Saturn animation

Animation showing the Moon passing Saturn and Jupiter at 10 pm on August 20 & 21, 2021. Beside the Moon jumping position between the two dates, the planets and stars do too, but to a lesser extent to the right. This is due to the Earth’s change in position as it orbits the Sun. Stars rise and set 3 minutes, 56 seconds earlier each night. The Created using Stellarium and GIMP.

07/19/2021 – Ephemeris – How does your telescope’s image orientation compare to how it looks to the naked-eye?

July 19, 2021 Comments off

This is Ephemeris for Monday, July 19th. Today the Sun will be up for 15 hours and 6 minutes, setting at 9:22, and it will rise tomorrow at 6:16. The Moon, 2 days past first quarter, will set at 2:35 tomorrow morning.

When you look through a telescope at the Moon, how does it look compare to how it looks to the naked-eye? Yes, it’s bigger and probably brighter. But how did its orientation change? Astronomical telescopes generally give an upside-own image, that is rotated 180 degrees. Newtonian reflector telescopes, with their eyepiece near the top of the telescope, give such an image, as do refractor telescopes where the diagonal mirror near the eyepiece is not used. When such a mirror is used a right side up, but mirror image is the result. The mirror image results when an odd number of reflections occur in the light path. Binoculars use two or four reflections. Newtonian reflectors have two reflections. It can be confusing sometimes.

The astronomical event times given are for the Traverse City/Interlochen area of Michigan (EDT, UT – 4 hr). They may be different for your location.

Addendum

Telescope image orientations

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06/15/2021 – Ephemeris – Today we had the earliest sunrise of the year

June 15, 2021 Comments off

This is Ephemeris for Tuesday, June 15th. Today the Sun will be up for 15 hours and 33 minutes, setting at 9:30, and it will rise tomorrow at 5:56. The Moon, 2 days before first quarter, will set at 1:29 tomorrow morning.

Today is the day of the year with the earliest sunrise, which in the Interlochen/Traverse City area is 6:56 am. We are 5 days before the summer solstice, the longest day in terms of sunshine hours. With the Sun nearing its maximum angle above the celestial equator, the projection of the Earth’s equator on the sky it cuts those longitude timelines quicker because they are closer together than at the equator. This is counters somewhat the Sun’s speed slowing down as the Earth is reaching the farthest point in its orbit. The latest sunset will occur about June 26th, a span of 11 days. In December the span between the earliest sunset and latest sunrise because of the Sun’s increased speed, by being nearly at its closest to us, is 24 days.

The astronomical event times given are for the Traverse City/Interlochen area of Michigan. They may be different for your location.

Addendum

Sun crossing time lines

How the Sun’s declination affects how rapidly it appears to cross time lines (meridians)

Analemma components animated

These graphs show how the earth’s orbit eccentricity and tilt of the Earth’s axis (obliquity) affect sundial time keeping vs. actual clocks. This also affects sunrise and sunset times. The figure 8 in the lower right is the analemma, sometimes seen on old Earth globes, a graphical representation of the equation of time (sundial corrections from apparent to mean solar time).

Earliest and Latest Sunrises and Sunsets

Table of Earliest and Latest Sunrises and Sunsets during the year for Interlochen/Traverse City area of Michigan. This table was created for 2017, 4 years ago. However, the instant of the summer solstice occurred just after midnight on June 21st, That instant slipped back into just before midnight in 2021. This is why we use the Gregorian calendar. The slide is corrected by having 3 out of four century years being normal years.

06/11/2021 – Ephemeris – Spotting the one-day-old Moon

June 11, 2021 Comments off

This is Bob Moler with Ephemeris for Friday, June 11th. Today the Sun will be up for 15 hours and 31 minutes, setting at 9:28, and it will rise tomorrow at 5:56. The Moon, 1 day past new, will set at 10:56 this evening.

Tonight the thin crescent Moon, some 40 hours old, or more properly 40 hours from eclipsing the Sun, will be to the right and a bit below the bright planet Venus. It might be possible to spot it. I do remember spotting the tiny sliver of a Moon the next evening after a solar eclipse in 1970. But that was in March*, when the ecliptic, the path of the Sun and near the path of all the planets and the Moon, was angled more vertically than it is this time of year. That means that the Moon and planets, when near the Sun, are lower in the sky after sunset than they would be in late winter and early spring. Venus is slowly moving away from the Sun, from our vantage point, while Mars, above and left of it, is slowly retreating toward the Sun. Their apparent paths will cross on July 13th.

The astronomical event times given are for the Traverse City/Interlochen area of Michigan. They may be different for your location.

* On the program, I mistakenly said April.

Addendum

Sunset ecliptic June 11, 2021

Sunset sky and ecliptic (orange line) 45 minutes after sunset tonight, June 11, 2021. Note the low angle of the ecliptic, the apparent path of the Sun and near the path of the planets. The angle will get even lower as summer progresses. So planets close to the Sun will set shortly after the Sun. Created using Stellarium.

Sunset ecliptic in March

This is the sky one day after the March 7, 1970 eclipse and 45 minutes after sunset. Being March, note how steep the angle of the ecliptic, so planets close to the Sun are higher in the sky. Also, twilight ends quicker in March than in June.

05/21/2021 – Ephemeris – For everything there is a season… even eclipses

May 21, 2021 Comments off

This is Ephemeris for Friday, May 21st. Today the Sun will be up for 15 hours and 3 minutes, setting at 9:11, and it will rise tomorrow at 6:07. The Moon, 2 days past first quarter, will set at 4:14 tomorrow morning.

There are seasons for everything: baseball season, football season, spring, summer, what have you. There are also eclipse seasons. The Moon’s orbit is tilted by about 5 degrees to the ecliptic, the path of the Sun in the sky. The points where they cross are called nodes, 180 degrees apart. When the Sun is near one of those nodes we are in an eclipse season, where a solar eclipse can occur at new moon, and a lunar eclipse can occur at full moon. We are guaranteed one of each per eclipse season, and on rare occasions a third eclipse. Of course one has to be at the right place to see an eclipse. This eclipse season we will be at a marginal place to see both eclipses. Both are at sunrise, so we’ll see just a part of each of them.

The astronomical event times given are for the Traverse City/Interlochen area of Michigan. They may be different for your location.

Addendum

Apparent paths of the Sun and Moon against the sky
A diagram of the paths of the Moon and Sun projected on the sky (celestial sphere). N1 and N2 are the nodes (crossing points). Nodes are ascending or descending depending on the northerly or southerly component of the Moon’s motion in crossing them. The Sun and Moon move in an easterly direction, but the Moon’s orbit precesses so that the line of nodes move in a westerly direction once around in 18.6 years. That’s why eclipse season intervals are 173.3 days and move backward in the calendar one year to the next. Eclipse seasons occur when the Sun is less than about 17.5 degrees from a node. Credit Earthsky.org.

For a more extensive treatment of this subject check out: https://earthsky.org/astronomy-essentials/definition-what-is-an-eclipse-season