Archive
07/13/2022 – EPHEMERIS – Let’s search for the naked-eye planets for this week
This is Ephemeris for Wednesday, July 13th. Today the Sun will be up for 15 hours and 17 minutes, setting at 9:26, and it will rise tomorrow at 6:10. The Full Buck Moon, also a supermoon, will rise at 10:05 this evening.
Let’s search for the naked-eye planets for this week. All the naked-eye planets are in the morning sky, although Mercury is too close to the Sun to be seen. On the Saturday it will leave the morning sky crossing over to the evening sky. At 5 am tomorrow, the planets will be spread out from brilliant Venus low in the east-northeast to Saturn higher in the south-southwest. Mars will be a lot higher than Venus in the east-southeast. Jupiter is a bit higher in the southeast. Mars is dimmer than Jupiter, but is slowly getting brighter as the Earth creeps up on it. Saturn ends the line of planets in the south-southwest. Tonight, Saturn will rise about 11:03 pm, though it won’t be an official evening planet until it rises before sunset, which happens in mid-August.
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
Tonight’s full supermoon shortly after it will rise at 10:30 pm July 13, 2022. Created using Stellarium.
The morning planets and the Moon at 5 am tomorrow morning, July 14, 2022. The planets and Moon actually appear in a straight line in the sky, being placed along the ecliptic, or path of the Sun in the sky. The ecliptic is a great circle on the celestial sphere. Click on the image to enlarge it. The span of the planets from Venus to Saturn is 122 degrees. Two of winter’s first magnitude stars, Aldebaran and Capella, are now visible in morning twilight. Click on the image to enlarge it. Created using Stellarium.
Views of Saturn, Jupiter, and Venus (north up) as they would be seen in a small telescope, with the same magnification, tomorrow morning at 5:00 am, July 14, 2022. I do not show planets less than 10 seconds of arc in diameter. Apparent diameters: Saturn 18.46″, its rings 43.01″; Jupiter 42.63″. Mars is not shown, its apparent diameter is 7.63″; Venus 11.31″. The ” symbol means seconds of arc (1/3600th of a degree.) Click on the image to enlarge it. Created using Cartes du Ciel (Sky Charts).
The naked-eye planets and the Moon at sunset and sunrise on a single night, starting with sunset on the right on July 13, 2022. The night ends on the left with sunrise on the 14th. Notice that all the naked-eye planets are in the morning sky now. Click on the image to enlarge it. Created using my LookingUp program.
07/06/2022 – Ephemeris – Let’s search for the naked-eye planets for this week
This is Bob Moler with Ephemeris for Wednesday, July 6th. Today the Sun will be up for 15 hours and 26 minutes, setting at 9:30, and it will rise tomorrow at 6:04. The Moon, at first quarter today, will set at 1:32 tomorrow morning.
Let’s search for the naked-eye planets for this week. All the naked-eye planets are in the morning sky, although Mercury is too close to the Sun to be seen. On the 16th, it will leave the morning sky, crossing over to the evening sky. At 5 am tomorrow, the planets will be spread out from brilliant Venus low in the east-northeast to Saturn higher in the south. To the right and above of Venus, in the east-southeast, will be the Mars. Jupiter is a bit higher in the southeast. Mars is dimmer than Jupiter, but is slowly getting brighter as the Earth creeps up on it. Saturn ends the line of planets in the south. Tonight, Saturn will rise about 11:30 pm. It won’t be an official evening planet until it rises before sunset. That won’t happen until mid-August.
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
First quarter Moon tonight with prominent features labeled. Created using Stellarium, GIMP and LibreOffice.
The morning planets at 5 am tomorrow morning, July 7, 2022. The planets actually appear in a straight line in the sky, being placed along the ecliptic, or path of the Sun in the sky. The ecliptic is a great circle on the celestial sphere. Click on the image to enlarge it. The span of the planets from Venus to Saturn is 113 degrees. Click on the image to enlarge it. Created using Stellarium.
Distortions of rendering a spherical sky on a flat plane. The morning planets as seen in a stereographic view where great circles, like the ecliptic and horizon, are either circles or straight lines. In this image, the ecliptic, orange line, runs through the center of the plot, so it appears straight. In the real sky, both the planets and the horizon appear to be in straight lines. This assumes that your horizon is flat. Click on the image to enlarge it. Created using Stellarium.
Views of Saturn, Jupiter, and Venus (north up) as they would be seen in a small telescope, with the same magnification, tomorrow morning at 5:00 am, July 7, 2022. I do not show planets less than 10 seconds of arc in diameter. Apparent diameters: Saturn 18.32″, its rings 42.68″; Jupiter 41.68″. Mars is not shown, its apparent diameter is 7.41″ and is 85.4% illuminated; Venus 11.60″, 87.5% illuminated. Jupiter’s 4th Galilean moon, Io, is missing because it is in Jupiter’s shadow. The ” symbol means seconds of arc (1/3600th of a degree.) Created using Cartes du Ciel (Sky Charts).
The naked-eye planets and the Moon at sunset and sunrise on a single night, starting with sunset on the right on July 6, 2022. The night ends on the left with sunrise on the 7th. Notice that all the naked-eye planets are in the morning sky now. Click on the image to enlarge it. Created using my LookingUp program.
06/29/2022 Ephemeris – Let’s search for the naked-eye planets for this week
This is Ephemeris for Wednesday, 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, 1 day past new, will set at 10:32 this evening.
Let’s search for the naked-eye planets for this week. All the naked-eye planets are in the morning sky, although Mercury is too close to the Sun to be seen. At 5 am tomorrow the planets will be spread out from Mercury invisible on the horizon, brilliant Venus low in the east-northeast to Saturn higher in the south. To the right and above of Venus, in the east-southeast, will be the Mars. Jupiter is in the southeast. Mars is dimmer than Jupiter, but is slowly getting brighter as the Earth is slowly advancing on it. Saturn ends the line of planets in the south. By tomorrow night, Saturn will rise a minute before midnight. It won’t be an official evening planet until it rises before sunset. That won’t happen until mid-August.
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 morning planets at 5 am tomorrow morning, June 30, 2022. The planets actually appear in a straight line in the sky, being placed along the ecliptic, or path of the Sun in the sky. The ecliptic is a great circle on the celestial sphere. Click on the image to enlarge it. The span of the planets from Venus to Saturn is 114 degrees. Click on the image to enlarge it. Created using Stellarium.
The image above was plotted using the Miller cylindrical projection. While the azimuths are correct, the other plots are not. The planets actually appear to be in a straight line in the sky. I’ve finagled a stereographic projection to show that fact, as seen below.
Distortions of rendering a spherical sky on a flat plane. The morning planets as seen in a stereographic view where great circles, like the ecliptic and horizon, are either circles or straight lines. In this image, the ecliptic, orange line, runs through the center of the plot, so it appears straight. In the real sky, both the planets and the horizon appear to be in straight lines. This assumes that your horizon is flat. Created using Stellarium.
Views of Saturn, Jupiter, and Venus (north up) as they would be seen in a small telescope, with the same magnification, tomorrow morning at 5:00 am, June 30, 2022. I do not show planets less than 10 seconds of arc in diameter. Apparent diameters: Saturn 18.16″, its rings 42.31″; Jupiter 40.75″. Mars is not shown, its apparent diameter is 7.20″ and is 85.7% illuminated; Venus 11.91″, 85.8% illuminated. Jupiter’s moon Io will be behind the planet at that time. The ” symbol means seconds of arc (1/3600th of a degree.) Created using Cartes du Ciel (Sky Charts).
The naked-eye planets and the Moon at sunset and sunrise on a single night, starting with sunset on the right on June 29, 2022. The night ends on the left with sunrise on the 30th. Notice that all the naked-eye planets are in the morning sky now. Click on the image to enlarge it. Created using my LookingUp program.
06/22/2022 – Ephemeris – Let’s search for the naked-eye planets for this week
This is Ephemeris for Wednesday, June 22nd. Today the Sun will be up for 15 hours and 34 minutes, setting at 9:32, and it will rise tomorrow at 5:57. The Moon, 2 days past last quarter, will rise at 2:48 tomorrow morning.
Let’s search for the naked-eye planets for this week. All the naked-eye planets are in the morning sky, although Mercury may be too close to the Sun to be seen. It might just be visible low in the east-northeast after 5. That’s at least for those as far north as we are. At 5 am tomorrow the planets will be spread out from Mercury, actually invisible, near the horizon, brilliant Venus low in the east-northeast to Saturn higher in the south. To the right of Venus, tomorrow morning, stretching from east to southeast, will be the Moon, Mars and Jupiter. Mars is quite a bit dimmer than Jupiter. All will be in line sloping to the upper right with Saturn all by its lonesome in the south. The naked-eye planets are arranged in the morning sky, in the same order as their distances from the Sun.
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 morning planets and the waning crescent Moon at 5 am tomorrow morning, June 23, 2022. Click on the image to enlarge it. The span of the planets from Venus to Saturn is 95 degrees. Click on the image to enlarge it. Created using Stellarium.
Waning crescent Moon closeup, annotated, as seen in binoculars or a small telescope. Created using Stellarium, Libreoffice and GIMP.
Views of Saturn, Jupiter, and Venus (north up) as they would be seen in a small telescope, with the same magnification, tomorrow morning at 5:00 am, June 23, 2022. I do not show planets less than 10 seconds of arc in diameter. Apparent diameters: Saturn 17.99″, its rings 41.90″; Jupiter 39.86″. Mars is not shown, its apparent diameter is 7.00″ and is 86.1% illuminated; Venus 12.27″, 84.1% illuminated. The ” symbol means seconds of arc (1/3600th of a degree). Created using Cartes du Ciel (Sky Charts).
The naked-eye planets and the Moon at sunset and sunrise on a single night, starting with sunset on the right on June 22, 2022. The night ends on the left with sunrise on the 23rd. Notice that all the naked-eye planets are in the morning sky now. Click on the image to enlarge it. Created using my LookingUp program.
06/15/2022 – Ephemeris – Let’s search for the naked-eye planets for this week
This is Ephemeris for Wednesday, 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, 1 day past full, will rise at 11:27 this evening.
Let’s search for the naked-eye planets for this week. All the naked-eye planets are in the morning sky, although Mercury may be too close to the Sun to be seen. It might just be visible low in the east-northeast after 5. That’s at least for those as far north as we are. At 5 am tomorrow the planets will be spread out from Mercury near the horizon, brilliant Venus low in the east to Saturn higher in the south-southeast. To the right of Venus, tomorrow morning, in the east-southeast are Mars and Jupiter. Mars is quite a bit dimmer than Jupiter. All will be in line sloping to the upper right with Saturn all by its lonesome in the south-southeast. The naked-eye planets are arranged in the morning sky, in the same order as their distances from the Sun.
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 might appear at midnight June 16, 2022, through binoculars or a small telescope. Atmospheric refraction will affect the shape of the Moon when it’s very low in the sky. Created using Stellarium.
Morning planets at 5 am tomorrow morning, June 16, 2022. Click on the image to enlarge it. The span of the planets from Venus to Saturn is 87 degrees. Click on the image to enlarge it. Created using Stellarium.
Views of Saturn, Jupiter, and Venus (north up) as they would be seen in a small telescope, with the same magnification, tomorrow morning at 5:00 am, June 16, 2022. I do not show planets less than 10 seconds of arc in diameter. Apparent diameters: Saturn 17.80″, its rings 41.47″; Jupiter 39.02″. Mars is not shown, its apparent diameter is 6.81″ and is 86.4% illuminated; Venus 12.66″, 82.2% illuminated. The ” symbol means seconds of arc (1/3600th of a degree.) Created using Cartes du Ciel (Sky Charts).
The naked-eye planets and the Moon at sunset and sunrise on a single night, starting with sunset on the right on June 15, 2022. The night ends on the left with sunrise on the 16th. Notice that all the naked-eye planets are in the morning sky now. Click on the image to enlarge it. Created using my LookingUp program.
06/08/2022 – Ephemeris – Let’s search for the naked-eye planets for this week
This is Ephemeris for Wednesday, June 8th. Today the Sun will be up for 15 hours and 29 minutes, setting at 9:26, and it will rise tomorrow at 5:57. The Moon, 1 day past first quarter, will set at 3:08 tomorrow morning.
Let’s search for the naked-eye planets for this week. All the naked-eye planets are in the morning sky, although Mercury may be too close to the Sun to be seen. It might just be visible low in the east-northeast after 5 am around mid-month. That’s at least for those as far north as we are. At 5 am tomorrow the planets will be spread out from brilliant Venus low in the east to Saturn higher in the south-southeast. To the right of Venus, tomorrow morning, in the east-southeast are Mars and Jupiter. Mars is quite a bit dimmer than Jupiter. All will be in line sloping to the upper right with Saturn all by its lonesome in the south-southeast. The naked-eye planets are arranged in the morning sky, in the same order as their distances from the Sun.
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
Waning gibbous Moon tonight with prominent features labeled. Created using Stellarium, GIMP and LibreOffice.
Morning planets at 5 am tomorrow morning, June 9, 2022. Click on the image to enlarge it. The span of the planets from Venus to Saturn is 79 degrees. Created using Stellarium.
Views of Venus, Jupiter, and Saturn (north up) as they would be seen in a small telescope, with the same magnification, tomorrow morning at 5:00 am, June 9, 2022. I do not show planets less than 10 seconds of arc in diameter. Apparent diameters: Venus 13.10″, 80.3% illuminated; Saturn 17.60″, its rings 41.01″; Jupiter 38.23″. Mars is not shown, its apparent diameter is 6.63″ and is 86.8% illuminated. The ” symbol means seconds of arc (1/3600th of a degree.) Created using Cartes du Ciel (Sky Charts).
The naked-eye planets and the Moon at sunset and sunrise on a single night, starting with sunset on the right on June 8, 2022. The night ends on the left with sunrise on the 9th. Notice that all the naked-eye planets are in the morning sky now. Click on the image to enlarge it. Created using my LookingUp program.
06/01/2022 – Ephemeris – Let’s search for the naked-eye planets for this week
This is Ephemeris for Wednesday, June 1st. Today the Sun will be up for 15 hours and 21 minutes, setting at 9:21, and it will rise tomorrow at 5:59. The Moon, 2 days past new, will set at 11:49 this evening.
Let’s search for the naked-eye planets for this week. All the naked-eye planets are in the morning sky, although Mercury is too close to the Sun to be seen, and might just be visible low in the east-northeast after 5 am around mid-month. That’s at least for those as far north as we are. At 5 am tomorrow the planets will be spread out from brilliant Venus low in the east to Saturn higher in the south-southeast. To the right of Venus, tomorrow morning, in the east-southeast are Mars and Jupiter. Mars is quite a bit dimmer than Jupiter. All will be in line sloping to the upper right with Saturn all by its lonesome in the south-southeast. Though Mercury will enter the evening sky first, it won’t have great visibility. Saturn will enter the evening sky August 14th.
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 two-day-old Moon as it might be seen in binoculars tonight, June 1, 2022. Earth shine might illuminate the Moon’s night side. Created using Stellarium and GIMP.
Morning planets at 5 am tomorrow morning, June 2, 2022. Click on the image to enlarge it. The span of the planets from Venus to Saturn is 70 degrees. Click on the image to enlarge it. Created using Stellarium.
Views of Venus, Jupiter, and Saturn (north up) as they would be seen in a small telescope, with the same magnification, tomorrow morning at 5:00 am, June 2, 2022. I do not show planets less than 10 seconds of arc in diameter. Apparent diameters: Venus 13.58″, 78.3% illuminated; Saturn 17.40″, its rings 40.54″; Jupiter 37.49″. Mars is not shown, its apparent diameter is 6.46″ and is 87.2% illuminated. The ” symbol means seconds of arc (1/3600th of a degree.) Created using Cartes du Ciel (Sky Charts), planet information from Stellarium.
The naked-eye planets and the Moon at sunset and sunrise on a single night, starting with sunset on the right on June 1, 2022. The night ends on the left with sunrise on the 2nd. Notice that all the naked-eye planets are in the morning sky now. Click on the image to enlarge it. Created using my LookingUp program.
Update on the Tau Herculid meteor shower of May 31st.
The meteor shower was rather weak. I saw one during an hour and a half of observing, slowly moving over the Big Dipper. The sky was “clear”, but there was a haze to it. It definitely wasn’t crystal clear. I’ve heard from others who had a bit more success.
05/25/2022 – Ephemeris – Let’s search for the naked-eye planets for this week
This is Ephemeris for Wednesday, May 25th. Today the Sun will be up for 15 hours and 10 minutes, setting at 9:15, and it will rise tomorrow at 6:04. The Moon, 3 days past last quarter, will rise at 4:22 tomorrow morning. | Let’s search for the naked-eye planets for this week. All the naked-eye planets are back in the morning sky, although the newcomer, Mercury, is too close to the Sun to be seen, and may stay that way for the rest of its morning appearance. That’s at least for those as far north as we are (45° N). At 5 am tomorrow the planets will be spread out from brilliant Venus low in the east to Saturn higher in the southeast. To the right of Venus, tomorrow morning, will be the thin crescent Moon. Farther right is the quite bright Jupiter. Just to the right of Jupiter will be the dimmest of the 4, Mars, which is closing on Jupiter. The two will seem to pass each other on Sunday. All will be in line sloping to the upper right with Saturn all by its lonesome in the southeast.
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
All the morning planets except Mercury, which is too close to the Sun to be seen, will be visible at 5 am tomorrow morning, May 26, 2022. The labels for Mars and Jupiter are on top of each other. Click on the image to enlarge it. Created using Stellarium.
The waning crescent moon as it might appear in binoculars tomorrow morning, May 26, 2022. Earth shine might also illuminate the Moon’s night side. Created using Stellarium.
Views of Venus, Jupiter, and Saturn (north up) as they would be seen in a small telescope, with the same magnification, tomorrow morning at 5:00 am, May 26, 2022. I do not show planets less than 10 seconds of arc in diameter. Apparent diameters: Venus 14.13″, 76.1% illuminated; Saturn 17.20″, its rings 40.06″; Jupiter 36.80″. Mars is not shown, its apparent diameter is 6.30″ and is 87.7% illuminated. The ” symbol means seconds of arc (1/3600th of a degree.) Created using Cartes du Ciel (Sky Charts).
The naked-eye planets and the Moon at sunset and sunrise on a single night, starting with sunset on the right on May 25, 2022. The night ends on the left with sunrise on the 26th. Notice that all the naked-eye planets are in the morning sky now. Click on the image to enlarge it. Created using my LookingUp program.
05/18/2022 – Ephemeris – Let’s search for the naked-eye planets for this week
This is Ephemeris for Wednesday, May 18th. Today the Sun will be up for 14 hours and 56 minutes, setting at 9:07, and it will rise tomorrow at 6:10. The Moon, 2 days past full, will rise at 12:43 tomorrow morning.
Let’s search for the naked-eye planets for this week. The one bright planet in the evening sky, Mercury, will pass between us and the Sun this Saturday to join the rest of the naked-eye planets in the morning sky. So that’s where the planet action is. At 5:15 am tomorrow, the planets will be spread out from brilliant Venus low in the east to Saturn higher in the southeast. Venus may be missed at that time, but may be up sufficiently by 5:30. To the right of Venus is the quite bright Jupiter. Farther right will be the dimmest of the 4, Mars, which is closing on Jupiter. The two will seem to pass each other on the 29th of this month. All will be in line, sloping to the upper right. They are still quite a sight to behold in the morning twilight.
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 might appear in binoculars or a small telescope tomorrow morning at 1:30 May 19, 2022. Created using Stellarium, GIMP and LibreOffice.
The morning planet parade is widening as Venus is moving away from Jupiter and toward the Sun. Mars is approaching Jupiter and will catch up to it on the 29th. These are shown at 5:15 am, or about an hour before sunrise tomorrow morning, May 19, 2022. Click on the image to enlarge it. Created using Stellarium.
Views of Venus, Jupiter, and Saturn (north up) as they would be seen in a small telescope, with the same magnification, tomorrow morning at 5:15 am, May 19, 2022. I do not show planets less than 10 seconds of arc in diameter. Apparent diameters: Venus 14.73″, 73.9% illuminated; Saturn 16.99″, its rings 39.59″; Jupiter 36.17″. Mars is not shown, its apparent diameter is 6.14″ and is 88.1% illuminated. The ” symbol means seconds of arc (1/3600th of a degree.) Created using Cartes du Ciel (Sky Charts).
The naked-eye planets and the Moon at sunset and sunrise on a single night, starting with sunset on the right on May 18, 2022. The night ends on the left with sunrise on the 19th. Notice that all the naked-eye planets except Mercury are in the morning sky now. Click on the image to enlarge it. Created using my LookingUp program.
05/11/2022 – Ephemeris – Let’s search for the naked-eye planets for this week
This is Bob Moler with Ephemeris for Wednesday, May 11th. Today the Sun will be up for 14 hours and 40 minutes, setting at 8:59, and it will rise tomorrow at 6:18. The Moon, 3 days past first quarter, will set at 4:45 tomorrow morning.
Let’s search for the naked-eye planets for this week. The one bright planet in the evening sky, Mercury, is now too dim and close to the Sun to be seen, so the only planet action is in the morning sky where the other 4 naked-eye planets are. At 5:15 am tomorrow the planets will be spread out low from the east to southeast with brilliant Venus lowest and due east to Saturn almost exactly in the southeast. Venus may be missed at that time, but may be up sufficiently by 5:30. To the right of Venus is the quite bright Jupiter. Farther right will be the dimmest of the four, Mars. Farther to the right will be Saturn. All will be in A sloping to the upper right. They are still quite a sight to behold in the morning twilight.
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
Animated annotated Binocular Moon for this evening, May 11, 2022. Created using Virtual Moon Atlas, GIMP and LibreOffice.
Translations
Mare Crisium – Sea of Crises
Mare Fecunditatis – Sea of Fertility
Mare Frigoris – Sea of Cold
Mare Imbrium – Sea of Showers
Mare Nectaris – Sea of Nectar
Mare Nubium – Sea of Clouds
Mare Serenitatis – Sea of Serenity
Mare Tranquillitatis – Sea of Tranquility
Mare Vaporum – Sea of Vapors
Sinus Iridium – Bay of Rainbows
Sinus Medii – Bay of the Center
Note that Mare is pronounced Mar-é
The morning planet parade is widening as Venus is moving away from Jupiter, and Mars is approaching Jupiter. These are shown at 5:15 am, or about an hour before sunrise tomorrow morning, May 12, 2022. Created using Stellarium.
Views of Venus, Jupiter, and Saturn (north up) as they would be seen in a small telescope, with the same magnification, tomorrow morning at 5:15 am, May 12, 2022. I do not show planets less than 10 seconds of arc in diameter. Apparent diameters: Venus 15.42″, 71.6% illuminated; Saturn 16.79″, its rings 39.12″; Jupiter 35.60″. Mars is not shown, its apparent diameter is 5.99″ and is 88.6% illuminated. The ” symbol means seconds of arc (1/3600th of a degree.) Created using Cartes du Ciel (Sky Charts).
The naked-eye planets and the Moon at sunset and sunrise on a single night, starting with sunset on the right on May 11, 2022. The night ends on the left with sunrise on the 12th. Notice that all the naked-eye planets except Mercury are in the morning sky now. Click on the image to enlarge it. Created using my LookingUp program.
Bob Moler's Ephemeris Blog 