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Measuring Jupiter Without Optics
(and without getting out of bed)
© Bob Graham 2014

One is glad to hear that the naked eye still retains some importance in the estimation of astronomers. Henry David Thoreau, Journal, July 9, 1851

On Tue, Jan 14, 2014, I sent an email to Andrew T. Young, astronomer at San Diego State University.

Hi Andrew,
Bob Graham in Sacramento here--about 12 years ago you helped me with using the rule of the obliquity of the ecliptic in calculating the height of the sun at meridian transit for a string of 36 Julian calendar days on the coast of California in June-July, 1579
(Francis Drake observations for latitude).

Yesterday morning, just before my alarm was to awaken me, I awoke to see Jupiter about to set below the horizon formed by a muntin bar in our 2nd story wooden casement window. So, setting myself in bed as immobile as possible, propped by a pillow, I watched it come down to that bar. When it dropped behind the bar, it went out like someone controlling a dimmer switch.

A star would have winked out, not d-i-m-m-e-d out. The dimming took about a second and three quarters--one-chim-pan-zee, two-chim-pan-
Wow! Did I observe the planetary disk without optics, and measure the angular diameter in time?
--Note my image is an animated gif for illustration, not a video, and not precisely timed.

Sure sounds like it. Jupiter's disk is almost a minute of arc across, but strongly limb-darkened. And you probably wouldn't notice the first 10% or even 20% decrease in brightness anyway. So let's say "about 1/2 minute of arc" for an effective diameter.

Just as the diurnal motion carries objects through 1 degree (of arc) in 4 minutes of time, it carries them 1 minute of arc in 4 seconds of time. So half a minute of arc would correspond to 2 seconds. This is a very rough estimate -- I should have allowed a little more for the effects of refraction near the horizon, and especially for the obliquity of the diurnal motion to the horizon. But it's certainly good to a factor of 2.

I readjusted my position in bed and watched a repeat several times.

Good for you! Few people would have the presence of mind to check that way.

 I had never observed, or even considered this. But maybe it was something else?

No, I think you got it just right.

I made sure I was awake a few minutes earlier this morning to observe again.

I am reminded that John [longitude] Harrison's star tracking instrument for time was the border of his windowpane and a neighbor's chimney stack :-)

This is a very old game. Probably the oldest example in the on-line bibliography is Pierre Perrault's De l'origine des fontaines (1674); he used a fixed telescope and a building some distance away to observe the diurnal variations in (terrestrial) refraction. For naked-eye observations, I'd say Ricco's 1889 observations of the variations in dip of the horizon might be the earliest recorded account; he used some architectural features on a cathedral a few blocks from his window as the reference.

There have been speculations that someone in antiquity might have played this game to determine the angular diameters of planets, but I know of no actual accounts. There are wholly specious estimates of the apparent diameters of bright stars, but they are evidently based on observations made with uncorrected vision in the days before eyeglasses.

Thanks for your fine observation! It's probably worth sending a letter to Sky & Telescope or The Observatory.

-- Andy

I forwarded the above emails to Harvard University astronomer Katherine Haramundanis, who wrote back:

Hi Bob,
What an interesting conversation! Thanks very much for sharing it with me. And what a fascinating concept, to make such an observation with the naked eye. There's a lot we don't know about what the ancients did before telescopes, for sure.

All best wishes - hope you had a grand Xmas and New Year.

Small world department: It turns out that Katherine Haramundanis' mother, Cecelia Payne-Gaposchkin, was Andrew's thesis advisor when he was a graduate student at Harvard.

go Calculate your local setting times of Jupiter online.

Update May 14, 2014. Jupiter is back setting in the same casement window, but now at bedtime, eight hours earlier than on that January morning of four months ago. My rough timing of the dimming of the setting in January had been one and three-quarter seconds of time,

one-chim-pan-zee two-chim-pan-

because on that date the angular diameter of the disk was about 47 arc seconds. The same observation in May required just over a second of time,


because Jupiter's now greater distance from Earth made it's angular diameter about 34 arc seconds.

Andrew commented on this.

Interesting. These intervals of a fraction of a second require some practice to measure reliably. They are certainly easier to do these days, with a stopwatch, than in the days before telescopes could reveal to diameter information.

But your observation reminds me of Cassini's measurement of the shape of the Earth's orbit by careful measurements of the Sun's diameter at different times of the year, using a giant pinhole camera. Presumably, someone using your technique could have determined the relative sizes of Earth's and Jupiter's orbits back in those days.

-- Andy

I would never have noticed this setting phenomenon except that in 1929 the developer of Land Drive Terrace adopted the then new vogue of picturesque meandering streets in residential subdivisions, which resulted in my house sitting on a lot declining 22 degrees east of north. Still, it took me thirty years to be awake on the right winter morning, at the right hour, in clear weather, and watching through old fashioned wooden sash windows, to take notice.

400 years ago Galileo looked through his telescope and saw things the eye could not detect. He saw that "wandering stars" [the planetes of the Greeks] appeared as disks, not points of light. But might this have been previously inferred from the Jupiter setting observation above? Was it?

Star observations:

Today, Betelgeuse, the bright star that is Orion's shoulder, being big enough, and near enough, has had its angular diameter resolved by the Hubble telescope. But at about five hundreths of an arc second, I won't be trying to measure it.

Update February 24, 2015. Jupiter is back setting in the same casement window, behind the same muntin bar, a month later than last year. The setting time has increased, indicating a greater angular diameter: ie., closer to Earth.

Next to be looked for this year about mid June at bedtime.

goSee Andrew T. Young's Green Flash pages.

"Green flashes are real (not illusory) phenomena seen at sunrise and sunset, when some part of the Sun suddenly changes color (at sunset, from red or orange to green or blue). The word "flash" refers to the sudden appearance and brief duration of this green color, which usually lasts only a second or two at moderate latitudes."
Green Flash, Andrew Young with a telephoto lens at Torrey Pines, California, on 7 January, 1996.

More of my farmer astronomy--
interesting astronomical problems I have run up against.
To Nicollet, an astronomical observation was a solemnity, and required such decorous preparations as an Indian makes when he goes where he thinks there are supernatural beings.
John Charles Frémont, Memoirs of My Life

goA look at a 16th century determination of longitude by a lunar eclipse observed in the South Pacific (Mar del Zur) on September 15, 1578 during Francis Drake's Circumnavigation of the Earth.

The event was reported in Hakluyt's The Famous Voyage, Francis Drake's [Bart.] The World Encompassed, and the diary of Edward Cliffe's voyage on Captain Winters accompanying ship Elizabeth. And we can now easily go online to fine that very event cataloged for that Julian calendar date.

goWatching the heavens change at Frémont's 1844 Long Camp.

Because of precession (wobble of earth's pole), in Frémont's day Polaris was nearly 1.5 degrees from the celestial pole. Today it is less than 1 degree from that pole. Going back further in California history, polaris was nearly 3 degrees from the pole in 1579 when Francis Drake spent 37 days on the coast making repairs to his ship

goLongitude, and solar declination tables.

What happens to the latitude determinations made by a sixteenth century seaman who has sailed south, west, and north again, across three hemispheres, and finds himself in a place where where he is one third of a day west of the longitude for which his published tables of solar declinations were calculated? But he could not know his longitude to interpolate between dates to correct the declinations, even if he knew how.

goFrémont's telescopic observations of Jupiter for longitude.

The Galilean moons Calisto, Europa, Io, Ganymede

Frémont's cartographer Charles Preuss, 0ctober 10, 1943: "Half-passed ten in the evening. I am sitting alone by the fire to watch till twelve o'clock, when an immersion of satellites will occur. To tell the truth, I wish the dear Lord had not attached any satellites to Jupiter. One can loose one's mind over it. These immersions occur so often that one forgets how to sleep."

©1999, 2014
Bob Graham