2023, January 29: Mercury, Greatest Elongation, Evening Moon, Pleiades

January 29, 2023: Mercury is at its greatest angular separation from the sun during morning twilight.  After sundown, look for four planets and the gibbous moon near the Pleiades star cluster.

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by Jeffrey L. Hunt

Chicago, Illinois:  Sunrise, 7:06 a.m. CST; Sunset, 5:02 p.m. CST.  Check local sources for sunrise and sunset times for your location.  Times are calculated from the U.S. Naval Observatory’s MICA computer program.

Jupiter’s Great Red Spot’s transit times, when it is in the center of the planet in the southern hemisphere: 3:36 UT, 13:32 UT, 23:28 UT. Convert the time to your time zone. In the US, subtract five hours for EST, six hours for CST, and so on.  Use a telescope to see the spot.  Times are from Sky & Telescope magazine.

Here is today’s planet forecast:

Morning Sky

Mercury is at greatest elongation – its largest separation from the sun – at 11:54 p.m. CST. At forty-five minutes before sunrise, the planet is about 6° above the southeast horizon.

Mercury is the lone bright planet in the morning sky.  It is fairly bright but likely blocked by obstacles near the horizon. Find a clear view of the horizon toward the southeast and use a binocular to initially locate the world.

Antares, the brightest star in Scorpius, is about 20° above the south-southeast horizon, to the upper right of Mercury.  Altair, is about the same altitude as Antares, but in the east, to Mercury’s upper left. Both stars are dimmer than Mercury.

Should we consider today the greatest elongation date or tomorrow morning when the planet’s visibility is closer to the greatest elongation time?  While the planet moves quickly, its rising time is quickly decreasing.  Tomorrow morning it loses two minutes of rising time.  For the purposes of spotting the planet, we will take today as the greatest elongation date.

Greatest elongation is a time when the planet’s distance from the sun can be measured and calculated.  The answer is not in miles or kilometers, but as a fraction of Earth’s solar distance.  For those who want to go through the math, the details are at the end of this article.

Evening Sky

Four bright planets and the moon are visible after sundown.  This is one of the last evenings to see all four of them simultaneously.  Saturn is slipping into brighter evening twilight.  Depending on the clarity of the sky the next few evenings, it might be visible without an optical assist from a binocular.

To find the Ringed Wonder, first locate brilliant Venus, over 10° above the west-southwest horizon.  Saturn is 8.0° to the Evening Star’s lower right.  That distance is about the width of your fist – from thumb knuckle to pinky finger knuckle – at arm’s length.

Saturn passes behind the sun during mid-February and reappears from the bright blush of morning twilight near the equinox.

Venus passed Saturn a week ago and is moving toward Jupiter – “that bright star” that is about halfway up in the southwest.  The Venus-Jupiter gap is 32.0° this evening and closing at about 1° each night.  On February 20^th, Venus closes to within 10° of Jupiter, two of the night’s brightest starlike objects are near each other.  Venus passes the Jovian Giant on March 1^st.

Jupiter is slowly moving eastward in a dim Pisces starfield, nearing the border with Cetus.

Farther eastward, the gibbous moon, 64% illuminated, is high in the south-southeast and 5.5° from the Pleiades star cluster.  Block the moon with your hand as you would to cover the sun to see the cluster. The Pleiades and the moon fit into the same binocular field of view. 

During the night as Earth rotates, the sky appears to pivot westward, while the moon moves eastward.  The lunar orb sets about 2:30 a.m. CST tomorrow morning from Chicago.  About 90 minutes before the moon sets, it is 3.3° of the Pleiades cluster.  Set an early alarm and use a binocular to view them again. Sky watchers farther westward can see the moon fractions of a degree closer to the moon before it sets, but there is no occultation.  The moon passes by heading toward a nice grouping with Mars.

This evening, Mars is nearly 15° to the lower left of the lunar orb.  The Red Planet is slowly moving eastward in front of Taurus, near Aldebaran.  Mars passes the star tomorrow evening in a wide conjunction, the third of a triple conjunction series.

At 5:28 p.m. CST – during brighter twilight – Jupiter’s Great Red Spot is center stage in the southern hemisphere.  As noted above, the planet is about halfway up in the southwest at this hour.  The red spot feature can be spotted through a telescope as this level of twilight, but the view is better for sky watchers farther eastward where the sky is darker and the planet is high enough to be above the atmosphere’s filtering effects.

Mathematical Note

For the Mercury question above, how do we calculate the distance of Mercury from the sun when the planet is at greatest elongation?  Knowing the sun’s location and the planet’s place in front of the Sagittarius starfield, the angle – Sun-Earth-Mercury – is at its maximum. Today that is 25.0°.  Next assume the planet orbits are circles; not exactly, but for this estimation we’ll use it. 

When the planet is at its maximum angle from the sun, the line of sight is tangent to the planet’s imaginary orbit.  That tangent line is perpendicular to Mercury’s radius.  So, there’s a right angle and a second angle.  Not knowing Earth’s distance from the sun, let’s use one as its distance.  This represents the hypotenuse of a triangle. With a right angle and Mercury’s greatest elongation, the values needed to determine Mercury’s solar distance are known.  Using some trigonometry – sine 25° = opposite divided by 1, the distance from Earth to the sun.  The opposite side or Mercury’s distance is 0.42 Earth’s distance.

That’s an initial estimate.  Additional measurements are needed to refine the value because the planet’s orbit is not a circle.

This method was used by Copernicus to estimate the planets’ distances from the sun compared to Earth’s distance.

The calculation to measure the distance of the outer planets to the sun is somewhat similar to the method for Mercury and Venus.  How might this work?  How is a right angle formed to use the simpler trigonometric function?

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