Like Sun, Like Moon

The Earth orbits the Sun once every 365.256363 (mean solar) days relative to the distant stars.  The Earth’s orbital speed ranges from 18.2 miles per second at aphelion, around July 4th, to 18.8 miles per second at perihelion, around January 3rd.  In units we’re perhaps more familiar with, that’s 65,518 mph at aphelion and 67,741 mph at perihelion. That’s a difference of 2,223 miles per hour!

As we are on a spinning globe, the direction towards which the Earth is orbiting is different at different times of the day.  When the Sun crosses the celestial meridian, due south, at its highest point in the sky around noon (1:00 p.m. daylight time), the Earth is orbiting towards your right (west) as you are facing south. Since the Earth is orbiting towards the west, the Sun appears to move towards the east, relative to the background stars—if we could see them during the day.  Since there are 360° in a circle and the Earth orbits the Sun in 365.256363 days (therefore the Sun appears to go around the Earth once every 365.256363 days relative to the background stars), the Sun’s average angular velocity eastward relative to the background stars is 360°/365.256363 days = 0.9856° per day.

The constellations through which the Sun moves are called the zodiacal constellations, and historically the zodiac contained 12 constellations, the same number as the number of months in a year.  But Belgian astronomer Eugène Delporte (1882-1955) drew up the 88 constellation boundaries we use today, approved by the IAU in 1930, so now the Sun spends a few days each year in the non-zodiacal constellation Ophiuchus, the Serpent Bearer. Furthermore, because the Earth’s axis is precessing, the calendar dates during which the Sun is in a particular zodiacal constellation is gradually getting later.

Astrologically, each zodiacal constellation has a width of 30° (360° / 12 constellations = 30° per constellation).  But, of course, the constellations are different sizes and shapes, so astronomically the number of days the Sun spends in each constellation varies. Here is the situation at present.

Constellation
Description
Sun Travel Dates
Capricornus
Sea Goat
Jan 19 through Feb 16
Aquarius
Water Bearer
Feb 16 through Mar 12
Pisces
The Fish
Mar 12 through Apr 18
Aries
The Ram
Apr 18 through May 14
Taurus
The Bull
May 14 through Jun 21
Gemini
The Twins
Jun 21 through Jul 20
Cancer
The Crab
Jul 20 through Aug 10
Leo
The Lion
Aug 10 through Sep 16
Virgo
The Virgin
Sep 16 through Oct 31
Libra
The Scales
Oct 31 through Nov 23
Scorpius
The Scorpion
Nov 23 through Nov 29
Ophiuchus
Serpent Bearer
Nov 29 through Dec 18
Sagittarius
The Archer
Dec 18 through Jan 19

 

The apparent path the Sun takes across the sky relative to the background stars through these 13 constellations is called the ecliptic.  A little contemplation, aided perhaps by a drawing, will convince you that the ecliptic is also the plane of the Earth’s orbit around the Sun.  The Moon never strays very far from the ecliptic in our sky, since its orbital plane around the Earth is inclined at a modest angle of 5.16° relative to the Earth’s orbital plane around the Sun.  But, relative to the Earth’s equatorial plane, the inclination of the Moon’s orbit varies between 18.28° and 28.60° over 18.6 years as the line of intersection between the Moon’s orbital plane and the ecliptic plane precesses westward along the ecliptic due to the gravitational tug of war the Earth and the Sun exert on the Moon as it moves through space.  This steep inclination to the equatorial plane is very unusual for such a large moon.  In fact, all four satellites in our solar system that are larger than our Moon (Ganymede, Titan, Callisto, and Io) and the one that is slightly smaller (Europa) all orbit in a plane that is inclined less than 1/2° from the equatorial plane of their host planet (Jupiter and Saturn).

Since the Moon is never farther than 5.16° from the ecliptic, its apparent motion through our sky as it orbits the Earth mimics that of the Sun, only the Moon’s angular speed is over 13 times faster, completing its circuit of the sky every 27.321662 days, relative to the distant stars.  Thus the Moon moves a little over 13° eastward every day, or about 1/2° per hour.  Since the angular diameter of the Moon is also about 1/2°, we can easily remember that the Moon moves its own diameter eastward relative to the stars every hour.  Of course, superimposed on this motion is the 27-times-faster-yet motion of the Moon and stars westward as the Earth rotates towards the east.

Now, take a look at the following table and see how the Moon’s motion mimics that of the Sun throughout the month, and throughout the year.

 
——— Moon’s Phase and Path ———
Date
Sun’s Path
New
FQ
Full
LQ
Mar 20
EQ
EQ
High
EQ
Low
Jun 21
High
High
EQ
Low
EQ
Sep 22
EQ
EQ
Low
EQ
High
Dec 21
Low
Low
EQ
High
EQ

 

New = New Moon
near the Sun
FQ = First Quarter
90° east of the Sun
Full = Full Moon
180°, opposite the Sun
LQ = Last Quarter
90° west of the Sun

 

EQ
= crosses the celestial equator heading north
High
= rides high (north) across the sky
EQ
= crosses the celestial equator heading south
Low
= rides low (south) across the sky

 

So, if you aren’t already doing so, take note of how the Moon moves across the sky at different phases and times of the year.  For example, notice how the full moon (nearest the summer solstice) on June 27/28 rides low in the south across the sky.  You’ll note the entry for the “Jun 21” row and “Full” column is “Low”.  And, the Sun entry for that date is “High”.  See, it works!

Average Orbital Distance

If a planet is orbiting the Sun with a semi-major axis, a, and orbital eccentricity, e, it is often stated that the average distance of the planet from the Sun is simply a.  This is only true for circular orbits (e = 0) where the planet maintains a constant distance from the Sun, and that distance is a.

Let’s imagine a hypothetical planet much like the Earth that has a perfectly circular orbit around the Sun with a = 1.0 AU and e = 0.  It is easy to see in this case that at all times, the planet will be exactly 1.0 AU from the Sun.

If, however, the planet orbits the Sun in an elliptical orbit at a = 1 AU and e > 0, we find that the planet orbits more slowly when it is farther from Sun than when it is nearer the Sun.  So, you’d expect to see the time-averaged average distance to be greater than 1.0 AU.  This is indeed the case.

The Earth’s current osculating orbital elements give us:

a = 0.999998 and e = 0.016694

Earth’s average distance from the Sun is thus:

Mercury, the innermost planet, has the most eccentric orbit of all the major planets:

a = 0.387098 and e = 0.205638

Mercury’s average distance from the Sun is thus:

Saturn V

Today we celebrate the 50th anniversary of the inaugural flight of Wernher von Braun’s magnum opus, the giant Saturn V moon rocket.  This first flight was an unmanned mission, Apollo 4, and took place less than 10 months after the tragic launch pad fire that killed astronauts Gus Grissom, 40, Ed White, 36, and Roger Chaffee, 31.

Apollo 4 launch, November 9, 1967
Apollo 4 image of Earth at an altitude of 7,300 miles

The unmanned Apollo 4 mission was a complete success, paving the way for astronauts to go to the Moon.  After another successful unmanned test flight (Apollo 6), the Saturn V rocket carried the first astronauts into space on the Apollo 8 mission in December 1968.  On that mission, astronauts Frank Borman, Jim Lovell, and Bill Anders orbited the Moon for 20 hours and then returned safely to Earth.

Bill Anders took this iconic photo of Earth from Apollo 8 while in orbit around the Moon

“As of 2017, the Saturn V remains the tallest, heaviest, and most powerful (highest total impulse) rocket ever brought to operational status, and holds records for the heaviest payload launched and largest payload capacity to low Earth orbit (LEO) of 140,000 kg (310,000 lb), which included the third stage and unburned propellant needed to send the Apollo Command/Service Module and Lunar Module to the Moon.  To date, the Saturn V remains the only launch vehicle to launch missions to carry humans beyond low Earth orbit.”

Reference (for quoted material above)
Wikipedia contributors, “Saturn V,” Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/w/index.php?title=Saturn_V&oldid=808028027 (accessed November 9, 2017).

Changing Solar Distance

Between January 2 and 5 each year, the Earth reaches orbital perihelion, its closest distance to the Sun (0.983 AU).  Between July 3 and 6 each year, the Earth reaches orbital aphelion, its farthest distance from the Sun (1.017 AU).  These dates of perihelion and aphelion slowly shift across the calendar (always a half year apart) with a period between 22,000 and 26,000 years.

These distances can be easily derived knowing the semi-major axis (a) and orbital eccentricity (e) of the Earth’s orbit around the Sun, which are 1.000 and 0.017, respectively.

perihelion
q = a (1-e) = 1.000 (1-0.017) = 0.983 AU

aphelion
Q = a (1+e) = 1.000 (1+0.017) = 1.017 AU

So, the Earth is 0.034 AU closer to the Sun in early January than it is in early July.  This is about 5 million km or 3.1 million miles.

How great a distance is this, really?  The Moon in its orbit around the Earth is closer to the Sun around New Moon than it is around Full Moon.  Currently, this difference in distance ranges between 130,592 miles (April 2018) and 923,177 miles (October 2018).  Using the latter value, we see that the Moon’s maximum monthly range in distance from the Sun is 30% of the Earth’s range in distance from the Sun between perihelion and aphelion.

How about in terms of the diameter of the Sun?  The Sun’s diameter is 864,526 miles.  The Earth is just 3.6 Sun diameters closer to the Sun at perihelion than it is at aphelion.  Not much!  On average, the Earth is about 108 solar diameters distant from the Sun.

How about in terms of angular size?  When the Earth is at perihelion, the Sun exhibits an angular size of 29.7 arcminutes.  At aphelion, that angle is 28.7 arcminutes.

Can you see the difference?