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:

Evening Planets

The most convenient time for most of us to observe the planets is in the early evening.  With that in mind, I’ve prepared an ephemeris of favorable evening times to view each of the eight major planets of the solar system over the next ten years.  Some interesting patterns emerge, which I will comment on.

With the exception of Mercury, what follows is a range of dates when each planet is at least 10° above the horizon at the end of evening twilight at latitude 43° N.  Mercury, however, is never even above the horizon at the end of evening twilight.

Mercury’s Maximum
Altitude at 43° N
Solar Depression
Angle
End of
Twilight
13°
Civil
12°
Nautical
below horizon
18°
Astronomical

Here is a list of dates when Mercury is highest above the western horizon at the end of evening civil twilight.

Mercury

Dates – Highest Above
Evening Horizon
Altitude
Constellation
July 18, 2017
Leo
November 28, 2017
Sgr
March 15, 2018
12°
Psc
July 2, 2018
Cnc
November 10, 2018
Oph
February 27, 2019
11°
Psc
June 16, 2019
10°
Gem
October 20, 2019
Lib
February 11, 2020
11°
Aqr
May 30, 2020
12°
Gem
September 25, 2020
Vir
January 25, 2021
10°
Cap
May 14, 2021
13°
Tau
September 2, 2021
Vir
January 9, 2022
Cap
April 28, 2022
13°
Tau
August 14, 2022
Leo
December 24, 2022
Sgr
April 11, 2023
13°
Ari
July 28, 2023
Leo
December 8, 2023
Sgr
March 24, 2024
12°
Psc
July 11, 2024
Cnc
November 20, 2024
Oph
March 8, 2025
12°
Psc
June 25, 2025
Cnc
November 1, 2025
Sco
February 20, 2026
11°
Psc
June 9, 2026
11°
Gem
October 10, 2026
Lib
February 4, 2027
11°
Aqr
May 24, 2027
13°
Tau
September 15, 2027
Vir

Mercury, the innermost planet, whips around the Sun every 88 days (116 days relative to the Earth—its synodic period).  It never strays more than 28° from the Sun.

As you can see in the graph below, Mercury is presently highest above our evening twilight horizon when it reaches greatest eastern elongation in April, and lowest in October.

Similarly, greatest eastern elongations that occur in the constellations Taurus and Aries present Mercury highest above our evening twilight horizon, and Libra, the lowest.

Now, let us turn to Venus.  Unlike Mercury, Venus usually spends a considerable number of days well above the horizon near greatest elongation.  This occurs because Venus orbits further from the Sun—reaching a maximum angular separation of 47°— and because its orbital period is only 140.6 days shorter than the Earth’s: the Earth “keeps up” with Venus reasonably well as the two planets orbit the Sun (the synodic period of Venus is 583.9 days), so it is a long time between successive elongations.  In the next ten years, we will see Venus high above the evening horizon during only three intervals, though for a generous three or four months each time.

Venus

Dates – At Least 10° Above the Horizon
at the End of Evening Twilight
Constellation
January 2, 2020 – May 7, 2020
Cap – Tau
February 26, 2023 – June 3, 2023
Cet – Cnc
November 30, 2024 – March 2, 2025
Sgr – Psc

Now, we turn to the superior planets: Mars, Jupiter, Saturn, Uranus, and Neptune.  These planets are visible in our evening sky during and after opposition.

Mars has the longest synodic period of all the major planets—780 days—so it takes an unusually long period of time for the orbital positions of Mars and the Earth to change relative to one another.  Approximately every two years we get the opportunity to see Mars at least 10° above the horizon at the end of evening twilight.  The number of evenings Mars is visible varies quite a lot (due to its significant orbital eccentricity): 293 evenings during the 2018 perihelic opposition of Mars, down to 145 evenings during the aphelic opposition of Mars in 2027.  In any event, Mars spends a considerable amount of time during these intervals very far away from Earth and therefore disappointingly small in our telescopes.  The best time to observe Mars is during the early weeks of the intervals listed below when Mars is at or near opposition.

Mars

Dates – At Least 10° Above the Horizon
at the End of Evening Twilight
Constellation
July 21, 2018 – May 10, 2019
Cap – Tau
October 5, 2020 – May 27, 2021
Psc – Gem
November 28, 2022 – June 11, 2023
Tau – Cnc
January 7, 2025 – June 22, 2025
Cnc – Leo
February 12, 2027 – July 7, 2027
Leo – Vir

Jupiter orbits the Sun every 11.9 years, so it is easy to see why it is in a different constellation along the zodiac each year.

Jupiter

Dates – At Least 10° Above the Horizon
at the End of Evening Twilight
Constellation
March 30, 2017 – July 24, 2017
Vir
April 29, 2018 – August 29, 2018
Lib
May 28, 2019 – October 19, 2019
Oph
June 26, 2020 – December 10, 2020
Sgr
July 30, 2021 – January 22, 2022
Aqr
September 10, 2022 – March 1, 2023
Psc
October 21, 2023 – April 5, 2024
Ari
November 28, 2024 – May 5, 2025
Tau
January 1, 2026 – May 28, 2026
Gem
February 2, 2027 – June 16, 2027
Leo

The orbital periods of Saturn, Uranus, and Neptune are 29.5, 84.0, and 164.8 years, respectively, so we can see why they take a successively longer amount of time to traverse their circle of constellations.  You’ll also notice that the interval of visibility shifts later each year, but the shift is less with increasing orbital distance.  The synodic periods of Saturn, Uranus, and Neptune are 378.1, 369.7, and 367.5 days, respectively.

Saturn

Dates – At Least 10° Above the Horizon
at the End of Evening Twilight
Constellation
May 31, 2017 – October 25, 2017 Oph
June 10, 2018 – November 11, 2018 Sgr
June 20, 2019 – November 28, 2019 Sgr
June 30, 2020 – December 12, 2020 Cap – Sgr
July 12, 2021 – December 27, 2021 Cap
July 24, 2022 – January 9, 2023 Cap
August 7, 2023 – January 23, 2024 Aqr
August 21, 2024 – February 4, 2025 Aqr
September 5, 2025 – February 17, 2026 Psc
September 20, 2026 – March 2, 2027 Cet – Psc

Uranus

Dates – At Least 10° Above the Horizon
at the End of Evening Twilight
Constellation
October 2, 2017 – March 16, 2018
Psc
October 7, 2018 – March 20, 2019
Ari
October 12, 2019 – March 23, 2020
Ari
October 15, 2020 – March 27, 2021
Ari
October 20, 2021 – March 31, 2022
Ari
October 25, 2022 – April 4, 2023
Ari
October 30, 2023 – April 7, 2024
Ari
November 3, 2024 – April 12, 2025
Tau
November 8, 2025 – April 16, 2026
Tau
November 13, 2026 – April 20, 2027
Tau

Neptune

Dates – At Least 10° Above the Horizon
at the End of Evening Twilight
Constellation
August 13, 2017 – January 30, 2018
Aqr
August 16, 2018 – February 2, 2019
Aqr
August 19, 2019 – February 4, 2020
Aqr
August 21, 2020 – February 6, 2021
Aqr
August 24, 2021 – February 8, 2022
Aqr
August 27, 2022 – February 11, 2023
Aqr
August 30, 2023 – February 13, 2024
Psc
September 1, 2024 – February 15, 2025
Psc
September 4, 2025 – February 17, 2026
Psc
September 7, 2026 – February 17, 2027
Psc