Synodic Period vs. Sidereal Period

As mentioned before, the sidereal period of an object depends on that object's alignment with the body it orbits and with a distant, background star.  When we talk about the Moon, we need to clarify the difference between the sidereal month and the synodic month.

Last time, we talked about the lunar resonance, explaining why the same face of the Moon is always pointed towards Earth.  When we measure the time from Full Moon to Full Moon (or New Moon to New Moon), it takes about 29.5 days to complete one cycle of phases.  We call this the synodic month and it is also the reason why months are approximately 30 days.  But the sidereal month is only 27.3 days.  The reason why it is shorter than the synodic month is because as the Moon orbits the Earth, the Earth is also orbiting the Sun.

A Day on Venus

Venus has a unique day.  Granted, Mercury can have a day where the Sun travels from west to east in the sky, can even set again in the east only to rise again later, but this does not happen every day on Mercury.  Venus day is even weirder.

VENUS HAS A DAY LONGER THAN ITS YEAR



Yes, that is correct. It takes Venus less time to complete one revolution around the Sun than it takes to complete one full rotation on its axis.  Its orbital period is 224.7 Earth days.  Its rotational period is 243.0 Earth days.  Recall that both these are in reference to distant stars.

The orbital period, or sidereal period, of Venus is how long it takes for Venus, the Sun, and a distant star to be in the same configuration.  This is generally called its year.

The rotational period, or sidereal day, is how long it takes for a star to appear at the same longitude in the sky.  For Venus, this is 243 Earth days.  However, the solar day is how long it takes for the Sun to go from noon to noon.  For Venus, this is actually 117 Earth days.  How are these so different?

*This is my awesome artistic skills

 

As you can see, as Venus goes around the Sun, it's rotation is slow enough that it takes just over half a solar year for Venus to go from noon to noon.  However, it has just completed over half a rotation in that time.  Therefore, it takes almost another half a solar year to complete one full rotation on its axis.

 

There is another strange phenomena about the rotation of Venus.  On almost all the planets, the Sun generally rises in the east and sets in the west.  We've already discussed Mercury's strange day and Uranus day is strange as well, but Venus is the weirdest.  The Sun exclusively rises in the west and sets in the east.  We call this retrograde rotation.  If we view the solar system from above (i.e. looking down on the Earth's north pole), all the planets rotate counterclockwise (also called anticlockwise).  Venus, however, rotates clockwise.  

The way this is explained is by describing the inclination of Venus' orbit.  The Earth is tilted 23.5° with respect to its orbital axis.  Venus's inclination is 177°.  Why not 3°?  A 3° inclination would suggest that Venus rotates like all the other planets, counterclockwise (west to east).  By saying Venus has an inclination of 177°, we know that Venus rotates clockwise (east to west).  That is why the Sun rises in the west and sets in the east on Venus. 

 

 

Both the slow rotational speed of Venus and its almost 180° inclination are probably explained by the same thing: early in its creation, Venus was hit but a large planetoid body which caused it to flip upside down and considerably slowed down its rotation.

 

 

*Forgive my horrible drawings, as I am not an artist.  But I feel I should probably start using my own images instead of resorting to Google to find them.

 

Mercury's Orbit

Mercury has a unique orbit around the Sun.  It was long believed that Mercury had a 1:1 resonance with the Sun, much like the Moon has a 1:1 resonance with Earth, i.e. the same face is always facing the Sun.  However it was discovered that Mercury has a 3:2 resonance, i.e. for every three complete rotations, Mercury completes two full orbits around the Sun.  This resonance, its proximity to the Sun, and its highly eccentric orbit leads to some strange phenomena.

Mercury, by far, has the highest eccentricity of all the planets (e=0.206). What does this mean?  An orbit that is eccentric means that the orbit is elliptical, or oval. The closer the eccentricity of an orbit is to zero, the more circular the orbit is. For reference, the orbital eccentricity of the Earth is 0.017.

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Eccentricity leads us to mention Johannes Kepler's three laws of planetary motion, specifically Kepler's Second Law:

• A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.

This is just a fancy way of saying the closer the planet is to the Sun, the faster it goes.

Shashi M. Kanbur, Professor of Physics and Earth Science, SUNY Oswego

 

Isaac Newton later proved this with physics and calculus in his three laws of motion,

 

We also know that Mercury is 0.4 AU, on average, from the Sun. Because it is so close, it is by far the fastest moving planet in terms of orbital speed.  And from its highly eccentric orbit, when Mercury is at perihelion, it is moving its fastest.

Before we move on to the funky stuff, let's discuss more about Mercury's sidereal rotation and sidereal period, or its day and its year, A sidereal day is how long it takes a planet to rotate once on its axis completely, or how long it takes a star to appear at the same spot in the sky.  For Earth, this is about 23 hours and 56 minutes.  On Mercury, it takes about 58.5 Earth days.  A sidereal year is how long it takes to complete one complete orbit around the Sun.  Earth takes about 365.25 days to complete one sidereal year. Mercury has a sidereal year of approximately 88 days.  So for every three sidereal days on Mercury, Mercury completes two full orbits, hence 3:2 resonance.

But because of its unique position in the solar system, funny things happen on Mercury. As Mercury approaches perihelion, its orbital angular velocity increases.  At around four days before perihelion, the orbital angular velocity equals the rotational angular velocity. When these two angular velocities are equal, the Sun appears stationary in the Mercury sky.  As Mercury gets closer to perihelion, the angular orbital velocity increases and becomes larger than the rotational velocity. The Sun then appears to move backwards in the sky!  In some cases, it is possible that the Sun could actual set in the east.  At perihelion, the orbital angular velocity begins to decrease. Four days after reaching perihelion, the orbital rotational velocity once again equals the rotational orbital velocity. The Sun again appears stationary then again begins its apparent movement to the west.

Another interesting fact about Mercury's orbit, is that the time from true noon to true noon, what we call a solar day, is larger than a Mercury year. One Earth, our solar day is 24 hours. On Mercury, it is 176 Earth days, or two Mercury years.  Mercury has one of the slowest rotational angular velocities in the solar system, comparable to that of Venus, which is a topic for later.

NOAA

 

In conclusion, because of its proximity to the Sun, its highly eccentric orbit, and its tidally locked 3:2 resonance with the Sun, strange things happen in the sky of Mercury.