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.

Lunar Resonance

Despite what my wife thinks (and the Pink Floyd albums says), there is no such thing as a "Dark Side of the Moon". Granted, the face of the Moon facing away from the Sun is dark, but that face changes as the Moon orbits the Earth.  A better description of the faces of the Moon would be to call them the Near Side of the Moon and the Far Side of the Moon.  The near side is the face that always pointed to the Earth, and the far side is always pointed away.  Why is this?

The reason why we should use near side and far side is because the Moon is in a 1:1 resonance with the Earth.  Remember that the Sun-Mercury system has a 3:2 resonance, so for every two orbits around the Sun, Mercury rotates three times on its axis.  For the Moon-Earth system, this means that for every one complete orbit around the Earth, the Moon rotates on its axis just one time.  Because of this, the same side of the Moon is always facing Earth.  It wasn't until 1959, when the Soviet Union's Luna 3 space probe photographed the far side.  In 1968, it wasn't observed by human eyes for the first time during the Apollo 8 mission.

Eclipses

Previously, we learned about the phases of the Moon. We saw how it goes from new Moon to full Moon back to new Moon again. We know that during the new phase, the Moon is between us and the Sun. During the full phase, the Earth is between the Sun and the Moon. We also know the apparent diameter of the Sun and the Moon are nearly identical, at about 0.5°.  So how come we don't see the Moon blocked out when its full and why isn't the Sun always eclipsed during the new Moon phase?

The main reason why is the Earth and the Moon do not orbit in the same plane.  The Moon's inclination is about 5° compared to the ecliptic.  Therefore, during most new Moon phases or most full Moon phases, the Moon is not in the same alignment with the Earth and the Sun.  This 5° inclination leads to the eclipses to happen every six months.

 



There are two types of eclipses: solar eclipses and lunar eclipses.  Solar eclipses occur when the Moon crosses in front of the Sun, blocking us from seeing the Sun on Earth.  Lunar eclipses occur when the Moon passes through the shadow of the Earth.  A lunar eclipse (or a solar eclipse) follows two weeks after the associated solar (or lunar) eclipse.  Solar eclipses and lunar eclipses never occur more than 14 days apart.

Lunar eclipses occur during the full Moon phase as the Earth is between the Moon and the Sun.  If the Moon is completely in the shadow, or umbra, of the Earth.  Since the Earth is so much larger than the Moon, the shadow of the Earth completely envelopes the Moon during a lunar eclipse.  Also, this allows a lunar eclipse to occur even if the Earth, Sun and Moon are not completely in line.  If the Moon is slightly out of the umbra and partially in the penumbra, partial lunar eclipses will occur.  From viewing partial lunar eclipses, ancient astronomers could tell that the Earth was round, not flat, because of the shape of the Earth's shadow on the Moon.

Solar eclipses occur during the new Moon phase when the Moon crosses in front of the Sun.  These are only total if the Moon is near perigee and the Sun, Moon, and Earth are completely aligned.  If the Moon is nearer apogee than perigee, a solar eclipse will be annular, or ring-like, because there will be a ring of sunlight around the outline of the Moon.  As with lunar eclipses, if the Moon is slightly off center of the ecliptic, then a partial solar eclipse will occur.

Total Solar Eclipse (NASA)

Annular Solar Eclipse (Wikipedia)

In the future, total solar eclipses will not longer occur because the Moon is moving away from the Earth at a rate of 2 cm/century.  We will learn more about the recession of the Moon later.

Apollo 11

Forty-five years ago today, a human stood on another celestial body for the first time.  Remember that Neil Armstrong, Buzz Aldrin, and Michael Collins weren't sure if they were going to come back.

Also, remember that NASA performed this feat with computers that had the computing power of today's smart phones, but took up a lot of room.

We need to go back.

Our Nearest Neighbor

The nearest celestial body to the Earth is obviously our Moon.  We've already discussed the phases of the Moon and how they relate to the Moon's position with respect to the Sun and the Earth.  In the next few posts, we will learn about the Moon.

For example, how come eclipses don't happen every month? Why is there a supermoon? Where did the Moon come from?  What would life be like if the Moon had never existed or what would life be like if we decided to blow up the Moon (it was actually thought of at one point)?  Why should did we go to the Moon originally, why haven't we gone back, and should we go in the future?

Before we get into these topics, let's learn a little about our Moon. 

• It is the only natural satellite of the Earth and is the fifth largest satellite in the solar system, behind Ganymede, Titan, Callisto, and Io. It is the only celestial object, besides the Earth, that humans have stood on.
• It is approximately 238,900 miles from Earth or about 384,400 kilometers, and it took Neil Armstrong, Buzz Aldrin, and Michael Collins about 4 days to reach it from Earth. 
• It has a sidereal period of 27.3 days and a synodic period of 29.5 days. We will talk about this in a future post. 
• It has no atmosphere to speak of and therefore, no life. 
• The Moon has a radius of 1,737 km (27.3% of Earth's) and a mass of 7.35x10²² kg (1.23% of Earth’s). On the Moon, you would weight approximately 1/6 of what you weigh on Earth. That’s why in videos, the astronauts on the moon always looked like they were bouncing.  It would actually be more difficult to walk normally.
• At one point in its history, the Moon was active. This was likely to the cooling it went under after it formed and its constant bombardment by asteroids early in its life.
• It has an inclination of about 5° to the ecliptic, which I realize now I have never talked about.  To learn about the ecliptic and what it is, click here.

 

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.

 

The Morning Star and The Evening Star

Have you ever heard the terms "Morning Star" or "Evening Star"?  These terms are actually misnomers.  Neither object is actually a star.  They both refer to planets, either Venus or Mercury.  Today, we will answer why they are referred to either of these terms.

The ancients knew that both Mercury and Venus were close to the Sun.  They could only see them either in the morning or the evening.  This is how they got the name of Morning Star or Evening Star.  When they are the Morning Star, they rise just before the Sun and therefore, are only seen in the eastern sky.  When they are the Evening Star, they set just after the Sun and therefore, are only seen in the western sky.

If the ancients believed that everything in the solar system orbited around the Earth, how did they explain how Venus and Mercury stayed close to the Sun?  In the Ptolemaic model, the epicycles for both Mercury and Venus were connected to the Sun by a line.

Copernican Revolution



 

This line was needed in the model to keep Venus and Mercury close to the Sun in the sky.  Otherwise, in this model, Venus or Mercury and the Sun could be at opposition, which we know is not true.

 

When the Copernican Revolution occured and the heliocentric model came to prominence, the line was no longer needed.  Since Mercury and Venus orbit the Sun and in the model, are closer to the Sun than the Earth, their proximity to the Sun in the sky is easier to explain.

Copernican Revolution



We discussed the Phases of Venus in our last post and mentioned the greatest eastern elongation and the greatest western elongation.  For Mercury and Venus, we use these terms to tell us the point in Mercury's and Venus' orbits when they appear the farthest from the Sun in the sky depending on their position relative to the Sun.

Greatest eastern elongation occurs when Venus (or Mercury) is the farthest east of the Sun.  When either planet is at greatest eastern elongation, the planet is only visible from Earth just after sunset, which means we only see it when it’s in the western sky.  We call this the Evening Star.

Greatest western elongation, however, occurs when Venus (or Mercury) is the farthest west of the Sun.  When either planet is at greatest western elongation, the planet is only visible from Earth just before sunrise, which means we only see it when it’s in the eastern sky.  We call this the Morning Star.

Remember that the terms refer to the planet’s position with respect to the Sun in the sky, and not its location in the sky when it is visible.

By comparing the position of Mercury or Venus to the Sun, we can determing the angle between the planet and the Sun at either greatest elongation.  Venus cannot be any more than 47.8° from the Sun in the sky. At greatest western elongation, Venus rises about 2.5 hours before the Sun and at greatest eastern elongation, Venus sets about 2.5 hours after the Sun.  Mercury cannot be any more than 27.8° from the Sun in the sky.  At greatest western elongation, Mercury rises about 1.5 hours before the Sun and at greatest eastern elongation, Mercury sets about 1.5 hours after the Sun. 

Note that these elongations occur when the planet is at aphelion.  If either planet is at perihelion, the angle is smaller.  For Mercury, greatest elongation at perihelion is only 18° and is visible an hour before or after the Sun rises or sets.  For Venus, greatest elongation at perihelion is 45° which doesn't change its appearance before or after sunrise or sunset by much.

The reason for the huge difference for Mercury's elongations is its relatively elliptical orbit.  Venus' orbit is closer to circular so the angles are much closer.