Night Sky Course – Planets, Earth and Orbits around the Sun

Celestial Motion of Planets – Orbits in the Ecliptic Plane

The planets fall into two groups relative to Earth’s location:

• Outer Planets : Sun–Earth–Planet — Mars, Jupiter, Saturn,  Uranus,  Neptune, [pluto]*

• Inner  Planets : Sun–Planet–Earth — Mercury, Venus

*As of August 24, 2006 – The International Astronomical Union reclassified Pluto as a ‘dwarf planet’. It is regarded as one of the largest members of distant objects called Trans-Neptunian Objects (objects orbiting the Sun at a greater average distance than Neptune. Also note that Pluto’s orbit does sometimes slip inside of Neptune’s due to its ellipticity.

All planets, including the earth rotate around the Sun in the plane of the Ecliptic.

Outer or Superior Planets (beyond Earth) :

• Mars – naked eye visible when positioned away from the Sun with respect to Earth
• Jupiter – ditto –
• Saturn – ditto –
• Neptune – need telescope and time of transit
• Uranus –  ditto

When are Planets Visible?

Assuming the planet is not too distant, and hence too tiny to observe naked eye or in the eyepiece (as in the case of Neptune and Uranus… and pluto), we can see the planet when its orbit is not in the glare of the sun relative to our orbit. There is no preferred season that this happens on Earth (or Mars for that matter) but rather depends on the relative orbital positions of the Earth and the Planet.

• Inner Planets: Sun – Planet- Earth alignment (away from the glare of the Sun)
• Outer Planets: Sun-Earth-Planet alignment (away from the glare of the Sun)

Planets become visible when their orbital location relative to Earth is away from the glare of the Sun as shown above.  We look for nights when the two planets are on the same side of the Sun in their respective orbits. Hence planets are visible based on their Synodic period with respect to Earth:

Synodic Period: The period between two successive alignments of a planet and the earth is called the Synodic Period. For Jupiter it is 1.08 years which means we get to see Jupiter in the evening sky for many months  and without too much interruption.

Sidereal Period: The real period of the planet is the time it takes in years to go around the Sun. Jupiter’s Sidereal Period around the Sun is 11.86 years.

Opposition – Best Time to view  Outer Planets

The best time to view planets is when they

1. Appear largest in the sky so that the disk is large and well-illuminated. This occurs at Opposition
2. When the planet culminates high up in the sky. Since all planets orbit along the ecliptic, this occurs in the Winter months (Northern Hemisphere) when the Sun and hence the planets following or preceding it are located at a higher elevation in the Summer (Northern Hemisphere) Summer Constellations.

Opposition occurs when the angle Sun-Earth-Planet is is a straight line, and the configuration is Sun-Earth-Planet.  Opposition of the  Outer planet means the planet receives full Sun illumination as seen from Earth –  like the full moon. We get to see the whole disk. 

• The best times to view an outer planet is in the Opposition configuration which happens whenever the two orbits line up in this way.
  
• The best oppositions are those in which the planet is close to the earth (measured in a.u.s- the distance between the Earth and the Sun) This is seen in the next diagram where the distance between Mars and Earth in 2014 is just 0.62 a.u.

Notes:

• The relative size of the disk of the planet depends on how close to the earth is is in  the units of AU (astronomical unit = a fundamental unit of distance measured from the sun to the earth 150 million km)
• The most favourable oppositions occur at the smallest distance between the Earth and Mars  – we can see this around 2020. Here it is roughly .41 AUs
• The diagram provides a graphical representation of the variation in size of the Martian disk at opposition. The size varies according to distance from earth.
  • Note also that the Martian disk will never be larger than the lunar one because it is so much further away. The distance of the moon from the earth is only a tiny fraction of an Astronomical Unit distance 0024 AUs .. much much closer -. This makes the moon  appear much much bigger!

The Motion of the Planets – Night After Night

• The farther the planet lies from the Sun, the slower it moves around the Sun.

T: orbital period Time
R: Average Distance from the Sun
This is a consequence of Kepler's 3rd law of planetary motion:

For orbital velocity:

 which means the orbital velocity of a planet is proportional to 1 / square root of the distance.

Example:
Earth’s orbital velocity is 30 km/sec .
For a planet 20 x distant, like the orbit of Uranus

Hence these slower speeds end up looking like retrograde motion as the earth overtakes the outer planet or lags behind an inner planet.

When the Earth and another planet pass each other on the same side of the Sun, the apparent retrograde loop occurs. This is an observational phenomena, not an actual loop in space. It is caused by the relative angular speeds of the Earth and the outer planet.This shows up as a change in direction from one night to the next when we make our observations.

• Retrograde Motion Described…

Then for a few nights, the planet goes into retrograde (moves in the opposite direction from the night before) as the earth in its closer orbit to the Sun speeds past it. (This is the case for outer planets – for inner planets, the inner planet speeds past us)

Retrograde motion happens when the angular speed of  planets appears to slow down (outer) or speed up (inner) when planet and Earth are moving in the same direction, around the sun, and the earth ‘overtakes’ the planet, like a faster car on a highway.

• Here is an animation of Mars (outer planet) as it approaches opposition. We observe the motion as West to East (R-L) with respect to earth until we come closer to opposition. https://millstonenews.com/new/wp-content/uploads/2013/04/opposition.gif

Inner  or  Inferior Planets

At greatest Eastern Elongation, the inferior planet appears higher and higher in the Western Sky and appears as an evening ‘star’ .It follows the Sun and is visible after sunset. It then moves closer to the horizon at sunset as it sweeps through the sun, disappears in the glare of the Sun.

This disappearance occurs at Inferior Conjunction. The planet then reappears as a pre-dawn morning ‘star’, preceding the sun (west of) before sunrise so we can see it while still dark.

• Best and Brightest times for Inner Planets are at Greatest Elongations from the Sun.
• When Venus is at Inferior Conjunction, it’s apparent diameter is much larger because it is  only at the distance of Earth’s Orbit – Venus’s orbit (roughly 1 AU – .7 AU) . This occurred around January 2006, the disk is much larger. Both conjunctions are hard to see because of the glare of the Sun
• When Venus is at Superior Conjunction, it appears  much smaller because it is opposite the Sun at a distance of the Earth’s Orbit + Venus’s Orbit (roughly 1 AU + .7 AU), This occurred around October 2006, the disk is much smaller.

Courtesy Tenho Tuomi, RASC member Saskatoon ttp://www.lex.sk.ca/astro/

In October 2013, planet Venus was very very very bright at Sunset: Here’s the post about that:  http://www.mvc.on.ca/venus-bright-sunset-october-2013/   (Later in the year, it was very bright in the April Morning sky)

Tilt of the Earth’s Axis to the Ecliptic – Why we have Seasons.

Earth Orbit – The earth also orbits in the  Ecliptic plane . However the Earth’s axis is tilted with respect to this plane, and this causes the seasonal variations as we tilt towards and away from the Sun:

• The angle between the Earth’s celestial sphere and the plane of the ecliptic is the tilt of the axis, that is 23.5 degrees.
• This is what causes the seasons, as we tilt towards  and then away from the Sun. In-between these two seasons of Winter and Summer (extreme tilt) is the intersection of the plane of the ecliptic with the plane of the equator. At that point, we have equal solar illumination or Equinox.

When the Sun is on the celestial equator at the Equinoxes *everybody* on earth experiences 12 hours of daylight and 12 hours of darkness for about 2 days. Hence the term EQU-nox – equal night.

We see that the Sun crosses the celestial equator moving northward at the Spring Equinox around March 21. In the Fall it crosses the celestial equator moving southward. As we get into the winter of the Northern Hemisphere, the Sun does not rise very high in the Sky (shorter daylight hours). As we get into Summer in the Northern Hemisphere, the Sun rises higher until we get to Summer solstice (longer daylight) .

As more direct sunlight is incident on the Northern hemisphere from March onwards to June, we have Summer, and the opposite happens in Winter in the months after September – northern winters are due to the low light level of the Sun in this period.

Earth’s Rotation  on its own Axis

( Direction away from the Sun…determines which stars will rise above our horizon…)

The earth rotates around its own axis every 24 hours. If we extend the Earth’s rotational axis into space it intersects the North Celestial Sphere in two places, the North Celestial Pole (NCP) and the South Celestial Pole (SCP) . The Great Circle that goes through the observer’s zenith (directly overhead) and the North Celestial Pole is called the Meridian. Stars are at their highest point when they cross the Meridian. Similarly the Sun crosses at its highest point roughly at noon on our local Meridian. As we move through the constellations different stars will rise and set above our horizon. Stars are ‘seasonal’ too in this regard , for in the Northern Hemisphere, we do not see the brilliant winter stars of Orion, like Betelgeuse in the Summer sky… it remains below our night sky horizon and rises closer to the time of sunrise.

Stars remain ‘fixed’ in the sky at their coordinates of Right Ascension and Declination. The planets and the Sun ‘wander’, and in their close courses appear at different celestial coordinates. The Sun’s declination goes from -23 and 1/2 degrees to +23 and 1/2 degrees. At the Spring and Autumn equinox, the Sun’s Declination is 0 degrees and intersects the Celestial Equator.