Planetary Motions in the Universe

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Planetary Motions in the Universe

Stellar Astronomy: Astronomy 111

Abstract:

Planetary motions involve how each planet orbits in our Solar System, stars motions, as well as Earth’s behaviors and patterns. This term paper describes Celestial Sphere, Retrograde Motion, the Geocentric Model, the Heliocentric Model, the Seasons, Planets and their orbits as well as irregularities in orbits and more. Planetary motions can be better understood with laws such as Kepler’s Laws of Planetary Motion and Newton’s Laws of Motion and can be viewed from observatories using tools and instruments such as telescopes. Most observatories if not all focus on behavior and patterns of celestial objects and therefore gather information on the planetary motions of the universe to simplify and further explain Stellar Astronomy.

Astronomy

Astronomy, as defined by Merriam- Webster, is “the study of objects and matter outside the Earth’s atmosphere and of their physical and chemical properties.” This science focuses on the measurements of positions and motions among other characteristics. Astrophysics is a branch that focuses on the application of theories and laws of physics as applied to astronomy. (Balter 2017) It involves “behavior, properties, and motion of objects” in space (Redd 2017). Planetary motions involve the movement patterns of all planets, moons and astronomical bodies (including Earth), the evolution of planetary systems and studies laws such as Kepler’s and Newton’s laws.  

Celestial Sphere & Geocentric Model: 

The celestial sphere is a model that simplifies the motions of the sky. (Schroeder 2011) Stars are in constant motion even though from our perspective they seem to be still because they are so far. These are known as fixed stars. Earth’s tilt and rotation also make stars and planets look like they move around the sky once a day. (Hotlzman 2013) 

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The celestial sphere is an imaginary sphere that consists of the Celestial Equator, an Ecliptic, North Celestial Pole (NCP), South Celestial Pole (SCP), Right Ascension (RA) and Declination (Dec). The Celestial Equator is a projection of Earth’s equator. North and South Celestial Poles are extensions of the North and South Poles. Right Ascension and Declination are similar to longitude and latitude and are used as celestial coordinates to determine the location of stars. (Pearson 2010) 

The Celestial Sphere. (Image Courtesy of the Lunar and Planetary Institute)

Star Motions 

There are two categories of star motions: Observed motions which consist of proper motions and radial velocity, and true space motion. Proper motion “is the apparent angular motion of a star across the sky with respect to more distant stars. This is the projection onto the sky of the star’s true motions through space relative to the Sun”. Radical velocity “is how fast it is moving directly towards or away from us.” True Space Motion is the “Combination of radial velocity, proper motion, & distance.” (Pogge 2006) 

From Earth, stars seem to move around the celestial sphere. Depending on the location objects may seem to move in smaller circles if it is near a pole, and in bigger circles, if the object is further from the poles. This means the apparent motion of the object depends not only on the location of the observer from Earth but also the location of the object in respect to the rotation axis. An example of this is how we view the Sun from Earth, it takes 24 hours for the Sun to be in the same location or position in the sky or go in a full circle around the sky. (Holtzman 2013)  

In reality, though, it is Earth traveling around the Sun, in conjunction with the rest of the planets and objects. The motions of the planets are categorized by qualitative motions and apparent motions. Qualitative motions consist of 3 facts: 1) planets move around the Sun in the same plane, 2) planets move in the same direction, 3) orbits of planets near to the Sun are faster than those that are far away. Apparent motion is how motions are viewed as from Earth, for example, retrograde motion. (Holtzman 2013) 

Retrograde Motion 

Retrograde motion is the apparent backward or westward motion of objects as seen from Earth. (Seligman 1993) This illusion is caused because of the size and speed of the object’s orbit. There are several planets that experience apparent retrograde motion such as, Jupiter, Saturn, and Mars. (Crockett 2017) Retrograde motion is a term that supports the heliocentric model proposed by astronomer Copernicus, explaining that the planets in our Solar System revolve around the Sun and not around Earth as previously explained in the geocentric model; and thus, simplifying that retrograde isn’t the planets moving in opposite directions but just slower in the same direction. This event is further explained by the study of stellar parallax. (Palma n.d.) 

 

Mars in retrograde motion. Image courtesy from Universe Today 2009. Credit: 1997 Wadsworth Publishing Co.

Heliocentric Model 

All planets in our solar system orbit around the Sun this is also better known as the heliocentric model. The reason the planets rotate around the Sun is because of its gravitational pull, even though the Sun is far away from all the planets by a good distance it has a higher gravitational pull than all the other heavenly bodies, and this is why all the planets travel around the Sun on elliptical orbits just like how the moon revolves around the earth. 

Planets & Their Orbits 

Each planet rotates at a different speed and distance from the Sun. The order of the eight official planets according to their distance from the Sun is as follows: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. This doesn’t include dwarf planets in our solar system also orbiting the Sun, including but not limited to: Ceres that sits somewhere between Mars and Jupiter that was previously classified as an asteroid; Pluto, Haumea, Makemake, and Eris that are located somewhere in the skirts of our solar system past Neptune. (Atkinson 2015) 

Originally it was believed that there were nine planets, the official eight planets, and Pluto, revolving around the Sun. 76 years after its discovery in 2006, thanks to technology advancement, Pluto was reclassified as a dwarf planet. This was because in the 2000s there were changes in the definition of planets, dwarf planets and the creation of a new subcategory of dwarf planets “plutoids”. (Atkinson 2015)  

The term “Planet” as redefined by the International Astronomical Union or IAU in our Solar System to a celestial body that:  

  •       “is in orbit around the Sun, 
  •       has sufficient mass to assume hydrostatic equilibrium (a nearly round shape), 
  •       has “cleared the neighborhood” around its orbit. 
  •       is not a moon.” (Atkinson 2015)  

Plutoids are defined by the International Astronomical Union (IAU) about 10 years ago in 2008 as “celestial bodies in orbit around the Sun at a distance greater than that of Neptune that have sufficient mass for their self-gravity to overcome rigid body forces so that they assume a hydrostatic equilibrium (near-spherical) shape, and that have not cleared the neighborhood around their orbit.” (Atkinson 2015)  

Mercury  

Mercury for example while being the closest planet to our Sun, takes just over 58 Earth days for it to make a full rotation on its axis. “However, this is not to say that Mercury experiences two sunrises in just over 58 days. Due to its proximity to the Sun and rapid speed with which it circles it, it takes the equivalent of 175.97 Earth days for the Sun to reappear in the same place in the sky. Hence, while the planet rotates once every 58 Earth days, it is roughly 176 days from one sunrise to the next on Mercury.” (Williams 2016)   The revolution of Mercury being that it’s the closest to the Sun is about 88 days and that means a year on Mercury is just about a half of Mercury’s day. (Williams 2016) 

Venus

Venus is the next in planet in order has a peculiar way of moving. It rotates counter-clockwise on its axis as compared to the rest of the planets. Even though it does this, it takes about 243 Earth days for it to make a full rotation and about 224.7 days for it to make a revolution about the Sun. Then comes our home planet Earth which takes 24hrs to make a rotation on its own axis and about 365 days to make a revolution around the Sun which brings about the difference in seasons. (Williams 2016) 

Earth 

On average it takes about 24 hours for Earth to orbit around the Sun and 24 hours for Earth to rotate on its own axis. (Williams 2016) 

Mars 

Followed by Mars which can also be known as Earth’s twin because of its close relationship to Earth, regarding our atmospheres, gases present and having a similar axial tilt as our planet. It takes just over 24 hours for Mars to make a full rotation and being the 4th planet from the Sun, it takes Mars about 687 Earth days to make a full revolution. (Williams 2016) 

Jupiter 

Jupiter, which is the biggest planet in our solar system, we would expect it to have a longer day but a day on Jupiter lasts about 10 hours long and this is due to the giant having rapid speed on its own axis. Although it rotates fast on its own axis, it takes Jupiter about 12 Earth years to complete a full revolution. (Williams 2016) 

Saturn 

The next giant in our solar system is Saturn and like Jupiter even being as huge as it is, it rotates at a rapid pace, completing a rotation in 10 hours. A year on Saturn would take about 29 Earth years being that its so far away from the Sun. (Williams 2016) 

Uranus 

Determining a day on Uranus, which is the second to last, is a bit of a problem for astrologists as the planet has a very pronounced axial tilt of 97.77° and because of this tilt, Uranus orbits the Sun on its side. Although this is a problem of calculating the day, there has been an estimate that Uranus takes about 84 Earth years for the planet to have a day; that is from sunrise to sunrise. Exceptionally enough, a year on Uranus also takes 84 Earth years which means a day on Uranus is also a year on Uranus. (Williams 2016) 

Neptune 

The eighth and last planet of our Solar System, Neptune, where days are also a bit complicated and confusing to calculate. This is because the poles on Neptune move faster than the equator due to the fact that it is an ice and gas giant, but a rough estimate is that one Neptune day is equivalent to 0.6713 Earth days. (Williams 2016) 

Exceptions 

With regards to the speed of planets in perspective to their distance from the sun, it can be easy to assume that the inner planets move faster on their axis and when revolving around the Sun but that is not necessarily always the case.  

The Sun and all the planets were all formed from the same nebula cloud, this influences how the planets rotate, therefore it explains why most of the planets rotate in a counterclockwise direction exception Venus and Uranus and “these differences are believed to stem from collisions that occurred late in the planets’ formation”. (Spagna 2003) 

Although the planets revolve around the Sun in a similar fashion, the last four planets being; Jupiter, Saturn, Uranus and Neptune rotate faster on their axis even though they are bigger in size as compared to the inner planets and this is because “these biggies must have accumulated most of their mass from gas in the surrounding solar nebula. That gas formed individual spinning disks (from which many satellites formed), and most likely it carried a lot of angular momentum as it fell onto the outer planets’ cores, causing them to spin faster and faster as they coalesced” (Beatty 2006). 

Planets Aligned 

Rarely we see the planets aligned in the sky because of how all planets while moving on the same plane move at different speeds as they orbit around the Sun, but approximately every two years, at least five planets can be seen in a row. This year, 2018, was one of the years where the brightest planets are visible at the same time. In the month October, we were able to witness “Mercury and Venus are low to the west, with bright Jupiter shining just above. Higher up in the northwestern sky is Saturn and completing the set of five is the red planet Mars, high overhead.” (Hill 2018) 

After sunset around Australia, the five  

bright planets can be seen in the western  

sky this week.  

Credit: Museums Victoria/Stellarium

The five planets were last seen together  

in the western sky, August 2016.  

Credit: Alex Cherney.

Irregularities in Orbits

Planets barely ever influence each other’s gravitational pull but the farther away from the Sun they are, there could be possibilities of irregularities in their orbits. An example being Uranus having irregularities in its orbit in the 19th century (UCSB 2012). Irregularities in a simple system, the orbit of a planet around a star would be a perfect circle, but the gravitational influence of other large bodies in the system. In our case, Jupiter and the other gas giants) perturbs the circular orbits into elliptical ones. 

Earth’s Tilt & Orbit 

Earth’s orbit and tilt cause the seasons as described by timeanddate.com. Earth’s orbit takes about 24 hours to go around its own axis and Earth’s axis tilt is at an angle of 23.4 degrees, this angle is known as obliquity; the direction of the tilt does not change, what changes is the position of the hemispheres. The combination of these factors that affect how Earth receives sunlight not only on a daily basis but annually are causes that make the seasons occur. The tilt causes our planet, Earth, to point different areas away from the Sun at different times of the year. When the Northern Hemisphere points toward the Sun during the northern summer because it is getting more direct sunlight and when the Northern Hemisphere is away from the Sun it causes the northern winter because it is receiving less sunlight, this is the reason of opposite seasons.   

 

Earth’s axis is the imaginary red line that runs through the North and South Poles. 

timeanddate.com 

The Seasons 

The seasons are broken up into four categories and are separated by four events. Spring equinox or Vernal equinox is opposite to Fall equinox, and the Summer solstice is the opposite of Winter solstice.  

 

Earth orbits the Sun at a slant, which is why equinoxes and solstices happen. timeanddate.com 

Equinoxes

Equinoxes are the dates that mark when the day and night lengths are equal. This phenomenon happens twice a year. The first known as Spring equinox can also be referred to as March equinox, because the date range is between March 19th to March 21st in the Northern Hemisphere; while in the Southern Hemisphere it will be the Fall or Autumnal equinox instead. In the Northern Hemisphere the Fall equinox is anywhere from September 22nd to September 24th and can be referred to as the September equinox. 

 

Earth’s position at the September equinox. 

Illustration of Earth’s position in relation to the Sun’s rays at the September equinox  

(Illustration is not to scale.) timeanddate.com 

Solstices 

Solstice is defined by Merriam-Webster as “the time of the sun’s passing a solstice which occurs about June 21 to begin summer in the northern hemisphere and about December 21 to begin winter in the northern hemisphere”. The date of the solstices like the equinoxes varies between a range from the 20th and the 22nd of June for the Summer Solstice and of December if it relates to the Winter Solstice.  

 

 

The June Solstice. (Not to scale) timeanddate.com 

The North Pole is tilted furthest away from the Sun at the December solstice. (Not to scale) timeanddate.com 

Eclipses

As defined by Merriam-Webster is “the total or partial obscuring of one celestial body by another.” From Earth, these events occur when the Sun, Earth, and Moon align, where one celestial object then blocks another. 

Solar Eclipse & Lunar Eclipse

Solar eclipses or eclipses of the Sun explained in timeanddate.com, are when the three celestial bodies move and are arranged in an alignment as follows: Earth, Moon, Sun and only happens during a New Moon, which is a phase of the Moon.  

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Lunar eclipses, as explained in timeanddate.com, only happen on a Full Moon and happens when the Earth comes between the Sun and the Moon since the Moon does not have its own light and depends on the Sun’s reflection.  

Misconceptions 

Although the total solar eclipse is a phenomenon which happens occasionally, there have been some misconceptions built around it by people. The most popular one being that; “the phenomenon of a total eclipse of the sun is a rare occurrence.” But this is quite the opposite as it happens once every 18 months and is visible from someplace on Earth’s surface. (Rao 2017) 

Kepler’s Three Laws of Planetary Motion 

Johannes Kepler’s discovered the three laws of Planetary motion in the 16th century. (Britannica 2018) 

 

Credit: Copyright 2013. The University of Waikato.

Kepler’s First Law 

All planets move about the Sun in elliptical orbits, having the Sun as one of the foci. (Britannica 2018) An elliptical orbit is similar to a circle but flattened, and the flatness can be described by the eccentricity of the ellipse. Eccentricity can be described the two foci of the shape, the further apart they are together the flatter the ellipse and the eccentricity will be closer to 1, vice versa. The ellipse will stretch by two outermost points known as the perihelion and the aphelion. As defined by Dictionary.com the perihelion is closest to the Sun and the aphelion is the most distant to the Sun. (Illustrated below. Credit: University of Waikato, 2013) 

  

Credit: Copyright 2013. The University of Waikato. All rights reserved.  

https://www.sciencelearn.org.nz/images/277-kepler-s-laws 

Kepler’s Second Law 

A radius vector joining any planet to the Sun sweeps out equal areas in equal lengths of time. (Britannica 2018) Because of the gravitational pull between the Sun and the planets, when the planets are closer to the Sun, they will move the fastest and slower when it is furthest apart, making the planet travel equal areas in equal time. 

Kepler’s Third Law

“The squares of the sidereal periods (of revolution) of the planets are directly proportional to the cubes of their mean distances from the Sun.” (Britannica 2018) 

Credit: R Nave. http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html 

Anomalies of Kepler’s Laws 

Anomalies in astronomy can describe the apparent or abnormal motions of the planets. There are three known kinds of anomalies in astronomy: true, eccentric, and mean anomalies; that describes the position in the orbit of an object around the center of a mass. (Britannica 2018) 

 

Credit: 2013 Encyclopaedia Britannica Inc.

True anomaly  

Refers to the angle (V) created between the perihelion or outer point closest to the Sun of the planets orbit, the center of the Sun, and the planet in question. (Britannica 2018) 

Eccentric anomaly 

Is the “angle between lines drawn from the Sun to the perihelion B and to a point (not shown) moving in the orbit at a uniform rate corresponding to the period of revolution of the planet.” (Britannica 2018) 

Mean anomaly 

Is the angle (E) created by the connection of the major axis, the center of the ellipse, “and the point P′, which is located by drawing a perpendicular to AB passing through the planet and intersecting a circle of diameter AB.” (Britannica 2018) 

Newton’s Three Laws of Motion

From Kepler’s laws of planetary motion, Newton was able to define and further develop the laws of motion.  

Newton’s First Law

Describes the concept that unless a force is put onto an object it will not change states.  

“Law I. Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon. 

In essence, a moving object won’t change speed or direction, nor will a still object start moving, unless some outside force acts on it. The law is regularly summed up in one word: inertia.” (NASA 2009) 

Newton’s Second Law 

Focuses on the concept that, F = ma or, Force is equal to mass times acceleration. 

“Law II. The alteration of motion is ever proportional to the motive force impressed, and is made in the direction of the right line in which that force is impressed. 

Newton’s second law is most recognizable in its mathematical form, the iconic equation: F=ma. The strength of the force (F) is defined by how much it changes the motion (acceleration, a) of an object with some mass (m).” (NASA 2009) 

Newton’s Third Law 

States that for every action or force there is a reaction of equal force.  

“Law III. To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal and directed to contrary parts.” (NASA 2009) 

Observatories and Satellites: Planetary Motions

Observatories can be defined as buildings or structures that have telescopes and instruments to observe celestial objects. Though most observatories even if unintentionally one way or another study motions of celestial bodies, the most modern instruments with technology advancement can observe even waves. (Bhutia 2017)  

Different observatories focus on different activity, motions, and phases. For example, The Classical Observatory located in Middle Tennessee State University, observes objects like Mar’s retrograde motion. The Uranidrome Observatory also located in Middle Tennessee State University consists of twelve columns arranged for celestial advantage and they observe The North Star, the beginning of seasons, apparent paths of planets; and it measures Earth’s rotation rate and Earth rate of revolution around the Sun. (MTSU) 

 

 

Classical Observatory.  

Credit: MTSU by AWJ-photography 

Uranidrome. https://mtsunews.com/wp-content/uploads/2012/09/MTSU-Observatory-graphic.jpg Credit: MTSU NEWS 2012

  

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