Introduction
Comets, or what are also known as “dirty snowballs,” are balls of gases containing dust and rock particles. A comet is made up of a nucleus, coma, hydrogen envelope, and two tails (the ion tail and the dust tail). This ball of gas has a large scale of length, the tail ranging to be up to 100 million miles long. The speculation of comets lies in how they were formed, although it is believed that they were formed with the solar system from gas and dust particles merging from the formation of the planets. The activity of a comet is to orbit the sun in either an elliptic orbit, parabolic trajectory, or a hyperbolic trajectory. Additionally, the two types of comets: the short period and long period comet have different origins. Theoretically, the long period comet comes from the Oort Cloud (an imperfect spherical shaped cloud of icy debris) while the short period comets from Kuiper Belt (a large asteroid belt). Comets are known to last roughly half a million years and they are considered “dead” when it loses too much of its mass by secreting debris.
Historical Aspects
Scientists that have contributed research on the history of comets and its trajectories are Copernicus, Tycho Brahe, Galileo, Newton and Kepler. Tycho Brahe revealed that comets travel far beyond the Earth’s atmosphere at places that have greater distance than the moon. Newton made a significant discovery on the elliptical, oval-shaped orbits of comets around the sun and how comets can repeat this cycle. Chinese astronomers also played a huge role in the discovery and data of comets, including Halley’s Comet, the most famous comet that has been seen since the ancient times. These ancient Chinese helped provide evidence for sightings of Halley’s Comet and its incredible features for so long. According to the European Space Agency, Halley’s Comet was first discovered in 239 B.C., but Halley’s shape and appearance makes other scientists believe it dated back to 466 B.C., when ancient Greeks might have been the first to discover it. Even though he was not the first to discover this comet, Edmund Halley was the inspiration for its name because he discovered that one particular comet has been returning near Earth again and again for the past two centuries before he published “A Synopsis of the Astronomy of Comets” in 1705. He predicted the comet’s return to be in 1742, but he did not live to see its comeback. Gottfried Kirch was the first to discover comets with a professional telescope and was known for the discovery of the Great Comet of 1680. Other great comets include, Shoemaker Levy-9, for its collision into Jupiter in 1994 because of the planet’s intense gravity. The comet’s collision caused an explosion and fireball to occur stronger than the energy of TNT. Another one is Comet Borrelly, which is shaped like a bowling pin and was found to originate from the Kuiper Belt, instead of the Oort Cloud. The most recent discovery of a new comet was of last year 2017 and it consisted of water, carbon, nitrogen, oxygen and sulfur, which are vital elements and essentials found in Earth.
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Mathematical Elements
Comets are classified into two main categories: short-period and long-period. Short-period comets have periods of less than 200 years, and come from the Kuiper Belt, a region beyond the orbit of Neptune containing rock and ice. The short-period comets are further divided into two categories, based on how long their period is. Halley type comets have periods over 20 years, while Jupiter type comets have periods less than 20 years. On the other hand, long period comets come from the Oort Cloud, which is a sphere around our solar system composed of icy debris. With periods of over 200 years, these comets are more difficult to detect.
The orbits of comets are determined by its period. Short-period comets tend to have circular or elliptical orbits, while long-period comets tend to have parabolic or hyperbolic orbits. While comets with elliptical orbits continue to revolve around the sun, those with parabolic or hyperbolic orbits never return to our solar system, unless they are later influenced by some strong gravitational force. The eccentricity of the orbit of a comet varies depending on the path it takes. For instance, if the eccentricity of the path is close to one then the ellipse begins to take a parabolic path. As the eccentricity gets closer and closer to zero, the shape of the path resembles a circle. Finally, if the eccentricity is greater than one, the comet takes a hyperbolic path.
Formulas
In order for a comet to begin its orbit around the Sun, it must first gain velocity. As their nuclei begin as debris in either the Oort Cloud or Kuiper Belt, they are already orbiting around the Sun. However, the Sun provides the main gravitational force needed to power a comet. The Sun’s immense heat causes gases located in the nucleus of the comet to expand, which escapes in jets. These jets act as “thrusters” and propel the comet on its orbit. The Sun’s force also plays a role in determining the orientation of the tails of a comet. No matter at which point of the orbit the comet is in, the tails of a comet always point away from the sun. The ion tail points straight away from the Sun, while the dust tail curves towards the orbital path. As the comet gets close to the sun, the tails get longer.
The relative potential and kinetic energies of a comet is important in determining the shape of a comet’s orbit. The formulas for kinetic and potential energy are given by:
KE=12mv2 and PE=mgh
where m is the mass of the comet, v is its velocity, and h is its distance from the sun. If the kinetic energy of a comet is greater than its potential energy, its velocity is greater than what is known as the “escape velocity.” The escape velocity is the minimum velocity that a celestial body needs to escape the gravitational influence of a larger body. Comets that fall under this criteria either have a parabolic or hyperbolic orbits. The difference is that comets with parabolic orbits have the minimum velocity needed to exceed the escape velocity, while those with hyperbolic orbits have considerably greater velocities than that of the escape velocity, allowing it to have a less curved path line when it approaches the sun. However, when the overall potential energy of a comet is greater than its kinetic energy, it does not have enough velocity to escape the Sun’s gravitational influence and is bound by an elliptical orbit.
A comet with an elliptical orbit continuously revolves around the Sun, with its relative potential and kinetic energies fluctuating based on its distance to the sun. Two important points on any celestial body orbit around the sun are the aphelion and the perihelion. The aphelion is the point where the comet is farthest from the sun, while the perihelion is its distance closest to the sun. By Kepler’s Second Law, no matter how far the distance the comet is from the Sun, it travels an equal area of space in equal amounts of time. To follow this rule as well as the conservation of energy, the velocity of a comet changes based on its distance to the sun; at its aphelion, the comet moves at its slowest, while at its perihelion, it moves fastest. Therefore, at aphelion, the kinetic energy of a comet is at its minimum, while it is at its maximum at perihelion (because as shown by the formula, the kinetic energy is directly proportional to the square of the velocity).
Conclusion
In conclusion, comets can have different trajectories those being the elliptical orbit, parabolic trajectory, or hyperbolic trajectory each having different properties. These properties include the parabolic and hyperbolic comet trajectories exceeding the “escape velocity” although the hyperbolic trajectory having the greater velocity. As per the elliptical orbit of some comets it involves the understanding of the aphelion and perihelion points. The information gathered by scientists such as Brahe or Newton has significantly contributed to the knowledge people share of comets today. Fortunately, we are able to see these incredible “dirty snowballs” using the right equipment which includes binoculars or a barn door mount (which is a tool used to take pictures of comets). The next predicted comet you can watch is in December of 2018 and it is called the 46P. Don’t miss it!
