Handout on Solar System PDF

COLLEGE OF SCIENCE Department of Mathematics and Physics Handout on Solar System Formation of Nebular Hypothesis Solar System The most widely accepted theory for the formation of the solar system is the Nebular Hypothesi...

COLLEGE OF SCIENCE Department of Mathematics and Physics Handout on Solar System Formation of Nebular Hypothesis Solar System The most widely accepted theory for the formation of the solar system is the Nebular Hypothesis. It suggests that about 4.6 billion years ago, a giant cloud of gas and dust (a nebula) began to collapse under its own gravity. Formation of the Sun As the nebula collapsed, most of the material was pulled toward the center, forming the Sun. Formation of Planets The remaining material in the surrounding disk began to coalesce into planetesimals, which eventually formed the planets, moons, asteroids, and other bodies in the solar system. Planets in the Terrestrial Planets Solar System Mercury The closest planet to the Sun. It has a very thin atmosphere and experiences extreme temperature variations. Its surface is heavily cratered. Venus Similar in size to Earth, Venus has a thick atmosphere rich in carbon dioxide, leading to a runaway greenhouse effect. It has surface temperatures hot enough to melt lead. Earth The only planet known to support life, Earth has a moderate climate and liquid water on its surface. It has a dynamic atmosphere and active geology. Mars Known as the Red Planet due to its iron oxide-rich soil, Mars has the largest volcano and canyon in the solar system. It has a thin atmosphere, mostly composed of carbon dioxide. Jovian Planets Jupiter The largest planet in the solar system, Jupiter is a gas giant composed mostly of hydrogen and helium. It has a strong magnetic field and at least 79 moons, including the largest moon, Ganymede. Saturn Famous for its prominent ring system, Saturn is also a gas giant. It has a thick atmosphere and many moons, including Titan, which has a thick atmosphere of its own. Uranus An ice giant, Uranus has a blue-green color due to methane in its atmosphere. It rotates on its side, making its tilt extreme compared to other planets. Neptune Similar to Uranus, Neptune is also an ice giant. It has strong winds and storms, with a deep blue color due to its methane atmosphere. Terrestrial vs. Jovian Characteristics Terrestrial Jovian Solar System | Prepared by MROBalmeo  Size and Mass Smaller and denser Massive but have low densities Composition Rocky with metal Composed of gases cores and ices Atmospheres Thin Thick, rich in hydrogen and helium Moons and Rings Have few or no Numerous moons moons and no rings and ring systems Other Asteroids: Small rocky bodies primarily found in the asteroid belt Astronomical between Mars and Jupiter. Examples include Ceres, Vesta, and Bodies Eros. Comets: Icy bodies that originate from the Kuiper Belt or Oort Cloud. They develop tails when they approach the Sun, such as Halley's Comet. Dwarf Planets: Smaller than planets but still spherical in shape. Examples include Pluto, Eris, and Haumea. Moons: Natural satellites orbiting planets, such as Earth’s Moon, Europa (Jupiter), and Titan (Saturn). Meteoroids, Meteors, and Meteorites: Small rocky or metallic bodies. Meteoroids are in space, meteors burn up in Earth’s atmosphere, and meteorites reach Earth’s surface. Space Historical Missions: Explorations 1. Apollo Program: NASA's mission that landed humans on the Moon, including Apollo 11 in 1969. 2. Voyager Missions: Launched in 1977, these spacecrafts explored the outer planets and are now in interstellar space. Modern Missions: 1. Mars Rovers: Robots exploring the surface of Mars, looking for signs of past life. Curiosity Rover (Mars Science Laboratory) It was launched on November 26, 2011 Source: NASA Perseverance Rover It was launched on July 30, 2020, and landed on Mars on February 18, 2021. It is an ongoing mission and is currently active on Mars. Solar System | Prepared by MROBalmeo  Source: ESA Source: theweek.in 2. James Webb Space Telescope It is a powerful telescope designed to observe distant galaxies and study the formation of stars and planets. Start: Launched on December 25, 2021 End: Ongoing mission, with an expected operational lifetime of at least 10 years. 3. New Horizons: A mission that provided the first close-up images of Pluto and its moons. Start: Launched on January 19, 2006; flew by Pluto on July 14, 2015. End: Ongoing mission. After Pluto, it flew by another Kuiper Belt object (Arrokoth) on January 1, 2019, and is continuing to explore the Kuiper Belt. 4. International Space Station (ISS): A collaborative effort involving multiple countries to maintain a space laboratory in low Earth orbit. Start: First module launched on November 20, 1998. Solar System | Prepared by MROBalmeo  End: Ongoing. Current international agreements support operations through at least 2030. Orbit The orbits of the planets in our Solar System are elliptical. Eccentricity: A measure of how much an orbit deviates from being circular. Eccentricity values range from 0 (a perfect circle) to 1 (a parabolic trajectory). Example: Earth’s orbit has a low eccentricity, making it nearly circular, whereas comets often have high eccentricities, leading to elongated orbits. Drawing Ellipses: An ellipse can be drawn using two foci. The sum of the distances from any point on the ellipse to the two foci is constant. Step-by-Step Instructions: 1. Place two pins on a piece of paper to represent the foci. 2. Tie a string around the pins, keeping it taut with a pencil. 3. Move the pencil around, keeping the string tight, to draw an ellipse. Example: Elliptical Orbit of Mars around the Sun Semi-major axis (a): The average distance from Mars to the Sun (Mars' orbit) is about 227.9 million kilometers (1.524 AU). Eccentricity (e): Mars has an orbital eccentricity of 0.0934, meaning its orbit is slightly elliptical. We can calculate various properties of this elliptical orbit: Semi-minor Axis (b) The relationship between the semi-major axis (𝒂), semi-minor axis(𝒃), and eccentricity (𝒆) is given by: 𝑏 = 𝑎 √1 − 𝑒 2 where: 𝑎 = 227,900,000 𝑘𝑚 𝑒 = 0.0934 Calculation: 𝑏 = 227,900,000 × √1 − (0.0934)2 = 227,900,000 × √1 − 0.0087 = 227,900,000 × √0.9913 ≈ 226,870,000 km So, the semi-minor axis is approximately 226.87 million km. Solar System | Prepared by MROBalmeo  Distance from the Sun at Perihelion and Aphelion Perihelion (closest distance): This is the distance from Mars to the Sun at the closest point in its orbit. It’s calculated as: 𝑃𝑒𝑟𝑖ℎ𝑒𝑙𝑖𝑜𝑛 = 𝑎(1 − 𝑒) 𝑃𝑒𝑟𝑖ℎ𝑒𝑙𝑖𝑜𝑛 = 227,900,000 km × (1 − 0.0934) ≈ 206,550,000 km Aphelion (farthest distance): This is the distance from Mars to the Sun at the farthest point in its orbit. It is calculated as: 𝐴𝑝ℎ𝑒𝑙𝑖𝑜𝑛 = 𝑎(1 + 𝑒) 𝐴𝑝ℎ𝑒𝑙𝑖𝑜𝑛 = 227,900,000 km × (1 + 0.0934) ≈ 249,250,000 km Thus, Mars' closest approach to the Sun is 206.55 million km (perihelion), and its farthest point is 249.25 million km (aphelion). Area of the Ellipse The area 𝑨 of an ellipse is calculated as: 𝐴 = 𝜋𝑎𝑏 Calculation: 𝐴 = 𝜋 × 227,900,000 km × 226,870,000 km ≈ 162,083.4 million km2 Orbital Circumference (Approximation) The circumference of an ellipse can be estimated using Ramanujan’s approximation: 𝐶 ≈ 𝜋 [3(𝑎 + 𝑏) − √3(𝑎 + 𝑏)(𝑎 + 3𝑏)] Calculation: 𝐶 ≈ 𝜋 [3(227,900,000 km + 226,870,000 km) − √(3 × 227,900,000 km + 226,870,000)(227,900,000 + 3 × 226,870,000 km)] 𝐶 ≈ 𝜋 [3(454,770,000 km) − √(683,700,000 km + 226,870,000 km)(227,900,000 km + 680,610,000 km)] 𝐶 ≈ 𝜋 [1,364,310,000 km − √825,267,700,000 km] 𝐶 ≈ (455,860,000 km)𝜋 ≈ 1,432,090,000 km The approximate circumference of Mar’s orbit is 1,432.09 million km. Prepared by: Mary Rose O. Balmeo CLSU-DMP Solar System | Prepared by MROBalmeo