3rd Class Lecture Notes - Celestial Mechanics

3rd Class Lecture Notes - Celestial Mechanics: Pre Lecture Notes - Celestial mechanism or celestial dynamics is a field of astronomy that studies movement of objects in space as well as their gravitational interaction. - This field involves the use of principles of physics and mathematics to describe the motion and revolutions of planets, moons and other related formations. - Below are some important concepts in celestial mechanics:Below are some important concepts in celestial mechanics: Laws of Planetary Motion Johannes Kepler formulated three fundamental laws that describe the motion of planets around the Sun: ● ● ● Kepler's First Law (The Law of Ellipses): This law says that the orbit of planets is an ellipse for which the Sun is one of the foci. Kepler's Second Law (The Law of Equal Areas): As stated whereby, this law describes that an ellipse formed by a line segment joining a planet and the Sun, is such that it sweeps equal area during equal intervals of time. This means it takes a planet shorter time to move round the Sun when it is near the sun and take a longer time as it gets further from the sun. Kepler's Third Law (The Law of Harmonies): This law gives how long planet takes to complete one orbit around the sun relative to the distance between planet and the sun. Mathematically, the square of the orbital period (T) is proportional to the cube of the semi-major axis (a) of its orbit: It states that T² is directly proportional to ‘a’ raised to the power of three: T² ∝ a³. Newton's Law of Universal Gravitation - Isaac Newton build on what Kepler discovered with Newton’s law of universal gravitation, which argue that any mass attracts every other mass in the universe with a force that is directly proportional to the product of their masses and in reverse order proportional to the square of the distances that exist between their centers. - The formula is: F = G * (m₁ * m₂) / r² ➤ ➤ ➤ ➤ - Where: F is the gravitational force between two objects G is the gravitational constant m₁ and m₂ are the masses of the objects r is the distance between the centers of the two masses Orbits and Their Types: In celestial mechanics, an orbit is the gravitationally curved path of an object around a point in space. There are various types of orbits: ★ Circular Orbits: These orbits are characterized in that their distance to the central body remains constant. The linear velocity of the orbiting object un changes while the angular velocity of the orbiting object, will reduce. ★ Elliptical Orbits: They are the most widespread ones and in this type the distance from the orbiting body to the central one also changes. Thereby, the object is in motion faster when it is closer to the central body, and slower when it is farther. ★ Parabolic Orbits: These are the escape orbits in which the body to be disposed has just adequate velocity to enable it go out of the influence of the central body, traveling along a parabolic trajectory. ★ Hyperbolic Orbits: Such orbits exist unless the object acquires enough velocity to leave the influence of the central body, along a hyperbolic path. Knowledge of these principles is critical in space missions, satellite positioning, and the identification of God’s creations in the universe.