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Discover the intricate dynamics of orbital motion as explained by Kepler's laws and gravitational forces. Learn how planets move in curved orbits due to the Sun's gravitational pull, and delve into Newton's principles to comprehend the factors influencing planetary motion. Explore the applications of orbital mechanics, including calculating masses of celestial bodies and understanding escape velocities. From classical mechanics to Einstein's theories, trace the evolution of celestial motion studies. Gain insights into telescopes, refraction and reflection of light, and the functioning of refracting and reflecting telescopes. Delve into the challenges of chromatic aberration, optical perfection, and the importance of telescope size for enhancing angular resolution and resolving power. Understand the limitations imposed by Earth's atmosphere on astronomical observations.
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Orbital Motion = Kepler Explained “Compromise”: planet moves in curved orbit Sun’s gravitational pull forces planet into orbit by changing direction of planets velocity Planet wants to move in a straight line of constant velocity (Newton 1)
It takes a stronger force to make a high speed planet move in an orbit
Cannon “Thought Experiment” http://www.phys.virginia.edu/classes/109N/more_stuff/Applets/newt/newtmtn.html
Applications • From the distance r between two bodies and the gravitational acceleration a of one of the bodies, we can compute the mass M of the other F = ma = G Mm/r2 (m cancels out) • From the weight of objects (i.e., the force of gravity) near the surface of the Earth, and known radius of Earth RE = 6.4103 km, we find ME = 61024 kg • Your weight on another planet is F = m GM/r2 • E.g., on the Moon your weight would be 1/6 of what it is on Earth
Applications (cont’d) • The mass of the Sun can be deduced from the orbital velocity of the planets: MS= rOrbitvOrbit2/G = 21030 kg • actually, Sun and planets orbit their common center of mass • Orbital mechanics. A body in an elliptical orbit cannot escape the mass it's orbiting unless something increases its velocity to a certain value called the escape velocity • Escape velocity from Earth's surface is about 25,000 mph (7 mi/sec)
From Newton to Einstein If we use Newton II and the law of universal gravity, we can calculate how a celestial object moves, i.e. figure out its acceleration, which leads to its velocity, which leads to its position as a function of time: ma= F = GMm/r2 so its acceleration a= GM/r2is independent of its mass! This prompted Einstein to formulate his gravitational theory as pure geometry.
Telescopes From Galileo to Hubble: Telescopes use lenses and mirrors to focus and therefore collect light
Rain analogy: Collect light as you collect rain Rain/light collected is proportional to area of umbrella/mirror, not its diameter
Light hits Matter: Refraction • Light travels at different speeds in vacuum, air, and other substances • When light hits the material at an angle, part of it slows down while the rest continues at the original speed – results in a change of direction • Different colors bend different amounts – prism, rainbow
Application for Refraction • Lenses use refraction to focus light to a single spot
Light hits Matter (II): Reflection • Light that hits a mirror is reflected at the same angle it was incident from • Proper design of a mirror (the shape of a parabola) can focus all rays incident on the mirror to a single place
Application for Reflection • Curved mirrors use reflection to focus light to a single spot
Telescopes • Light collectors • Two types: • Reflectors (Mirrors) • Refractors (Lenses)
Problems with Refractors • Different colors (wavelengths) bent by different amounts – chromatic aberration • Other forms of aberration • Deform under their own weight • Absorption of light • Have two surfaces that must be optically perfect
Telescope Size • A larger telescope gathers more light (more collecting area) • Angular resolution is limited by diffraction of light waves; this also improves with larger telescope size
