lecture05

lecture05 - Astronomy 3: The Nature of the Universe...

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Astronomy 3: The Nature of the Universe Professor Alice Shapley Lecture 5: Motion, Force, Energy contd. Light, Matter, Telescopes (NGC 1499 Image credit: Markus Noller, Deep Sky Images)
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Logistics • Quiz #2: due Monday, April 18 th , 10 pm. • Available today after class at CCLE website: https://ccle.ucla.edu/course/view/11S-ASTR3-2 • Lab this week on “Light and Telescopes.”
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Review from Last Time • Motion: speed, velocity, acceleration. • Force, momentum, angular momentum. • Newton’s 3 Laws of Motion. • Conservation of angular momentum. • Energy and Conservation of energy. • Newton’s Law of Gravitation.
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The Universal Law of Gravitation 1. Every mass attracts every other mass. 2. Attraction is directly proportional to the product of their masses. 3. Attraction is inversely proportional to the square of the distance between their centers. . NOTE: Gravity is not a constant force; its value changes with distance.
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The Moon and the “Apple”: Universal Gravitation How are these two systems equivalent?
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Kepler’s first two laws apply to all orbiting objects, not just planets. Some comets have unbound orbits; they orbit the Sun only once. Ellipses are not the only orbital paths. Orbits can be: – bound (ellipses) – unbound • parabola • hyperbola Newton’s Law of gravity permits all these orbits.
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If an object gains enough orbital energy, it may escape (change from a bound to unbound orbit). Escape Velocity from Earth 11.1 km/s from sea level (about 40,200 km/hr; 25,000 mph or 7 miles per second). This velocity depends on the mass and radius of the Earth, not the mass of the object – i.e. v esc = (2GM Earth /R Earth ) 1/2 . Escape Velocity
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Newton’s Version of Kepler’s 3rd Law Newton’s version of Kepler’s Third Law : If a small object orbits a larger one, and you measure the orbiting object’s orbital period AND average orbital radius THEN you can calculate the mass of the larger object. Examples ( know these ): Calculate mass of Sun from Earth’s orbital period (1 year) and average distance (1 AU). • Calculate mass of Earth from the orbital period and average distance of any orbiting satellite, including the Moon. • Calculate mass of Jupiter from the orbital period and distance from Jupiter of one of its moons. This is an incredibly powerful discovery.
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p = orbital period a = average orbital distance (between centers) (M 1 + M 2 ) = sum of object masses So, if M 2 is tiny compared to M 1 then M 1 = 4 π 2 a 3 /Gp 2 . NOTE: Just know that this equation allows us to measure the mass of distant objects. p 2 = 4 π 2 G ( M 1 + M 2 ) a 3 See page 131. Newton’s Version of Kepler’s 3rd Law
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p = orbital period a = average orbital distance (between centers) (M 1 + M 2 ) = sum of object masses So, if M 2 is tiny compared to M 1 then M 1 = 4 π 2 a 3 /Gp 2 . NOTE: Just know that this equation allows
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lecture05 - Astronomy 3: The Nature of the Universe...

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