# Lecture 4 - Astro/Geo 160 Spring 2011 Lecture#4 – 31...

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Unformatted text preview: Astro/Geo 160 Spring 2011 Lecture #4 – 31 January 2011 Review – Kepler’s Laws Start with the geocentric model…. Need to explain apparent motion of objects in the sky Fails to correctly account for motion of the planets …switch to Copernicus’s heliocentric model… a better fit to the observations, still not perfect …end up with Kepler’s Laws (Know these!!!!) Just right! Planets move on elliptical orbits with Sun at one focus P 2 is proportional to a 3 Orbits sweep out equal areas in equal times Gravity is the basis of Kepler’s Laws Review - Gravity Let’s try an example: Assume astronomers detect a planet orbiting the Sun with an orbital period of 32 years. What is the semi-major axis of this planet’s orbit? A) 32 AU B) 1000 AU C) 10 AU D) 90 AU E) can’t tell from the information given Law of gravity F gravity = GM 1 M 2 /R 2 – “inverse square law” Acceleration due to gravity = GM 1 /R 2 change in velocity due to gravity velocity is just the change in position with time so there’s an equation of motion that says how an object moves in the presence of another mass Scale of the Solar System Kepler’s 3 rd Law P 2 is proportional to a 3 not an absolute distance P 2 = (4 π 2 /GM)a 3 No independent way of measuring a! Transit of Venus If you observe the transit of Venus from two different locations on Earth, you can get the distance to Venus and, therefore, a measure of the astronomical unit Scale of the Solar System Kepler’s 3 rd Law P 2 is proportional to a 3 not an absolute distance P 2 = (4 π 2 /GM)a 3 No independent way of measuring a! Transit of Venus (1761, 1769) If you observe the transit of Venus from two different locations on Earth, you can get the distance to Venus and, therefore, a measure of the astronomical unit. You know: Separation on Earth Angular size of the Sun That the distance to Venus is the same from both locations Hence distance to Venus, use Kepler’s 3 rd law, distance to Sun Planet Trek – Dane County Distances to the Stars Parallax Observe the relative motion of a star compared to a fixed background from two different locations D (pc) = 1/p (arcsecs) 360 degrees in a circle, 60 arcminutes in a degree, 60 arcsecs in an arcminute 1 pc = 3.09 10 18 cm = 3.26 light years Only gets you so far… Fundamental problem in astronomy – measuring distances!!! How far away are the “galaxies”? How far away are the “galaxies”?...
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Lecture 4 - Astro/Geo 160 Spring 2011 Lecture#4 – 31...

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