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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This note was uploaded on 02/14/2011 for the course ORGANIC CH 341 taught by Professor Idk during the Spring '11 term at University of Wisconsin Colleges Online.

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

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