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AST371: Introduction to Astrophysics
(Fall 2008)
HW3 – Solutions
1)
a)
The generated orbit for Mars are the blue circles. The main focus is the red circle with the
+ inside. The fitted circle is the circle given by
x
+ 0.1425
(
)
2
+
y
2
= 1.5235
(
)
2
, and its
center is marked by the blue square with the x inside. Ptolemy and Kepler were no fools:
this circle agrees very well with the data! The center of the circle is the center of the
ellipse (half way between perihelion and aphelion, or half way between the foci). The
center – perihelion distance will be the radius of the circle.
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View Full Document b) To check Kepler’s second law make two approximately right triangles, one from
perihelion to focus to a data point close to perihelion, and a second triangle with the
aphelion. Next, calculate the areas:
For the perihelion triangle, one side has length 1.381, the other 0.105, so that the area is
0.0725. For the other, one side is 1.666, the other 0.087, so that the area is 0.0725.
To check Kepler’s third law, vary the semimajor axis a, and measure the period P. The
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This note was uploaded on 11/23/2011 for the course AST 3003 taught by Professor Staff during the Fall '11 term at University of Central Florida.
 Fall '11
 Staff

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