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Assume for simplicity that for a visual binary one star is much more massive than the other so that it lies approximately at the center of mass and the other star orbits it. You do not know the tilt angle of the orbits with respect to the line of sight, but the orbit appears to be elliptical. If you can follow the motion of both stars over a long enough period of time, how could you decide whether the orbit is truly elliptical, or is just a flattened perspective of a tilted circular orbit? Hint: about what point does a star or planet orbit in Kepler's laws? |
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Consider a circular orbit tilted by an angle i, and in the following
diagram.
Use simple trigonometry to find a formula for the ratio of the apparent semimajor to apparent semiminor axis of the elliptical projection of the orbit that you would see because of the tilt. What is this ratio if i = 30 degrees? Draw the corresponding figure. |
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Why don't any visual binaries have short periods such as a few days or weeks as some of the other types of binary stars do? |