The Mathematics of Star Trek. Lecture 11: Extra-Solar Planets. Outline. Finding Extra-Solar Planets The Two-Body Model A Celestial Cubic Example-51-Pegasi. Finding Extra-Solar Planets. Recent discoveries of planets orbiting stars rely on a type of problem known as an inverse problem.
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The Mathematics of Star Trek
Lecture 11: Extra-Solar Planets
so the magnitude of the centripetal force on the star is
where G is the universal gravitation constant
we find that x and satisfy the following cubic equation:
Measured wavelength shifts of light from the star 51-Pegasi show that
v = 53 m/s,
T = 4.15 days, and
M = 1.99 x 1030 kg.
Use Mathematica to find r, , x, and m by finding the roots of (4) directly.