lecture-10

lecture-10 - These lecture notes were prepared for Rutgers...

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Unformatted text preview: These lecture notes were prepared for Rutgers Physics 341/342: Principles of Astrophysics by Prof. Chuck Keeton, and modified by Profs. Saurabh Jha and Eric Gawiser. All rights reserved. c 2011 Lecture 10: Extrasolar Planets A star+planet system is a binary system, but what kind? Visual binary? No, the planet is way too faint, and the astrometric wobble of the star is very difficult to measure. Two-line spectroscopic binary? No, again because the planet is too faint. One-line spectroscopic binary? Yes! The planet causes the star to wobble. Eclipsing binary? Maybe! The wobble is small the wobble of the Sun induced by Jupiter is just 12.5 m/s (see lecture 7) so it is hard to measure. In fact, only in 1995 did measurements become sensitive enough to measure star wobbles due to extrasolar planets. But with very careful and patient observations it is now possible to measure such small wobbles. A small fraction of extrasolar planet systems are close enough to edge-on that the planet eclipses the star. The dimming is very small, and was not measurable until 2000. Neverthe- less, these so-called transiting planets are exceedingly important, as we shall see. I. Doppler Planets This term is often applied to planets that are discovered by observations that use the Doppler effect to measure the wobble of a star that has a planet. Again, we can think of this as a one-line spectroscopic binary. As we saw above, if the planet is much less massive than the star then we can estimate its mass by m 2 sin i = m 2 1 P 2 G 1 / 3 K 1 where K 1 is the measured radial velocity amplitude of the star and P the measured period. This formula applies to a circular orbit; a similar formula would hold for an elliptical orbit, but there would be an additional factor that depends on the eccentricity. Note that we need to know m 1 , the mass of the star. This is usually inferred from the stars properties. 1 For example, the luminosity is related to the mass, as we saw in Lecture 9. Also, there is a good relation between mass and spectroscopic properties (the color and the collection of absorption lines). The first extrasolar planet discovered orbits the star 51 Peg. 1 The velocity curve is shown in Figure 1. The curve is nicely sinusoidal, indicating a circular orbit. The numbers are as follows: P = 4 . 230 day = 365 , 470 s K 1 = 54 . 9 m s- 1 = 5490 cm s- 1 m 1 = 1 . 06 M m 2 sin i = (1 . 06 1 . 99 10 33 g) 2 (365 , 470 s) 2 6 . 67 10- 8 cm 3 g- 1 s- 2 1 / 3 5490 cm s- 1 = 8 . 62 10 29 g = 0 . 45 M J also a 3 = G ( m 1 + m 2 ) 4 2 P 2 Gm 1 4 2 P 2 a = m 1 GP 2 4 2 1 /...
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This note was uploaded on 10/20/2011 for the course PH 341 taught by Professor Gawiser during the Fall '11 term at Rutgers.

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lecture-10 - These lecture notes were prepared for Rutgers...

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