# 801-Detection of Exoplanets - Whats going on? 51 Peg: the...

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1Detection of ExoplanetsA new era of discoveryWhat’s going on?51 Peg: the rhythmic wobble in the spectrum gave an orbital speedof 57 meters per second. The repetitive 4-day period of the star’s motion tells us the orbital periodof its planet. With a period of 4 days, this planet is really close to its star!We observe the motion of the star caused by the orbit of the planet. m1v1= m2v2Note what we can derive from measurements of Doppler velocitiesMeasuring Doppler Shiftsbig telescopes, dedicated instrumentsIn practicewe usethousandsof lines toget averyaccuratevelocity.The HIRES spectrographOne of mostproductiveplanet finders.Keck ObservatoryOptical layoutDetectorDeriving the Mass of an Extrasolar PlanetConservation of momentum gives: MstarVstar= MplanetVplanetPlanet’s mass is therefore:Mplanet= MstarVstar/ VplanetWe know the star’s mass (Mstar) from its Spectral TypeThe Doppler effect measures the star’s velocity (Vstar)But how do we get the planet’s velocity?The repetitive or periodic nature of the star’s velocity variations gives us the orbital period of the planet, PplanetNewton’s form of Kepler’s Third Law gives the planet’s orbital radius,aplanet, from the equation: a3= (GMstar/4π2)P2Therefore, Vplanet= 2πaplanet/PplanetSo, Mplanet= MstarVstarPplanet/ 2πaplanetFor 51 Peg, the mass of the planet is 9 x 1026kg = 0.5Mjupiter
2What you get from DopplerWe get orbital properties, like period and semi-major axis(average distance from star).We also get the shape or eccentricityof the orbit.A circular orbit is a regular sine wave; highly elliptical orbits looks distorted.Faster variations on top of slower variations reveal multiple planetsin different orbits. [Example later]We also get the massof the planet, but with a caveatas shown in the next slide.70 Virginis:uneven velocities imply a highly elliptical (eccentric) orbit.Discovered by Geoff Marcyand Paul Butler, UC BerkeleyEstimating the planet’s massThe Doppler shift provides the velocity directly toward or away from us, but a component of motion at right angles to our line of sight is not detected.If orbit is viewed faceon, then no Doppler Effect.If viewed edgeon, all motion is toward or away fromus, and observed velocity = total velocity.

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