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We present the solution to problems from the worksheet "Planet Host Stars Wobble But They Don't Fall Down" (which could be found here.) The outline of this worksheet is as following. First, we are going to see how a planet affects the movement of a star. From that knowledge, we can observe this "weird" characteristic of a star to find exoplanets. In this post, we present solution to question seven and eight.
(7) One way to detect radial velocity is from the Doppler shifts of stellar absorption lines. We can relate the shift, the typical absorption line, radial velocity and light speed by,
(7) One way to detect radial velocity is from the Doppler shifts of stellar absorption lines. We can relate the shift, the typical absorption line, radial velocity and light speed by,
What if we are observing a Jupiter orbiting at 1 AU (assume a 1 solar mass star)? First, we have to find the period of this planet through the Kepler's Third Law.
Second, we find the radial velocity through,
we can substitute in to find the radial velocity,
A typical iron absorption line has a center at 550.1 nm, so we can see the shift,
(8) Now, for the case of an Earth orbiting at 1 AU. Of course, that is what an Earth is right now so we can assume the period as 1 year. Find the radial velocity.
Again, for a typical iron absorption line, the shift is
(I think your numbers are correct) those are teensy tiny shifts! even for the Jupiter, that's 0.00001 nm. And Jupiters are the *easy* ones to detect...
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