Lectures 2 and 3 1. Kepler’s three laws 2. Use parallax, spectroscopic parallax, and the distance modulus to calculate distances to planetary systems 3. Use radial velocity and transit timing methods to understand exoplanetary conditions, and use surface temperature to determine exoplanet habitability, questions / answers, categorization activity to organize topics on the exam

H I, H II, [and H 2] regions H I-region of unionized hydrogen H II-region of ionized hydrogen [H 2 -molecular hydrogen or molecular clouds]

Kepler’s Laws 1.The orbit of a planet is an ellipse with the Sun at one of the two foci. 2.A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. 3.The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

Parallax and Spectroscopic Parallax A difference in the apparent position of an object viewed along two different lines of sight. Example link.Example link. Parallax arises due to a change in the perspective on an object due to the motion of the observer, of the observed, or of both. What is essential is relative motion. By observing parallax, measuring angles, and using geometry, one can determine the distance to stars. Spectroscopic parallax does not rely on distance measurements, but is a technique applicable to main-sequence stars for which a spectrum can be recorded.

Parallax p = parallax angle in arcseconds d = Distance in Parsecs

Spectroscopic Parallax OR Distance Modulus Apparent magnitude (m) and absolute magnitude (M) of the star. Distance (d, in parsecs) of the star.

Radial Velocity and Timing Methods Radial velocity is the detection of variation in the velocity of a star due to the changing direction of the gravitational pull from an (unseen) exoplanet as it orbits the star. Example Link.Example Link. When the star moves towards us the spectrum is blueshifted, while it is redshifted when it moves away from us.

Planet Habitability To determine the surface temperature of a distant exoplanet, first determine the effective temperature of a star, then calculate the power the planet would receive from this star.