![]() With the assumption of a circular orbit, the distance around an entire orbit is, where a is the radius of the orbit. 3: The orbital geometry of a transiting exoplanet system showing the projected distance travelled across the surface of the star,, between the points to and the angle this geometry forms, with the inclination,, and semi major axis,, shown. 3, the exoplanet moves from to around its orbit, creating an angle (measured in radians) with respect to the centre of the host star.įig. 2: Star-planet geometry showing the distance traversed by the planet,, impact parameter of the system, and the stellar and planetary radii, and respectively. 2 and using Pythagoras’s theorem, the length the planet has to travel across the disk of the star can be expressed as,įig. If the exoplanet crosses the centre of the stellar disc ( ), the transit duration is the longest with signifying a shorter transit duration. The total transit duration,, defined as the time during which any part of the planet obscures the disc of the star, depends on how the planet transits the host star. 1: The impact parameter varies from centre of stellar disk with being on the cusp of the disc. Assuming a circular orbit the impact parameter is expressed as:įig. The total transit duration is heavily dependent on the impact parameter, which is defined as the sky-projected distance between the centre of the stellar disc and the centre of the planetary disc at conjunction* and is shown in Fig. As described below, limb-darkening will have an affect on the transit light curve, but to first order, the equation above holds. Where and are the planetary and stellar radii respectively. To first order (assuming the stellar disc is of uniform brightness, and neglecting any flux from the planet) the ratio of the observed change in flux,, to that of the stellar flux can be expressed as: ![]() The transit method is particularly useful for calculating the radius of an exoplanet. The orbital distance between the exoplanet and its host star does not affect the transit depth due to the enormous distance from Earth. Both the size of the host star and the planet will determine the decrease in flux during the transit. Fitting models to the light curve, various characteristics such as orbital motions and atmospheric composition can be extracted. Measuring the change in flux over time, allows for the creation of a light curve. When exoplanets pass in front of their host star (as seen from Earth), a portion of the start light is blocked out and a decrease in the photon flux is measured.
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