Refining Planetary Radius Calculations by Exploring the Geometry of Transit Photometry

Author(s): Pranav AR

This paper has altered what appears to be the common equation taught and used to calculate the radius of an extrasolar planet, by way of transit photometry. The standard equation is: Where, RPlanet is the radius of the planet, RStar is the radius of the star and B is the percentage of light blocked by the planet during a transit, expressed as a decimal.

Where, a is the semi-major axis of the planet’s orbit (i.e. its orbital radius) and dStar is the distance from the observer to the star. There are also two additional derivations in this manuscript, which allow for calculation of the radius using angular measurements. In previous versions of this paper, author has labelled the variables in the equation differently. This is only important for those who have read or intend to read Versions 1 and 2 of this manuscript. The additional factor in the parentheses does not always make the most significant difference, considering the fraction evaluates to nearly zero in most exoplanetary cases, but it could make a difference considering other calculations depend on an accurate radius calculation, such as volume and density, for example. This aim of this equation and of this paper is to improve astronomical calculations that make use of exoplanetary transits and transit photometry. The previous, more common equation does not take into consideration the distance of the planet from its parent star. That is what this paper seeks to fix.

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