Weighing the Sun with five photographs

Abstract

With only five photographs of the Sun at different dates we show that the mass of Sun can be calculated by using a telescope, a camera, and the Kepler's third law. With these photographs we are able to calculate the distance between Sun and Earth at different dates in a period of time of about three months. These distances allow us to obtain the correct elliptical orbit of Earth, proving the Kepler's first law. The analysis of the data extracted from photographs is performed by using an analytical optimization approach that allow us to find the parameters of the elliptical orbit. Also, it is shown that the five data points fit an ellipse using an geometrical scheme. The obtained parameters are in very good agreement with the ones for Earth's orbit, allowing us to foresee the future positions of Earth along its trajectory. The parameters for the orbit are used to calculate the Sun's mass by applying the Kepler's third law and Newton's law for gravitation. This method gives a result wich is in excellent agreement with the correct value for the Sun's mass. Thus, in a span of time of about three months, any student is capable to calculate the mass of the sun with only five photographs, a telescope and a camera.