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Mandasphuta In Hinduism – Longitude Of Planets

The true longitude of planets in the heliocentric system is known as Mandasphuta in Hinduism. All the calculations of planetary longitudes in the geocentric system required for Panchangam (in Hindu astrology) are initially calculated for by heliocentric method, which in effect is calculation on the assumption of mean uniform velocities of the planets in perfectly circular orbits.

To know the place of a planet in the heliocentric method, three coordinates are required and some astronomical corrections are utilized. In the calculation for the sun, the mean longitude is determined by using ahargana for the day under consideration, and the longitude at the epoch day, as against the time at which it is required.

The heliocentric longitude of the sun is that of the Earth, and if the mean distance of the sun to the Earth is known it can be calculated. This is based on the assumption of a circular orbit. In reality all the planets move in elliptical orbits and thus the parameters of the ellipse, i.e the major axis, longitude or perihelion, initial line and ellipticity are required.

In the complete cycle of a planet, it once crosses the aphelion, perihelion, nodal points and the equinoctial points. The entire system is also dynamic, i.e. slowly moving. The timing of the cycle of the orbiting planets is found out, as on the equator the determination changes the sign, and on the node, changes the sign of latitudes and so on. The anomaly calculations are based on mean and true positions of planets. From initial calculation of mean longitudes, true longitudes are determined with the knowledge of orbit elements (eccentricity, longitudes of a-p points, and the radius vectors and angle of orbit to the elliptic).

The true longitudes of planets with the sun at the center are called mandasphuta. The calculations for the moon are complex and the numbers of corrections are also more.