The Force of Sun's Gravity on Planets calculator uses the force of gravity equation to compute the gravitational force between the sun and your selection of a planet.
INSTRUCTIONS:
Force of the Sun's Gravity (F): The calculator returns the force in newtons.
The Force of Gravity equation computes the gravitational force between the two masses: the Sun and the planet or other body from our solar system. In this equation, the masses are treated as point masses separated by a specified distance.
The Universal Gravitational Constant is 6.67384E11 m^{3} / kg * sec^{2}. Force of Gravity
Newton's law of universal gravitation states that any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. (Separately it was shown that large spherically symmetrical masses attract and are attracted as if all their mass were concentrated at their centers.) This is a general physical law derived from empirical observations by what Isaac Newton called induction. It is a part of classical mechanics and was formulated in Newton's work Philosophiæ Naturalis Principia Mathematica ("the Principia"), first published on 5 July 1687. (When Newton's book was presented in 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him) In modern language, the law states the following:
where:

Assuming SI units, F is measured in newtons (N), the mass of the Sun and a planet in kilograms (kg), r in meters (m), and the constant G is approximately equal to 6.674×10^{−11} N m^{2} kg^{−2}. However, vCalc enables the user enter units in any of the applicable mass units (see pulldown list). The value of the constant G was first accurately determined from the results of the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798, although Cavendish did not himself calculate a numerical value for G. This experiment was also the first test of Newton's theory of gravitation between masses in the laboratory. It took place 111 years after the publication of Newton's Principia and 71 years after Newton's death, so none of Newton's calculations could use the value of G; instead he could only calculate a force relative to another force.
Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of electrical force between two charged bodies. Both are inversesquare laws, in which force is inversely proportional to the square of the distance between the bodies. Coulomb's law has the product of two charges in place of the product of the masses, and the electrostatic constant in place of the gravitational constant.
Newton's law has since been superseded by Einstein's theory of general relativity, but it continues to be used as an excellent approximation of the effects of gravity. Relativity is required only when there is a need for extreme precision, or when dealing with very strong gravitational fields, such as those found near extremely massive and dense objects, or at very close distances (such as Mercury's orbit around the sun).
Main article: Newton's law of universal gravitation Sir Isaac Newton, an English physicist who lived from 1642 to 1727
In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inversesquare law of universal gravitation. In his own words, "I deduced that the forces which keep the planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the Earth; and found them answer pretty nearly."^{[3]}
Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted for by the actions of the other planets. Calculations by both John Couch Adams and Urbain Le Verrier predicted the general position of the planet, and Le Verrier's calculations are what led Johann Gottfried Galle to the discovery of Neptune.
A discrepancy in Mercury's orbit pointed out flaws in Newton's theory. By the end of the 19th century, it was known that its orbit showed slight perturbations that could not be accounted for entirely under Newton's theory, but all searches for another perturbing body (such as a planet orbiting the Sun even closer than Mercury) had been fruitless. The issue was resolved in 1915 by Albert Einstein's new theory of general relativity, which accounted for the small discrepancy in Mercury's orbit.
Although Newton's theory has been superseded, most modern nonrelativistic gravitational calculations are still made using Newton's theory because it is a much simpler theory to work with than general relativity, and gives sufficiently accurate results for most applications involving sufficiently small masses, speeds and energies.