How do people calculate gravitational acceleration?
universal law of gravitation states that every body sttract another body with a force(f) which is proportionate to the product of their masses and inversely proportionate to the square of the distance.this gives us F=GxMxm/(d)square (eq.1) where G is the constant. let the mass of the object be m.Gravitational force =g and since g =aceleration then in the formula F=ma we can write F=mg from eq .1 we can write mg =GxMxm/(d)square since the distance is equal to the radius of earth therefore g=GxM/(r)square to calculate the value of gravitational acceleration or g, we should put the value of G,M,R as G=universal gravitational constant=6.7×10 to the power -11 M=mass of earth=6×10 to the power 24 kg r=radius of earth=6.
Galileo found that the acceleration due to gravity (called “g”) depends only on the mass of the gravitating object and the distance from it. It does not depend on the mass of the object being pulled. In the absence of air drag, a huge boulder will fall at the same rate as a small marble dropped from the same height as the boulder. A tiny satellite at the same distance from the Sun as Jupiter’s orbit from the Sun feels the same acceleration from the Sun as the large planet Jupiter does from the Sun. How is this possible? Most people would agree with Aristotle that the bigger object should fall faster than the smaller object, but experiments show they would be wrong. A boulder falling toward the Earth is pulled by a stronger gravity force than the marble, since the boulder’s mass is greater than the marble, but the boulder also has greater resistance to a change in its motion because of its larger mass. The effects cancel each other out, so the boulder accelerates at the same rate as t
It is easy to verify that, if air resistence is negligable, all objects accelerate towards the earth at the same rate. This mystery, first verified experimentally by Galileo, is at least partially explained by Newton’s law of gravity. The “reason” is that the gravitational force on an object is proportional to its inertial mass. According to Newton’s second law, in order to calculate the acceleration of an object caused by gravity, we must take the gravitational force on that object and divide by the inertial mass. Thus, the inertial mass of the object cancels out of the resulting expression for the acceleration. In fact the acceleration of any object at the Earth’s surface is determined by the distance of the object form the center of the Earth (RE), Newton’s constant (G) and the mass of the Earth: g = GMe/R^2e If you put the value of Newton’s constant (G) 6.67428 x 10^-11m^3 kg^-1 s^-2 , the radius of the Earth ( 6 x 106 meters) and the mass of the Earth ( 6 x 1024kg) into the abov
