Why the velocities of falling bodies are not proportional to their weights?
Not necessarily. Two bodies co-orbiting can have different velocities depending on their mass and distance from the central body. The velocities of the bodies would be determined by the balance between gravitational force and centripetal force.
free falling bodies
Sir Isaac Newton and Galileo both studied the effects of gravity on falling bodies.
weights
No, the force between two bodies is not always inversely proportional to their masses. The force of gravity between two objects is actually directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
No, certainly not for the gravitational force.
Galileo (1564-1642) was the first to determine, at the start of the seventeenth century, the law of constant acceleration of free-falling bodies. The law states that the distances traveled are proportional to the squares of the elapsed times. In other words, in equal successive periods of time, the distances traveled by a free-falling body are proportional to the succession of odd numbers (1, 3, 5, 7, etc.).
gravitational force - (physics) the force of attraction between all masses in the universe; especially the attraction of the earth's mass for bodies near its surface; "the more remote the body the less the gravity"; "the gravitation between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them"; "gravitation cannot be held responsible for people falling in love"--Albert Einstein
It means that more massive objects will not fall faster than less massive objects after falling for a given period of time. This conclusion has been credited to Galileo who supposedly dropped different weights from the Tower of Pisa to demonstrate it (see link). The acceleration of a body will be proportional to its weight (it will be equal to its weight divided by its mass). I suspect you mean that, for example, a feather and a bullet will be falling to earth at the same speed at a given time if dropped from the same height. That is to say that a body will accelerate when falling independent of its mass (ignoring factors such as air resistance). You can think of this as being due to gravity interacting with mass linearly: if you double the mass of an object then the force exerted by gravity on the object will also double. Note that you mean 'mass' (Kilograms) and not weight (Newtons). In simple equations (under classic Newtonian principles etc etc): The force exerted on an object: F=mg The force exerted on an object that is accelerating: F=ma Thus mg=ma Thus a=g where m=mass (kg), g=gravitational field strength (~9.8ms^-2 at the surface of Earth), a=acceleration (ms^-2) So we can see that the acceleration and hence velocity of a falling object is not effected by mass.
The law of applied for states that bodies change in mass and proportional to the amount of force applied to it is false.
The force of attraction or repulsion between two charged bodies is directly proportional to the magnitude of the charges on the bodies. It is also inversely proportional to the square of the distance between the bodies. As the charges increase, the force of attraction or repulsion increases, while increasing the distance decreases the force.
Orbital velocities of celestial bodies are the speeds at which they move around a central object, like a star or planet. These velocities are determined by the gravitational force between the objects and are necessary for maintaining stable orbits. The orbital velocity of a celestial body depends on its distance from the central object and the mass of the central object.