3. Explain universal law of gravitation. (AS)
Answers
Answer:
Newton’s Law of Universal Gravitation states that every particle attracts every other particle in the universe with a force that is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.
The universal gravitation equation thus takes the form
F∝m1m2r2 ⇒F=Gm1m2r2
Sir Isaac Newton put forward the universal law of gravitation in 1687 and used it to explain the observed motions of the planets and moons.
In this article, let us familiarize ourselves with Newton’s law of Universal Gravitation.
Universal Gravitation Equation
Newton’s conclusion about the magnitude of gravitational forces is summarized symbolically as
F=Gm1m2r2
where,
F is the gravitational force between bodies
m1 is the mass of one of the objects
m2 is the mass of the second object
r is the distance between the centres of two objects
G is the universal gravitational constant
The constant proportionality (G) in the above equation is known as the universal gravitation constant. The precise value of G was experimentally determined by Henry Cavendish in the century after Newton’s death. The value of G is found to be G = 6.673 x 10-11 N m2/kg2.
Universal Gravitation Solved Example
Calculate the gravitational force of attraction between the Earth and a 70 kg man if he is standing at a sea level, a distance of 6.38 x 106 m from the earth’s centre.
Solution:
Given:
m1 is the mass of the Earth which is equal to 5.98 x 1024 kg
m2 is the mass of the man which is equal to 70 kg
d = 6.38 x 106 m
The value of G = 6.673 x 10-11 N m2/kg2
Now substituting the values in the Gravitational force formula, we get
F=(6.673×10−11)(5.98×1024)(70)(6.38×10−11)2=685N
F=685N
Weight and the Gravitational Force
In Newton’s law of gravity, we noticed that the mass is a crucial quantity. We consider mass and weight to be the same, but in reality, they are related but are different. Weight is the gravitational force exerted on an object of a certain mass. The weight of an object can be obtained by multiplying the mass m of the object by the acceleration due to gravity, g, at the surface of the Earth. The measured gravitational acceleration at the Earth’s surface is found to be about 980 cm/second/second.
The measure of how much material is in an object is known as mass, while weight is the measure of the gravitational force exerted on the material in a gravitational field; thus, mass and weight are proportional to each other, with the acceleration due to gravity as the proportionality constant. It is observed that the mass is constant for a given object, but the weight depends on the location of the object. To better understand, let us consider the following example, say we transported an object of mass m to the surface of Neptune, the gravitational acceleration would change because the radius and mass of the Neptune both differ from those of the Earth. Thus, our object has mass m both on the surface of the Earth and on the surface of the Neptune, but it will weigh much more on the surface of Neptune because the gravitational acceleration there is 11.15 m/s2.
Universality of Gravity
Gravitation interactions not only exist between the earth and other objects, but it also exists between all objects with an intensity that is directly proportional to the product of their masses. The law of universal gravitation helps scientists study planetary orbits. The small perturbations in a planet’s elliptical motion can be easily explained owing to the fact that all objects exert gravitational influences on each other.
Why doesn’t’ the moon crash into the earth?
The forces of speed and gravity are what keeps the moon in constant orbit around the earth. The Moon seems to hover around in the sky, unaffected by gravity. However, the reason the Moon stays in orbit is precise because of gravity. In this video, clearly, understand why the moon doesn’t fall into the earth
Is the force of Gravity the same all over the Earth?
Gravity isn’t the same everywhere on earth. Gravity is slightly stronger over the places with more underground mass than places with less mass. NASA uses two spacecraft to measure the variation in the Earth’s gravity. These spacecraft are a part of the Gravity Recovery and Climate Experiment (GRACE) mission