Gravity is very important to us. It’s impossible to live on Earth without gravity. The gravitational force of the sun keeps the Earth in orbit around it, keeping us far away from the sun and heat. It holds our atmosphere and the air we need to breathe. Gravity is what holds our earth together.
On Earth, gravity varies from place to place. Gravity is slightly stronger in overweight areas than underweight. NASA uses two spacecraft to measure these differences in Earth’s gravitational pull. These spacecraft are part of the Land Reform and Climate Change (GRACE) campaign.
Formula of Gravity
Gravity or Gravitation is a phenomenon which gives an idea about the existence of a force between any two objects having some mass. The force due to gravity is always attractive.
Law of Gravity states that if two masses, m1 and m2, are kept at a distance of r from each other, then force due to gravity is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
If ‘F’ is the force due to gravity, then mathematically,
[F] [alpha] [m_1 m_2] and [F] [alpha] [frac{1}{r^2}]
Therefore, [F] [alpha] [frac{m_1 m_2}{r^2}]
Where G = Gravitational constant = 6.673 x 10-11 N-m2/Kg2 (or) m3/Kg-s2. On Earth, the force due to gravity between Earth and an object on Earth can also be related to the same formula.
Let mass of the Earth is M and mass of the object is m and radius of earth is r. So, force due to gravity on an object on Earth’s surface is the force between both the masses is given by:
[F = G frac{M m}{r^2}]
[mg = G frac{M m}{r^2}]
The Importance of Gravity
The law of gravity applies to almost everything in the universe. Any two objects pull together like any other two galaxies. In addition, the attractions are small, even zero sometimes, when the distance is large enough.
You can find your value in the way all the stories come together. For example, you may have seen astronauts floating in space. That is because of the lack of gravity in the atmosphere. Therefore, you see that you can walk the earth because of the force of gravity.
Example: An object of mass 40 Kg experiences a force of 200N towards the center of a planet from a distance of 20Km. Find the mass of the planet.
Solution: Let mass of the planet = M, Mass of the object (m) = 40Kg, Distance between both the masses (r) = 20000m, Force due to gravity (F) = 200N.
Therefore, [F = G frac{M m}{r^2}]
[200 = 6.673 times 10^{-11} times frac{M times 40}{(20000)^2} ]
M = 2.997 x 1019 Kg
Mass of the planet is 2.997 x 1019 Kg
Question: Force between mass of two objects is 40N. If one of their masses is 2 kg and the distance between them is 1m, find the mass of the other object.
Solution:
[F = G frac{M m}{r^2}]
[40 = 6.673 times 10^{-11} times frac{M times 2}{1} ]
m = 2.99 x 1011 Kg.
Question: Find the magnitude of the gravitational force between the earth and a 1 kg object on its surface.
Solution: From Newton’s law of gravitation, we know that the force of attraction between the bodies is given by [F = G frac{m_1 m_2}{r^2}]
m1 = 6.4 x 106
m2 = 1 kg
r = 6.4 x 106
From the above equation,
[F = frac{6.4 times 10^{11} (6.4 times 10^{24}) times 1}{ (6.4 times 10^{6})^2} = 9.8 N]
Hence, earth exerts force 9.8 N on a body of mass of 1 Kg.