Gravity on The Earth
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:
\[F = G \frac{M m}{r^2}\]
\[mg = G \frac{M m}{r^2}\]
\[g = G \frac{M m}{r^2} = 9.8 m/s^2\]
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.
FAQs on Gravity Formula
1. What is ‘G’ in gravity?
The universal gravitational constant (G) links the magnitude of the gravitational force between two bodies with their mass and the distance between them. Its value is very difficult to measure by testing.
2. Is 9.8 gravity?
On the surface of the earth, the speed of gravity is 9.8 feet (32 feet) per second. Therefore, every second, the object is in free fall, its speed rises to about 9.8 meters per second. At the top of the Moon, the speed of a free-flowing corpse is 1.6 meters per second.
3. What is the SI unit of gravity?
For SI units, this acceleration is measured in meters per second (in symbols, m/s2) or equally in newtons per kilogram (N / kg). Minimum "medium" surface area, known as normal gravitational force, by definition, is 9.80665 m/s2.
4. How do we calculate gravity?
To calculate gravity, physicists use the formula f = ma (force = mass x acceleration). Since the gravitational force is 9.8 m/s2 on Earth, i.e., a small g, we can easily calculate Newton's strength of any weight.
5. What are the three gravitational laws?
According to the first law, unless a force acts on an item, it will not modify its motion. The force on an item is equal to its mass times its acceleration, according to the second law. When two things contact, the third law states that they apply forces of equal magnitude and opposing direction to each other.
6. What is a good illustration of Newton's third law?
Everyday life is full of examples of Newton's third law of motion. When you leap, for example, your legs exert a force on the ground, and the earth responds with an equal and opposite reaction force, propelling you into the air. When developing rockets and other projectile devices, engineers use Newton's third law.
