Newton's law of universal gravitation
Newton was able to derive an important conclusion about the dependence of gravity on distance by believing that gravitational forces were responsible for each. Isaac Newton measured the acceleration of the moon in comparison to the acceleration of things on Earth. He concluded that the gravitational pull between the Earth and other things is inversely proportional to the distance between the Earth's centre and the object's centre based on this comparison. Furthermore, distance isn't the only factor that influences the amplitude of gravitational forces.
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Newton's law of gravitation formula
Newton's universal gravitational law extends gravity beyond the earth. Universal gravity is the subject of Newton's law of universal gravitation. Newton's induction into the Gravity Hall of Fame is based on his finding that gravitation is universal, rather than his discovery of gravity. The gravitational attraction force is a force that attracts all things. Gravity is a ubiquitous phenomenon. This gravitational pull is proportional to the square of the distance between their centres and is directly proportional to the masses of both objects. The magnitude of gravitational forces is symbolically described by Newton's conclusion.
\[F\alpha \frac{m_{1}\times m_{2}}{r^{2}}\]
The universal gravitational constant formula is given by,
\[G=6.67\times 10^{-11}\frac{N.m^{2}}{kg^{2}}\]
Hence by using the gravitational we get the universal law of gravitation formula,
\[F= \frac{Gm_{1} m_{2}}{r^{2}}\]
Where,
F = force of gravity between two objects.
m1 = Mass of object 1
m2 = Mass of object 2
r2 = Distance separating the objects
G = Gravitational constant
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Dimensional formula for universal gravitational constant
The dimensional formula for universal gravitational constant is,
G = M-1L3T-2
Where,
M = Mass
L = Length
T = Time
Solved Examples
Ex.1. Suppose two satellites that orbit the earth pass close to each other. Also, for a moment they are 150 m apart. However, the first body mass of the satellites is 200 kg and the second body mass of the satellites is100 kg. So, calculate the magnitude of the force of gravity between these satellites by using the universal law of gravitation formula?
Solution:
Given,
m1 = 200 kg
m2 = 100 kg
r = 150 m
G = 6.6710-11 Nm2/kg2
By using the formula of gravity force we get,
\[F= \frac{Gm_{1} m_{2}}{r^{2}}\]
\[F=\frac{6.67\times 10^{-7}\times 200\times 100}{150^{2}}\]
\[F=\frac{1.334\times 10^{-6}}{22500}\]
F = 5.928810-11Nm2/kg2
Ex.2. What will be the force of gravity in between two balls of mass 5 kg and 8 kg separated by 4m distance?
Solution:
Given,
m1 = 5 kg
m2 = 8 kg
r = 4 m
G = 6.6710-11 Nm2/kg2
By using the formula of gravity force we get,
\[F= \frac{Gm_{1} m_{2}}{r^{2}}\]
\[F=\frac{6.67\times 10^{-11}\times 5\times 8}{4^{2}}\]
\[F=\frac{266.8\times 10^{-11}}{16}\]
F = 16.67510-11Nm2/kg2
Ex.3. The mass of the sun is 1.991030kg and the mass of the earth is 5.971024 kg separated by a distance 1.51011m. Calculate the gravitational force by using newton's law of universal gravitation formula.
Solution:
Given,
m1 = 1.991030kg
m2 = 5.971024 kg
r = 1.51011m
G = 6.6710-11 Nm2/kg2
By using the formula of gravity force we get,
\[F= \frac{Gm_{1} m_{2}}{r^{2}}\]
\[F=\frac{6.67\times10^{-11}\times1.99\times10^{30}\times5.97\times10^{24}}{(1.5\times 10^{11})^{2}}\]
\[F=\frac{79.2416\times 10^{43}}{22.5\times 10^{22}}\]
F = 3.52181022Nm2/kg2
FAQs on Universal gravitation formula
1. What is the law of gravitation formula?
Every object in the cosmos (universe) attracts every other body with a force that is proportional to their mass and inversely proportional to the square of their distance.
The formula of universal law of gravitation is given by,
\[F= \frac{Gm_{1} m_{2}}{r^{2}}\]
2. What is a force of gravity?
The acceleration that gravity gives to freely falling objects is used to measure gravity. The acceleration of gravity at the Earth's surface is about 9.8 metres per second. As a result, an object's speed increases by about 9.8 m/s for every second it is in free fall.
3. What is the force of gravity on the moon?
The Moon's surface gravity is about 1.6 m/s2.
