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### Course: Physics library>Unit 4

Lesson 3: Newton's law of gravitation

# Introduction to Newton's law of gravitation

Gravity is a force of mutual attraction between two objects that both have mass or energy. Newton's universal law of gravitation can be used to approximate the strength of gravitation forces between two objects as a function of the objects' masses and the distance between them. Created by Sal Khan.

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• Actually andrew sir there is a problem which i want to discuss with you sir because one of my collegue said to me that gravity of earth is directly proportional to the radius he further says to me
that he prove it by his geophysics fellow but my thinking is that gravity is inversly proportional to the radius kindly sir help me from this issue or give me a valid example i am very thankful to you if you help me.
• The gravitational force is F=G*m*M/d^2 (look at the video at )
But the mass M of a planet is its density [rho] times its volume and the volume V=4/3pi d^3 (I took the volume of a sphere). So if you plug this into the equation for force you get F=4/3 pi*G*m*[rho]*d
So in this representation the gravity of a planet is indeed proportional to its radius.
• Why would G not be constant everywhere in the universe? Would it be because the density of matter is different in different parts of space?
• G is the universal constant for the gravitational force. It never changes. The units for G are m^3/(kg*s^2)

g is the local acceleration due to gravity between 2 objects. The unit for g is m/s^2 an acceleration.

The 9.8 m/s^2 is the acceleration of an object due to gravity at sea level on earth. You get this value from the Law of Universal Gravitation.
Force = m*a = G(M*m)/r^2

Here you use the radius of the earth for r, the distance to sea level from the center of the earth, and M is the mass of the earth. Notice that little m cancels out on both sides of the equation.
m*a=G(M*m)/r^2

a=G*M/r^2

If you put in the mass of the earth and the radius to sea level you will get 9.8 m/s^2 for a. This is what we call little g.

Notice if you change your radius that the acceleration(g) will fall off as 1/r^2. If you are twice as far out 2*r, you will have 4 times less gravitational acceleration.

That is why g can change from place to place on earth. If you are on Mt. Everest your radius will be larger than if you were in Death Valley.. for example.

If you want to know how G came about, read on the "Cavendish experiment"

Hope that clears it up.
• What is the difference between g and G.?? Except the difference in values
• g = 9.8 m/s^2 (acceleration on Earth) whereas G = 6.67430(15)×10^-11 m^3⋅kg^–1⋅s^–2. Hope this helps!
(1 vote)
• I've read that the acceleration due to gravity in the center of the earth is zero. I believe this is b'cos the mass beneath the body at the center of the earth is practically nothing; and so the force experienced downward is zero (so acceleration is zero). But, in that case, the mass above the body should be huge, and the gravitational force should be acting upward from the center of mass of the body. Hence, the body should be attracted upward, shouldn't it?
(1 vote)
• If you are at the center of a sphere of mass, there is equal amounts of mass in all directions around you. This means that the gravitational pull of that mass is also equal in all directions which results in zero net gravitational force since all the forces have a component which is equal and opposite.
• how was the formula derived in the first place?
• What is the value of G (gravitational constant) ?
• G ≈ (6.7±0.6)×10−11 m3⋅kg–1⋅s−2
(1 vote)
• in which cases G is not constant? which sal said at .
• As far as we know, G is constant everywhere, but we don't know that to be true for certain. g = GM/r^2, so it varies depending on the mass and radius of a planet.
• If small earth has 1/2 mass of Earth, then what would be its density?
• what is the difference between the big G and the small g
(1 vote)
• They are not the same thing at all.
G is the universal gravitational constant. It's the constant in the equation F = GMm/r^2.
It's value is 6.67E-11 N*m^2/kg^2. Note the units.

g is the acceleration due to gravity, which on the surface of the earth is 9.8 m/s^2. See how these units are nothing like the other ones?

On the surface of earth, the force of gravity is m*g, and it is also GMm/r^2, so if we set those two things equal to each other we find that g = GM/r^2 where M is mass of earth and r is radius of earth.