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## Physics library

### Course: Physics library>Unit 4

Lesson 3: Newton's law of gravitation

# Gravitation (part 2)

A little bit more on gravity. Created by Sal Khan.

## Want to join the conversation?

• well moon is smaller but its gravity isnt double much less more than earth's gravity.why?i dont understand.
also what is the comparison between the two the planets? is it of same density but more compressed to get half the radius? • Gravitational acceleration at the surface of a body is:
a = GM/R^2
assuming a uniform density ρ and spherical body, the mass will be
M = ρV = ρ * 4/3πR^3
substitute that M into the acceleration equation...
a = G/R^2 * ρ * 4/3πR^3
a = 4/3GρπR
so the gravitational acceleration at the surface increases linearly with the radius of the body.
• gravitational field is the same as gravitational acceleration? if no, why its symbol is g?
why is g=a ? accelaration is the variation of the velocity in a certain time, so the earth moves if someone, for example, falls from a building. please someont to explain, i am really confused • Surely you've noticed that when you "convert" a mass to a weight (on earth) you use 9.8 N/kg, and you also know that the acceleration due to gravity on earth is 9.8 m/s^2. Is it coincidence that they are both 9.8? Nope.

g stands for gravitational field strength AND acceleration due to gravity. They are the same thing. Let's calculate the acceleration of something if we drop it. The force on it is mg. Newton's second law tells us F = ma.
So
mg = ma
m cancels out
g = a
So the acceleration will be exactly equal to the gravitational field strength, and mass does not matter.
This is why everything falls with the same acceleration (if we can neglect air resistance)
Now let's look at the units.
Gravitational field strength has units of Newtons/kg. That's why the force on a 10 kg mass is 98 N, because (9.8 N/kg)*10 kg = 98 N.
The units of acceleration of course are m/s^2. So how can g be BOTH gravitation field strength AND acceleration due to gravity? Let's look more closely at the units:
A newton is a kg*m/s^2
gravitational field strength is in N/kg
So g = 9.8 N/kg = (9.8 kg*m/s^2)/kg = 9.8 m/s^2
In other words, N/kg is the same thing as m/s^2.
• Why we call G as universal gravitational constant if it is derived by taking only earth's mass and acceleration due to gravity on earth 'g'.and distance between center of masses of masses of earth and object.If we have taken everything of earth here then why it is universal?
as we know Fg=(Gm1.m2)/r^2
then we find out G's value as G=(Fg.r^2)/(m1.m2).
here Fg is gravitational force on earth,r is distance between object having mass m1 on earth's surface and center of mass of earth having mass m2. • i didn't get the concept of higher gravitational attraction of a smaller planet than earths(ok,if its the radius adjusting itself with the masses),then how come moons gravity less than that of earths?
(1 vote) • It's not about size but about mass. In short: The heavier the object, the greater its gravity. Black holes, for example, are reeeally small (compared to the rest of the universe) but incredibly dense and thus incredibly heavy. This is what causes them to attract everything that comes too close to it - even light - and never let it go. So, if there's a planet that is smaller but heavier than Earth, its gravitational force will be stronger. And the moon's gravity is less than the Earth's because it is much lighter, as Andrew already said.
• If. The earth suddenly stopped in its orbit assumed to be circular how long it might take before it falls into the sun
(1 vote) • so.....now let's say a body is moving with uniform acceleration in space.......
this means that since there is no friction in space it keeps accelerating and eventually reach the speed of light and probably travel faster that light........
so.......can there be objects that are faster than light? • If G is there to cancel the units, why int it then just a whole number like 1?
(1 vote) • If a smaller planet has a larger gravitation, how does the moon has a smaller gravitational force than Earth?   