# Why objects of different masses accelerate at the same speed under gravity [closed]

If you push massive object it accelerates slowly compared to object which is of same size but less density/mass.

However, all objects do Accelerate at the same rate.

F=ma....according to this if gravity is a force than spherical ball made of cotton shouldn't also accelerate toward earth with acceleration of 9.8 m/s2 just as the ball made of steel would also do at the same acceleration.

But they both do. All i can think of is that force experienced by object increases or decreases linearly according to the mass an object has, is that true. Force object experiences changes according to its mass..

I guess the whole confusion could be that if gravity wasn't called a force, in my mind force is something that has magnitude which is same regardless of the mass of object it's touching. Word forcefield would make more sense even though i won't have any idea what does that really mean.

• Gravity can be thought of as acceleration (approximately). Dec 18, 2013 at 20:49
• Gravity exerts more force on more massive objects, so all objects accelerate at the same rate. Dec 18, 2013 at 20:51
• I don't understand the question as currently phrased, but it occurs to me that if you're trying to ask "why isn't gravity an inertial force?" (aka 'fictitious force', as centrifugal force also is), then it actually is... in the modern theory of gravity, the general theory of relativity. That it isn't in the Newtonian framework could be considered a defect of Newtonian physics. Dec 20, 2013 at 4:37
• hold on ill rewrite the question later... Dec 20, 2013 at 18:10
• i edited the question please reopen it thanks, it was pretty chaotic for someone who couldn't read my mind :D Dec 21, 2013 at 16:55

By Newton's Universal Law of Gravitation, the force between two object due to gravity

$F = \dfrac{GMm}{r^2}$

where $M$ and $m$ are the masses of the two bodies attracting each other. Let's say $M$ is the mass of the earth and $m$ of the object we're dropping.

Using $F = ma = \dfrac{GMm}{r^2}$

We can rearrange to find $a = \dfrac{GM}{r^2}$, independent of the mass of the object.

Thus all object accelerate at the same rate under gravity alone.

• thanks for answering...this equation specifically defines the force in terms of gravity right..G has to be some gravitational or similar field...you do get what i am trying to say that why gravity changes forces based on the mass of object. Dec 18, 2013 at 21:08
• @MuhammadUmer: if you like, $G$ (or $\sqrt{G}$) is a factor of conversion between inertial mass and gravitational charge. We could set it to anything by changing the system of units (just as Coulomb's law $F = kQq/r^2$ has $k=1$ in Gaussian units and $k=1/(4\pi\epsilon_0)$ in SI units). Dec 18, 2013 at 21:45
• Or, to just put Stan's point another way: $G$ is a universal constant, the same anywhere in the universe for any object, any mass, any speed, any conditions. Period. (not to be confused with $g$, acceleration of free-fall on earth) Dec 18, 2013 at 23:45
• i get that this equation is for gravitational force between any two masses and their distance. But i want to know that sort of why this equation is valid. Why M is the only factor determining the acceleration. Where does inertia go...is it right that then force experienced by object is dependent on small m. If a is contsant for all m then F= xa. So F is depended on x only like for same M distance etc. Dec 19, 2013 at 22:25
• @MuhammadUmer: I don't understand what you mean by asking "where does inertia go"--the mass measures inertia, so it's right there in the formula. The equivalence/proportionality of inertial mass and gravitational charge is an empirical fact that Newton's law encodes. It can be derived from something deeper, e.g., general theory of relativity, but then GTR was constructed so as to obey that equivalence. Also, in GTR, gravitational force is an inertial force, so your accusation of "not follow[ing] the rules of inertia" make even less sense there. Please rewrite your question to make it clearer. Dec 20, 2013 at 4:22

A little reflection will show that the law of the equality of the inertial and gravitational mass is equivalent to the assertion that the acceleration imparted to a body by a gravitational field is independent of the nature of the body. For Newton's equation of motion in a gravitational field, written out in full, it is:

(Inertial mass) * (Acceleration) = (Intensity of the gravitational field) * (Gravitational mass).


It is only when there is numerical equality between the inertial and gravitational mass that the acceleration is independent of the nature of the body.

— Albert Einstein