# Q & A: Heavy and Light - Both Fall the Same

Q:
Why do heavy and light objects fall at the same speed?
- Anonymous
A:
How fast something falls due to gravity is determined by a number known as the "acceleration of gravity", which is 9.81 m/s^2 at the surface of our Earth. Basically this means that in one second, any object's downward velocity will increase by 9.81 m/s because of gravity. This is just the way gravity works - it accelerates everything at exactly the same rate.

What you may be getting confused by is the fact that the force of gravity is stronger on heavier objects than lighter ones. Another way of thinking of this is to say that gravity has to pull harder on a heavy object than a light one in order to speed them both up by the same amount.

However, in the real world, we have things like air resistance, which is why sometimes heavy things do fall faster. For example, if you drop a feather and you drop a rock, the rock will land first since the feather is slowed down more by the air. If you did the same thing somewhere where there is no air, the feather and the rock would land at exactly the same time.

-Tamara

p.s. Although Galileo noticed that different things fall at the same rate, there was really no explanation of why until General Relativity was developed. If you would like us to try to say something about how that explanation works, we could make an attempt. mike w

(published on 10/22/2007)

## Follow-Up #1: Why fixed gravitational acceleration?

Q:
So the force of gravity pulls harder on heavier objects, and it pulls every object no matter what the mass (neglecting air resistance) toward the Earth with enough force to have it accelerate 9.81 m/s/s. But what i don't understand is how this force changes. Like how does gravity "know" how hard it needs to pull the object to make it go 9.81 m/s/s faster. And also, why does Earth have gravity and other objects do not?
- Will (age 18)
A:
Let me take your second question first. It's not true that other objects lack gravity. According to  Newton's theory of universal gravitation (published in 1687) absolutely every object exerts a gravitational pull on every other object. The Earth's gravity is most noticeable around here because the Earth is big. Smaller objects have smaller effects. The first direct measurement of the gravitational force between two small objects in a lab was published by Cavendish in 1798.

Now we get to the trickier issue- why the gravitational acceleration depends only on the position of an object, not on its size or what it's made of. Although this was described by Galileo in about 1590, it wasn't explained until Einstein developed general relativity in 1916. Gravity is most accurately described not as a force but as a warping of the spacetime within which all things move. Each object at a particular place and time sees the same warped spacetime. If you try to describe the motion as if it were occurring in Newton's flat spacetime, as we like to do, you get the same acceleration for any slow-moving objects, because that acceleration really just is a measure of the same spacetime curvature.

Mike W.

(published on 01/03/2013)

## Follow-Up #2: curving spacetime

Q:
Let's say e=mc^2. That would mean that the more mass i have, the more energy i have. Since spacetime is bent by energy, i can bend spacetime more than a feather and therefore i should be able to accelerate faster to earth. Why is that wrong?
- Smith (age 13)
NY
A:
This is the relativistic version of a classical question which we just got around to. (see other follow-ups)

The collision of you and the earth mainly comes from the big spacetime warping due to the earth, not the little warping due to you. However, you do a little warping yourself, and that does show up in the earth's trajectory. The feather does less. So, as you say, even ignoring air friction you and the earth would collide just barely sooner than a feather and the earth, if dropped from the same height.

Mike W.

(published on 01/30/2013)

## Follow-Up #3: Earth falling toward you

Q:
If you define "falling" as "the closing rate between two objects freely accelerating toward each other", assume everything is done in a perfect vacuum, then when comparing dissimilarly-weighted objects A and B and their closure rate toward the Earth, won't the heavier object actually fall faster? The acceleration imparted on objects A and B by the Earth is constant, close to 9.8m/s/s. But A and B themselves also impart acceleration on the Earth--minusculely so, but nonetheless so. If you now learn that A is a marble, and B is a marble with our sun compressed inside of it, will B *still* "fall toward the Earth" at the same rate as A?
- Erik E (age 40)
Monterey, CA, USA
A:
Whoops, this is one of those good questions that somehow fell through the cracks long ago. Everything you say is correct. The collision will be a tad sooner for the the heavy object, because the earth accelerates a tiny bit more toward it.

Mike W.

(published on 07/26/2012)

## Follow-Up #4: heavier falls faster?

Q:
This one guy told me that given enough time a heavier objet would game more speed like if it was dropped from orbit. But I don’t think that’s true, is it? He also said if you throw the two objects the heavy will hit first. but I think that has more to do with the angle and force you throw it with than gravity’s pull on them. Do think I’m right? It’s part of a bet. Thank you.
- jon epperson (age 30)
kennewic wa benton
A:
This too slipped through the cracks. I think the answer to the other follow-up should cover it. In practice, of course, what you notice is that air friction makes less difference for the heavier object.

Mike W.

(published on 08/07/2012)

## Follow-Up #5: falling objects pulling on Earth

Q:
In the answer to Follow-up #3, you said 'The collision will be a tad sooner for the the heavy object, because the earth accelerates a tiny bit more toward it'. How is that? Let the original distance between the objects and Earth be h. Suppose Earth moves towards the heavy object by a distance 'x' due to the heavy object's force, the heavy object has to travel (h-x) before they collide. But then shouldn't the lighter object (ignoring its gravitational force on earth) ALSO travel only (h-x) since the heavier object has already brought Earth x closer to both of them?
A:
Yes, if both objects are dropped together then they hit the Earth at the same time. If they are dropped at different times, the heavy one is just a tiny bit quicker to hit the Earth because it pulls the Earth toward it more.

Mike W.

(published on 03/23/2013)

## Follow-Up #6: times for different falling objects

Q:
Following up in follow up #5. That depends on the relative position of the objects. For instance if the objects are dropped simultaneously on opposite sides of the earth then the lighter object has to travel even farther (h + x) while the heavier only traveled h. OTOH, if the objects are dropped side by side with, let's say, the heavier object to the left, then the earth would be pulled slightly to the left and thus the heavier object again reaches the earth first.
- Abe (age 49)
Houston, Texas
A:

Yes, that all sounds right.

Mike W.

(published on 10/06/2013)

## Follow-Up #7: Gravitatonal attraction of two unequal mass objects

Q:
If two objects having same volume and shape but different masses, then which object will move towards the other or vice-versa or will both the objects move towards each other exactly the same distance?
- Tathagat Bhatia (age 15)
Lucknow,India
A:

There is an equal and opposite force on each of the two objects: they will both move.   Now since the acceleration of each object is inversely proportional to the mass, the lighter object will move a bit faster.  If you do the arithmetic you will find that they will meet at their common center of mass.  The lighter one will move a bit further than the heavier one.

LeeH

(published on 10/31/2013)

## Follow-Up #8: gravity on different weights

Q:
For two objects of different masses and densities in a vacuum, say a bowling ball and a feather, wouldn't the bowling ball accelerate slower than the feather due to inertia? If f = ma and gravity is the force acting pretty much equally on each object, shouldn't their different masses facilitate different accelerations?Thanks
- Nathaniel Scherrer (age 34)
San Diego, California, USA
A:

The acceleration is given by a=F/m. Since F=mg, you get a=g regardless of m.

So, in words, the key point is that the force is not "pretty much equal" on the different objects. It's proportional to their masses.  So that means the accelerations are exactly equal.

Mike W.

(published on 07/10/2015)

## Follow-Up #9: Newton vindicates Gallileo

Q:
In looking for the answer to the question, "Will two objects hit the ground at the same time, regardless of their weight", I found the current webpage and the following sentence from another webpage which seem to contradict each other. This is from the other page: "Heavier things have a greater gravitational force AND heavier things have a lower acceleration. It turns out that these two effects exactly cancel to make falling objects have the same acceleration regardless of mass." Is this true? If so, won't two objects hit the ground at the same time, differences in air displacement not considered?
- Father (age 55)
Detroit,MI, USA
A:

In the absence of air friction both heavy and light objects will reach the ground at the same time.

Galileo deduced this by devising clever experiments with balls rolling down inclined planes.  Newton gave it his blessing by observing that  a = F/M, i.e. the acceleration of an object  is proportional to the force, F, on it divided by its mass, M.  Furthermore the gravitational force on said object was proportional to its mass, F=Mg where g is the measurable acceration of a mass due to gravity on earth.  Putting these two equations together you get a = Mg/M = g.   The acceleration is independent of mass.