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Q & A: Gravity, Galileo, and Einstein

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Most recent answer: 10/22/2007
Q:
If two object of different weight are dropped at the same time why do they both land at the same time?
- If two object of different weight are dropped at the (age 10)
Gainesville florida
A:
Thatís a wonderful deep question, which people have wondered about since Galileo noticed that behavior.

Newton invented force laws which included these:

a=F/m, meaning that the amount some object accelerates is proportional to the force on it, and inversely proportional to the object's mass.

F=GmM/r^2, the gravitational force between two small objects is proportional to the masses of each of them, and inversely proportional to the square of the distance between them.

Combining these two equations gives: a=GM/r^2. The acceleration of mass m depends on how big the other mass M is, and how far away, but it is completely independent of any property of the object of mass m, except for where it is.

Now you may notice that Newton simply invented laws to reproduce the behavior that Galileo had observed. Einstein proposed a deeper reason, which I only partly understand and which I cannot easily explain. He said that gravity is not really a force like other forces. All the other forces give accelerations which depend on the thing being accelerated in some way. Gravity acts more like a change in the nature of space and time, so that the natural paths for ANY object are not like familiar straight lines. In Einsteinís picture, everything falls together because they are just following the straightest paths possible in that region of space and time, which do not depend on which object youíre looking at.

Mike W.

(published on 10/22/2007)

Follow-Up #1: falling weights

Q:
if all objects are falling at the same time, why does a 100 pound ball make more of an impact than a 5 pound ball?
- eric
new york
A:
Wouldn't you expect 20 5 pound balls to fall together with each other? And wouldn't you expect those 20 to have more impact than any single 5 pound ball? So if the 20 all fall in a tight cluster it's very much like a 100 pound ball.

Mike W.

(published on 10/22/2007)

Follow-Up #2: Mehran’s answer to: Gravity, Galileo, and Einstein

Q:
Alternate answer to: Gravity, Galileo, and Einstein Q: If two object of different weight are dropped at the same time why do they both land at the same time? Hailee (age 10) Answer: If 10 kids of the same weight jump off the same platform at the same time they will all hit the water at the same time. If 9 of them hold hands and one doesn’t, still all 10 will hit the water at the same time, since holding hands does not affect their weight. You can think of one heavy object as composed of many small objects holding hands which land at the same time as one small object. The above is true in vaccum. In the air, the small object has more contact surface with air, hence the air friction slows down and causes the small object to land later than the heavy object.
- Mehran
Miami
A:
Mehran- Thanks for this explanation. This is fundamentally the point that Galileo himself made. It's the most compelling argument for why different sizes of objects made of the same stuff should fall together.

We failed to make clear that our less compelling argument addressed a tougher question- why would objects made of all sorts of different stuff fall at the same rate. The argument that nature doesn't care which batch of things you lump together to call a falling object doesn't deal with that more general question.

it's great to see that you're reading this with such care.

Mike W.

These theories are tied very closely to observations, and the equivalence of gravitational mass and inertial mass is not something you can deduce from pure logic, because different things are made up of different kinds of matter. For example, the relationship between the m in F=GMm/r^2 and F=ma may be different for protons and neutrons. Why not, as they have different electric charges, perhaps they have different gravitational "charges" too. The experiments of Eotvos on different materials, repeated much later and with much higher precision by Dicke (and my book, Misner, Thorne and Wheeler's fine book "Gravitation" was written in the early 1970's and so later experiments are not covered) shows that different materials do in fact feel gravity the same way as each other, bolstering Einstein's equivalence principle. But we'd have to throw that principle out if we found evidence conflicting with it.

Such evidence was claimed to be had in the late 1980's when a group of physicists (Fishbach et al) reanalyzed the old Eotvos data and claimed to find correlations with gravitational interactions and properties of the materials Eotvos used. This investigation was roundly criticized -- after all, experiments can and should be repeated with better equipment and better control over the material samples (I seem to remember Eotvos used "porphyry" and "wormwood", the exact compositions of the particular samples used are to this day still uncertain). The claim wasn't that Einstein's GR was wrong, but rather that there was a "fifth force". Subsequent precision measurements ruled out a fifth force of this type.

This whole episode just underscores the need to confront theoretical ideas with observations in order to advance our understanding.

Tom

(published on 10/22/2007)

Follow-up on this answer.