1. Feb 9, 2012

### zarmewa

Galileo was first to demonstrate that in the absence of air, all things would truly fall with the same acceleration and 300 years later demonstrated this by the crew of Apollo-15 on the lunar surface (which has gravity & also lacks air) by dropping a hammer and a feather.

As moon was seen from two different gravitational fields ["gf" of feather & "gh" of hammer] therefore cognizance shows that hammer and moon should strike each other first as gh > gf

So, is Galileo's statement correct, theoretically?

2. Feb 9, 2012

### James Leighe

The gravitational field of the hammer would attract the moon, so the moon would move closer to the hammer, which would also make it move closer to the feather!

So Galileo's statement still holds.

3. Feb 9, 2012

### HallsofIvy

Staff Emeritus
It is true that the force on the hammer is greater than the force on the feather (the hammer has greater weight than the feather even on the moon). However, because F= ma, to find a= F/m, that greater force is divided by the greater mass.

Specifically, taking M as the mass of the moon as m as the mass of either hammer or feather,
$$ma= \frac{GmM}{r^2}$$
because m appears on both sides, it cancels. The acceleration of hammer or hammer depends only on the mass of the moon, not on the mass of the object itself.

4. Feb 10, 2012

### gsal

I wonder if the "gravitational" field was assumed to be un-movable, and so only the objects fell.

If not...

Independent of the force, though, having a system of two masses attracting each other, the center of mass is not suppose to move and so, as the hammer falls towards the moon, the moon falls towards the hammer, because the mass of the hammer is larger than that of the feather the moon should move closer to the hammer...

James assumed that the hammer and the feather were dropped simultaneously and on the same side of the moon...

...but what if we drop the hammer and the feather simultaneously but on diametrically opposite sides of the moon? Would the hammer and the feather touch the moon at the exact same time? or would the feather need to do some catch up?

A true measure whether it takes longer for one to fall and touch the moon would be two independent events, of course.

5. Feb 10, 2012

### Subductionzon

Or to save yourself a trip around the Moon you could drop the two at different times from the same place. Of course you would need an impossibly accurate clock to measure the difference in time. I did the calculation once for dropping items on the Earth and to notice a difference you would need a clock that was accurate to more than 20 places. I believe with the two objects I picked it took at least 23 places behind the decimal point to see any difference.

Your error in placement would be greater than that degree of error, not to mention the lack of a clock anywhere near that accuracy. So as far as any experiment that you can run goes, Galileo was right.

6. Feb 10, 2012

### sophiecentaur

All masses affect all other masses. Take three objects of equal order of mass, in a triangular formation, out there in deep space. They will all be attracted to a point at some point in their 'joint centre' but you would need to calculate, in detail, what would happen. It would be over-simplifying to say that they would all head off, initially, towards their joint centre of mass. If it were as simple as that, the hammer, dropped on the Moon, would have gone haring off towards the CM of the Earth and Moon - or the CM of the Earth Moon and Sun -- or even to the CM of the Galaxy etc etc. You also need to consider the orbital Motions involved but, in the absence of motion and, with the objects in a straight line, initially, they would end up at the CM.

Once you're dealing with one Massive object and two tiny ones, you can neglect any effect other than the g field of the big one.

7. Feb 10, 2012