Hello,
So I have come to understand that in addition to the force of gravity we experience from the planet we are on, there is a gravitational pull between objects depending on difference in mass (?).
Is there any way to demonstrate this in a way that is easily comprehended by a layman? How much mass/density of mass would you require from an object in real life in order to feel gravitational pull towards it?
Gravitational attraction is very small. You might like to read up on the Cavendish_experiment which uses high mass (lead) balls and measures the attraction between them. I vaguely remember doing something similar in high school physics.
To *feel *a gravitational pull, you would need a very large mass indeed.
As an aside - It is said, as a refutation of astrology, that the mass of a fat midwife would have more effect on a newborn baby than that of distant planets and stars.
There is no “in addition to.” It is all gravity and gravity is the weakest of all four forces.
The math is very simple and matches observations neatly.
The Cavenish experiment can be performed using at-hand materials*. My high school physics teacher told me about doing it, using buckets of sand as the weights, suspending the rod from a long rope, and using light reflected from a mirror across a long “throw” to make the motion obvious (nowadays, I’d use a laser). The experiment was performed in a large empty building (a barn or something), so that the wind could be shut out.
But he said that you could clearly see the difference between when the weights were on one side of the weights on the hanging rod and when they were on the other side.
yes there is. There’s nothing wrong with what was said.
What he said is perfectly sensible, especially as the answer is the question… there is other gravity ? yes , measure it.
There are well known ways to be sure there is other gravity.
tides in the oceans and seas ?
Orbits of planets… eg some were found due to correct (and some due to wrong) predictions based on perturbations of known planets.
I’ve heard this claim before, but never done the math. Here we go:
Distance between Earth and Mars: 225M km =225B m(depending on timing)
mass of Mars:639x10[sup]21[/sup]kg
Distance between midwife and baby: ~1m
mass of fat midwife: 100 kg
ratio of gravitational attraction: (100/1[sup]2[/sup])/((639x10[sup]21[/sup])/(225x10[sup]9[/sup])[sup]2[/sup])
=100/12.62
= 7.92
So a fat midwife at a range of 1 meter would have about 8 times as much gravitational influence on a baby as Mars would.
In order to believe that gravity doesn’t exist between everyday objects, one would have to posit that the matter which composes everyday objects is fundamentally different from the matter that composes the planets. One would have to show, then, that the matter composing everyday objects came from something other than Earth.
If you’re looking for a mathematical demonstration, there is an equation that you can use to calculate the force of gravitational attraction between objects as a function of their masses and the distance between them:
F = G* m[sub]1[/sub] * m[sub]2[/sub]/R[sup]2[/sup]
where:
F = force of gravitational attraction (in Newtons)
G = gravitational constant, 6.673 x 10[sup]-11[/sup] N(m/kg)[sup]2[/sup]
m[sub]1[/sub] = mass of one of the two objects (in kilograms)
m[sub]1[/sub] = mass of the other object (in kilograms)
R = distance between the centers of mass of the two objects (in meters)
With G being such a tiny value, you can see that it takes either enormous masses or very small distances (or both) in order to achieve gravitational forces that are palpable for a human being. The “Mars-versus-midwife” math shows how it all plays out: Mars vastly outweighs even the fattest midwife, but the midwife is vastly closer to the newborn baby and so exerts much greater gravitational attraction.
Ninja’ed before I ever even got to the thread. We’re going to have to step outside one of these days, bob… 
It’s a good point to make, though, because a lot of simple questions about the minor aspects of gravity do seem to devolve to something astrological or woo-ish.
Not difference in mass, just mass. Every bit of matter pulls on every other bit of matter in proportion to the product of their masses and the inverse of the square of the distance between them. It just happens that by far the biggest bit of matter in our immediate vicinity is the Earth, is its effect by far dominates. The gravitational attraction between you and other objects is still there, but is unnoticeable compared to the Earth’s gravity.
As others have noted, the Cavendish experiment demonstrates that objects other than the Earth also have gravity, by constructing a very sensitive instrument and arranging it so the Earth’s gravity has no effect on it.
If you want to “feel” gravitational effects, rather than just detect them with instruments, you’re going to have to play with masses that are more-or-less planet-sized, I’m afraid. If you can get yourself away from the Earth, you might notice the gravity of a comet like the one Rosetta is orbiting, but even that might be more “I seem to be drifting in that direction over time”, rather than “feeling” it.
Brilliant - I have stored that away to produce at some opportune moment - I will of course give due credit.
Keep in mind that gravity is by far the weakest force there is. When I pick up, say, my daughter, my own feeble little muscles are overcoming the pull that the entire EARTH is exerting on her.
Probably best not to say "Machine Elf told me."
Hmmm - maybe you are rigt. It’s the astrologers who are otherworldly.
Thank you all in this thread for great posts. I might add that the OP was inspired by the chapter on the neutron star mass in the book “What If”.
This might be redundant, but when does m[sub]1[/sub] begin and finish?
For example, will Mount Everest exert the gravitional pull of all its combined mass of all its stone as one body? Will the Eiffel Tower be one body although it is made up from many different parts?
The gravitational pull of the Earth seems to come directly from the Earth’s core (since this is the direction everything that falls on the surface is going towards). So that should make the core m[sub]1[/sub]?
A bucket of sand that masses 10 kilos exerts the same gravitational influence as a single 10-k ingot of lead. Shapes of more diffuse objects (such as the Eiffel Tower) act differently, as part of the mass of the Tower is much farther away from the observer than other parts.
That distance (the “R” of the equations) does add up differences quickly.
Right, so the Mount Everest will not have the gravity of one body so to speak, because it has in itself such a large distance that different parts of the mountain will have different effect on me. But if I could pack the mass of Mount Everest into a container the size of a shoe box, then the gravitational pull will be much more palpable.
If you do the math, the gravitational pull of a spherical object (like a planet) behaves exactly the same as if it were coming from a point of the same mass located at the center of the sphere.
For nonspherical objects, it’s more complicated. If you’re standing next to the Eiffel Tower, for instance, you’ll feel some pull straight ahead toward the base of the tower as well as some upward toward the parts of the tower above you.
For practical purposes, 99% of the time, any object big enough for us to care about calculating its gravity will be a sphere (planet, star, etc). Or maybe a disc, if you’re thinking about galaxies.
If you’re curious about this topic, I highly recommend the Steven Baxter book “Raft”, which is a science fiction book about a population of humans who accidentally found themselves stranded in an alternate universe in which the force of gravity is billions of times stronger than it is here.
Not true.
If you imagine that Everest has some mass X, and that when you stand on its slope you are Y distance from the center of that mass, then the force of attraction will be Z.
If you compress the mass of Everest into a shoebox, and maintain your separation at Y distance from the center of that shoebox, then the force of attraction will still be Z.
In the former case, if you tunnel into Everest to decrease your distance Y, you are moving yourself away from some of Everest’s mass as you tunnel deeper and deeper. Eventually when Y = 0, your attraction falls to zero.
In the latter case, because Everest is now so concentrated, you can decrease your distance Y substantially and find that your gravitational attraction does continue to increase. However, once you start tunneling through the wall of the shoebox, then you run into the same issue as before: you are starting to move away from some of the mass, and eventually when Y=0 your attraction will again fall to zero.
This is true; you have to do the triple integral over the entire volume to calculate the net force. For solid objects, using the distance to the center of mass usually gives a good approximation (which is exact in the case of a sphere).
Not quite, because Mt. Everest isn’t spherical. The difference will be small, but then, the gravitational force exerted by Everest is small to begin with. If we’re going to be sweating the petty details, then we might as well sweat them all the way.
For any object, large or small, you can calculate a center of mass. You could think of it as the geometric center of the object, but weighted by the density of each part of the object. If the whole object has the same density, the geometric center and the center of mass are the same.
As long as you’re outside the object (and any possible line drawn between two points on it) it excerts gravity like any other object with the same mass and a center of mass in the same position.