Newtons Law on Gravitational Force

[matthewmussen]

this is going to sound dumb, but here i go.

through out my schooling i was preached " in a vaccum, a feather and a bowling ball would fall at the same rate".
-thinking about the difference in theories with Aristotol, Galileo, and Newton, something didn't make sense to me. Talking about the Newtons' gravitational constant, wouldn't you have to measure the average gravitational constant of both m1 and m2 before finding it; furthermore, of all the mass of the particles involved, and doesn't the distance from the center point of each particle change the gravitational constant? If this is true, wouldn't Aristotol be, not perfect, but more accurate than Galileo? And one more thought, doesn't Newton's laws on gravitational attraction contradict the idea of, in a vacuum, a feather and a bowling ball falling at the same rate? The mass of the bowling ball is more than the feather, and when add to the mass of the planet, would have a greater attraction; and when adding Einstein's theories of perspective from the planet the bowling ball would fall and hit first.

 

[D H]

Setup: An Earth-like planet with Earth-like gravity but no atmosphere, a ball made of lead, and a foam ball the size as the lead ball but with much less mass.

If you drop the two balls separately from exactly the same height and time their falls with a perfect timer, the lead ball will be observed to fall a tiny bit faster than the foam ball. However, if you drop them separately and time them with a real-world timer you will not be able to measure the difference. The reason is that the while the planet does experience greater acceleration toward the lead ball than the foam ball, the acceleration in both cases is immeasurably small.

For example, let's up the ante a bit and consider the gravitational acceleration of the Earth toward a ten metric ton boulder versus that toward a one gram pea. While this represents a six order of magnitude difference in mass (and hence acceleration of the Earth), the Earth acceleration remains negligible. For a drop of 4.9 meters, the time difference is less than 10^-22 seconds. For a 50 kg lead ball versus a 0.5 kg foam ball, the timing difference drops to 4*10^-24 seconds. This is immeasurably small.

Now go back to the perfect situation, but release the balls simultaneously. This time the balls will hit the Earth simultaneously. The Earth accelerates toward both of the balls, and the balls are each accelerating toward the Earth.

So, pedantically speaking you are correct if the balls are released separately but you are incorrect if the balls are released simultaneously. Realistically speaking, you are just being overly pedantic.

 

[maverick_starstrider]

Furthermore, if you dropped the metric ton boulder mentioned by D H from a very high height (like the top of a sky scraper) and a feather, in a vacuum (guess the air called in sick that day) the difference in fall times would still be extremely immeasurable by any real-world timer and yet Aristotle would predict a VERY different fall time for each. So no he would never be more accurate, not even close.

 

[matthewmussen]

in my ideas defense

the idea behind asking this question would be challenging the original idea of the bowling ball and the feather in a vaccum. my comment about Aristotle was only to say that he was on the right path in realizing that there would be a difference. All other aspects are obviously untrue. now, you claimed that I was correct but that there was no point to my comment because the difference was "immeasurably small", ... just because technology today cannot currently measure the difference, does not necessarily mean that it is not worth considering. who knows what the future will bring. It bothers me that educators today would be willing to dole out untrue answers to long-asked questions just because the current answer is popular, and they believe easier to understand, and may not make much of a difference in their everyday lives. the point is the theory, not the parctice. I am respectfully here for intelligent feedback, good or bad, and so I thank you for responding.

furthermore; (for arguments sake)

-Physics is the science of matter and its motion, as well as space and time. It uses concepts such as energy, force, mass, and charge. Physics is an experimental science, creating theories that are tested against observations. Broadly, it is the general scientific analysis of nature, with a goal of understanding how the universe behaves. -Wikipedia

_Therefore, without men and women who were "pendant" and questioned reality, thirsted for knowledge for knowledge's sake, we wouldn't be where we are today. I'm sure past physicists didn't concern themselves whether air would somehow take a day off- otherwise the question would never have been asked. There is a difference in men. Those who are content with the knowledge others have given them, and those who question that knowledge, and try to learn more. Do not merely stand on the shoulders of genius, find your own.

 

[maverick_starstrider]

Well, for your own edification, Newton's Law of Gravitation has known to be incorrect for about 100 years now. Einstein's theory of general relativity is the theory of gravitation and the difference between its predictions and Newton's can be enormous (for example when it comes to things like black holes). However, to work with Einstein's theory of relativity requires some of the most complex mathematics that exist and for every day stuff like falling bowling balls and a rough examination of a solar system the difference between einstein's extremely complicated model and Newton's simple one is negligble. But it is ultimately a question of HOW to educate. I mean atoms aren't like little solar systems at all and the rutherford, thompson and bohr models were all wrong and the 'real' explanation at the atomic level is quantum mechanics (in fact it's technically not even quantum mechanics because quantum mechanics breaks down at speeds near that of the speed of light (when relativity becomes an issue) and the true model is really quantum field theory (QFT), at least until someone figures out a grand unified theory). However, quantum mechanics is VERY mathematically complex and you can't even approach that kind of math until late in a university undergrad degree (and quantum field theory is only taught in grad school).

So, I do sympathize, I remember being frustrated about the same thing how at every new level of learning I basically learned that what I learned before was ultimately flawed and incorrect only to be told that this new way was the 'correct' way (this is especially common in high school because high school teachers generally don't actually KNOW that what they're teaching is ultimately incorrect). And sometimes I do agree that maybe the best way would be to just load a student up with advanced math and teach them QFT (quantum field theory) first but that would be an unbelievably steep learning curve.

 

[Janus]

the idea behind asking this question would be challenging the original idea of the bowling ball and the feather in a vaccum. my comment about Aristotle was only to say that he was on the right path in realizing that there would be a difference. All other aspects are obviously untrue. now, you claimed that I was correct but that there was no point to my comment because the difference was "immeasurably small", ... just because technology today cannot currently measure the difference, does not necessarily mean that it is not worth considering. who knows what the future will bring. It bothers me that educators today would be willing to dole out untrue answers to long-asked questions just because the current answer is popular, and they believe easier to understand, and may not make much of a difference in their everyday lives. the point is the theory, not the parctice. I am respectfully here for intelligent feedback, good or bad, and so I thank you for responding.

The problem is that while Aristotle was slightly more correct in "practice" in that a lead ball dropped in a vacuum would hit first when dropped from an equal distance as an feather,(If dropped separately)) he was wrong in "principle". Aristotle considered the Earth as motionless, thus any difference in the fall times would have been due to a difference in the fall rates of the ball and feather alone. What happens instead is that the Earth also falls towards the ball or feather. The difference in fall times is due to the difference of fall rate for the Earth. It is still more correct to say that the feather and lead ball fall at the same rate, when eachs object rate of fall, (the ball, feather and Earth) separately.

This is why the ball and feather hit the Earth at the same time if dropped together. (the Earth falls towards the pair at a rate determined by the combined mass of the two.)

Aristotle would have held that the lead ball would have still hit first.

 

[rbj]

Setup: An Earth-like planet with Earth-like gravity but no atmosphere, a ball made of lead, and a foam ball the size as the lead ball but with much less mass.

If you drop the two balls separately from exactly the same height and time their falls with a perfect timer, the lead ball will be observed to fall a tiny bit faster than the foam ball. However, if you drop them separately and time them with a real-world timer you will not be able to measure the difference. The reason is that the while the planet does experience greater acceleration toward the lead ball than the foam ball, the acceleration in both cases is immeasurably small.

For example, let's up the ante a bit and consider the gravitational acceleration of the Earth toward a ten metric ton boulder versus that toward a one gram pea. While this represents a six order of magnitude difference in mass (and hence acceleration of the Earth), the Earth acceleration remains negligible. For a drop of 4.9 meters, the time difference is less than 10^-22 seconds. For a 50 kg lead ball versus a 0.5 kg foam ball, the timing difference drops to 4*10^-24 seconds. This is immeasurably small.

Now go back to the perfect situation, but release the balls simultaneously. This time the balls will hit the Earth simultaneously. The Earth accelerates toward both of the balls, and the balls are each accelerating toward the Earth.

So, pedantically speaking you are correct if the balls are released separately but you are incorrect if the balls are released simultaneously. Realistically speaking, you are just being overly pedantic.

we could be really, really pendantic and say that when the two balls are dropped simultaneously, since the two balls do not occupy the same space, then the (perfectly spherical) planet tips a little toward the lead ball and the lead ball hits the planet a teeny, weeny, immeasureable amount of time before the foam ball does.

but i agree that it's dumb.

 

[matthewmussen]

we could be really, really pendantic and say that when the two balls are dropped simultaneously, since the two balls do not occupy the same space, then the (perfectly spherical) planet tips a little toward the lead ball and the lead ball hits the planet a teeny, weeny, immeasureable amount of time before the foam ball does.

but i agree that it's dumb.

how about the idea of Newton's equation of finding the gravitational constant, doesn't the distance from the center point of each particle change it? the further from mass you get, the less pull it has, right?

 

[Janus]

how about the idea of Newton's equation of finding the gravitational constant, doesn't the distance from the center point of each particle change it? the further from mass you get, the less pull it has, right?

That doesn't change the value of the Constant G. The force gets less because the distance increases and the force falls off by the square of the distance,

 

[matthewmussen]

That doesn't change the value of the Constant G. The force gets less because the distance increases and the force falls off by the square of the distance,

where is the value of the Constant G measured from?

 

[dx]

where is the value of the Constant G measured from?

Are you talking about the acceleration due to gravity on the earth, or Newton's gravitational constant that appears in his law of gravitation?

 

[matthewmussen]

Are you talking about the acceleration due to gravity on the earth, or Newton's gravitational constant that appears in his law of gravitation?

Newton's "Gravitational Constant" that appears in his law of gravitation.

 

[Nick89]

where is the value of the Constant G measured from?

If you mean big G (the constant that appears in Newton's gravitational law) you can measure it, for example, by suspending a rod from a string, and placing a small known mass on one of the ends of the rod. Then you place a large known mass (fixed) near the small known mass.
The gravitational attraction between the two will make the rod with the small mass twist a little bit. You can measure the amount of twist in many ways, for example by shining a laser beam at a mirror on the rod; because it turns the reflected beam will deflect and you can measure the deflection quite accurately. This allows you to determine G.

 

[maverick_starstrider]

I think G was calculated by Cavendish using a torsion balance. But once again, Newton's theory of gravitation was replaced by general relativity about a 100 years ago but it still gives very excellent agreement with experimental data for these sort of small scale experiments but I believe GPS satellites need to make relativistic corrections (although those may be only SR corrections) so the discrepancy between Newton and GR is measurable even in terrestrial stuff.

 

[rcgldr]

I believe GPS satellites need to make relativistic corrections (although those may be only SR corrections) so the discrepancy between Newton and GR is measurable even in terrestrial stuff.

The correction is done for time dilation. The largest effect is due to the difference in the strength of the gravity at the Earth's surface versus at the alititude of the satellite. A much smaller effect is due to the speed of the satellites. The "net" result is clocks in satellites operate at a faster rate than the same type of clocks on the earth. A few links from doing a web search on gps time dilation:

http://www.leapsecond.com/history/Ashby-Relativity.htm

http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

http://www.kowoma.de/en/gps/errors.htm [Broken]

 

[D H]

I think G was calculated by Cavendish using a torsion balance. But once again, Newton's theory of gravitation was replaced by general relativity about a 100 years ago but it still gives very excellent agreement with experimental data for these sort of small scale experiments but I believe GPS satellites need to make relativistic corrections (although those may be only SR corrections) so the discrepancy between Newton and GR is measurable even in terrestrial stuff.

While general relativity is a more accurate model than Newtonian gravity, the two are identical in the limit of weak fields and slow relative motion. Newton's theory of gravity was not replaced by general relativity in the sense that we no longer use Newton's theory of gravity. For example, most space missions are designed and operated using Newtonian gravity rather than GR. The difference in predicted state (i.e., position and velocity) between GR and Newtonian gravity for vehicles in Earth orbit is negligibly small. The non-spherical shape of the Earth, aerodynamic drag, the effects of the Sun and the Moon, and even solar radiation pressure have a greater effect on satellite state than do the general relativistic effects. Even where general relativity is needed due to high accuracy requirements (e.g., satellite geodesy), we still use Newtonian gravity; general relativistic effects are models as a small corrective force.

The GPS satellites are an exception to this. The reason: the GPS satellites send time-stamped information to the GPS receivers on the Earth. Precision time stamps are needed to meet the accuracy requirements; to this end the GPS satellites carry atomic clocks. While the general relativistic effects on satellite state can be ignored, the general and special relativistic effects on the satellite clocks is significant. Bottom line: The Global Positioning System models relativistic effects because of the way these effects manifest themselves in a clock.

 

[D H]

I think G was calculated by Cavendish using a torsion balance.

That remains one of the ways to measure G. There are some more recent developments, none of them particularly good. We currently know G to only four decimal places. It remains one of the least well known physical constants. We know the product of G and some solar system bodies to a much higher accuracy. While the relative error in G is about 1 part in 10,000, the relative error in G*M_earth is 1 part in 500,000,000.

By the way, the exact same G that appears in Newton's law of gravitation is also a physical constant in general relativity.