Miscellaneous Science Questions

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Mettra
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Re: Common Questions

Postby Mettra » Tue Apr 29, 2008 1:50 am UTC

Øsse wrote:Yes, but as far as I know they still travel at the speed of light in that particular medium, don't they?

Let me put it this way: Can photons have different velocities in the same medium?


From what I understand, photons always travel at the speed of light, no matter the material they are in.

However, there is an important distinction to make here. When a photon travels through a medium like air, it sorta bumps around in a roundabout way such that the average velocity of the photon is less than C (though the speed is the same).

e.g.

['snapshots' below]

1. p-----> (air molecule)

2. <-----p

3. (air) <-----p

4. p----->

And so on.

The 'general bouncyness indicator' of this kind of event is the refractive index. It's not an exact or fundamental thing, it's just a useful quantity to have, like the coefficient of friction.

Someone with some quantum electrodynamics background could probably be a lot more specific on this.
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Re: Common Questions

Postby Tchebu » Tue Apr 29, 2008 3:52 am UTC

However, there is an important distinction to make here. When a photon travels through a medium like air, it sorta bumps around in a roundabout way such that the average velocity of the photon is less than C (though the speed is the same).


Actually what they really do is excite the medium to create special states in it known as phonons, and THOSE spread through the medium at a speed dictated by the properties of the medium. Unfortunately this is just about where my knowledge of this stuff ends, so maybe someone else can explain what kind of beasts these phonons really are.
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Re: Common Questions

Postby Arancaytar » Tue Apr 29, 2008 10:57 am UTC

Øsse wrote:Can photons be forced to travel at speeds lower than the speed of light in that particular medium?


Not a physicist, but you might slow it down further with some electromagnetic interference. Really, the question is how you define "particular medium". Does it include a specific temperature, density and electromagnetic radiation? Then it's probably impossible to influence the speed of light with any other factor...
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Re: Common Questions

Postby capella » Tue Apr 29, 2008 12:26 pm UTC

Here are some astronomical tidbits - enjoy:

1 Astronomical Unit (AU) = approx. 93 million miles = approx. 150km
Also, 1 AU = the distance to the sun.

1 Light Year = 5,878,625,373,183.61 miles = 9,460,730,472,580.8 km = 63,241 AU

1 Parallax Second of Arc [Parsec (pc)] = 3.26 Light years
A parsec is the distance to a star with a parralax of 1 arcsecond.

The Erf is approx. 7,926.41 mi in diamater and approx 384,000km from the Moon which is approx. 3474mi in diameter which is approx 1/400th the diameter of the Sun which is approx 400x further away than the Moon.

A decently good pair of binoculars can receive light with an apparent magnitude of 9.5 (15.8 times brighter than the dimmest star you could possibly see with the naked eye).

[EDIT:] Sorry for the earlier mistakes, I wrote this right after I woke up this mornin.

The approximate horizon of the universe is approx. 14 billion parsecs from Earth, right now. As the universe expands, this distance grows.
Last edited by capella on Tue Apr 29, 2008 8:41 pm UTC, edited 1 time in total.

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Re: Common Questions

Postby Øsse » Tue Apr 29, 2008 3:11 pm UTC

Arancaytar wrote:
Øsse wrote:Can photons be forced to travel at speeds lower than the speed of light in that particular medium?


Not a physicist, but you might slow it down further with some electromagnetic interference. Really, the question is how you define "particular medium". Does it include a specific temperature, density and electromagnetic radiation? Then it's probably impossible to influence the speed of light with any other factor...
Well, the answer I guess is everything. My other formulation of the question is perhaps easier to understand: Can photons have different velocities in the same medium?

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Re: Common Questions

Postby hyperion » Tue Apr 29, 2008 3:44 pm UTC

capella wrote:The Erf is ... approx 384,000mi from the Moon

That should be km, not mi.

A decently good pair of binoculars can receive light from distances of 25,000 light years.

Light how bright? The gamma ray burst a few weeks ago was billions of light years away and could be seen with the naked eye.
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Re: Common Questions

Postby thoughtfully » Tue Apr 29, 2008 4:03 pm UTC

capella wrote:A decently good pair of binoculars can receive light from distances of 25,000 light years.


Your binoculars, or eyes, don't care how far a photon of light has been travelling before it gets to you. It is the luminosity of the object that counts. There will be bright objects that will be visible with a given apparatus at some distance, while a dimmer object at the same distance will not be visible with that apparatus.

Now, for the obligitory pedantry. Most objects in the Universe (the exception being nearby galaxies to whom the Milky Way is gravitationally bound) are red shifted due to the expansion of the Universe. This red-shift increases with distance. Given enough red-shift, the light will pass outside the band of spectrum that our eyes are sensitive to. There is nothing at this distance that is sufficiently luminous to be visible through decent binoculars, however.
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Re: Common Questions

Postby oxoiron » Tue Apr 29, 2008 4:16 pm UTC

hyperion wrote:The gamma ray burst a few weeks ago was billions of light years away and could be seen with the naked eye.
You can see gamma rays with your naked eye? :wink:
thoughtfully wrote:Most objects in the Universe (the exception being nearby galaxies to whom the Milky Way is gravitationally bound) are red shifted due to the expansion of the Universe. This red-shift increases with distance. Given enough red-shift, the light will pass outside the band of spectrum that our eyes are sensitive to.
Wouldn't UV and higher energy light just get shifted into the visible range?

I know. I know. That wrecks the joke about hyperion's eyes. :(
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Re: Common Questions

Postby thoughtfully » Tue Apr 29, 2008 5:09 pm UTC

Wow. A visible gamma-ray burst. I would assume it's the optical emissions that we can see, right?

Hmm, another site has the redshift of that event as z=0.937.

Gamma rays cover a wide range of wavelengths. So, let's work the other way. What wavelength, when redshifted this amount, would just barely make into the blue end of the visible spectrum?

http://www.astro.virginia.edu/~jh8h/glo ... dshift.htm

z = (lambdablue-lambdarest) / lambdarest

lambdarest = lambdablue / (z+1)

So, the wavelength is about halved. Blue light has a wavelength of around 400 nm, so what's at 200 nm? 200 nm is the boundary between middle and far UV, hardly even X-rays. So what is visible started out visible, or near IR.
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Re: Common Questions

Postby ATCG » Tue Apr 29, 2008 10:41 pm UTC

Øsse wrote:Can photons have different velocities in the same medium?

Yup. This is how prisms work.
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Re: Common Questions

Postby Mabus_Zero » Thu May 01, 2008 8:58 am UTC

Explain the Strong Force, and how does it intertangle with the electromagnetic force?
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Re: Common Questions

Postby btarlinian » Fri May 02, 2008 3:42 am UTC

Mabus_Zero wrote:Explain the Strong Force, and how does it intertangle with the electromagnetic force?


That's a broad question. To actually explain it requires tons of math that I don't know. (There is one poster who works at Brookhaven on the RHIC and studies this for a living, but I can't remember his name). But the strong force is essentially the force that holds hadrons (protons, neutrons, and other far less common particles nowadays known as mesons) together. Basically, all of these particles have constituent parts called quarks. Protons and neutrons have 3. There are 6 types of quarks. (There are only two types in protons and neutrons however, up and down). Each quark has a fractional electric charge, and another property known as "color" charge, the analog to electric charge for the strong force. The mediator of the strong force, the analog to a photon, is called a gluon. But there is one crucial difference. While photons do not themselves have electric charge, gluons are color charged, which makes the math of quantum chromodynamics, the theory that describes the strong force, extremely complicated. Another interesting aspect of the strong force is that it gets stronger as particles move farther apart, up to a certain point, after which it basically disappears (I think, you should get a better source for this). That's why you will never find a "free" quark. They are always bound in protons and neutrons, or at higher energies, mesons. There is no actual accepted theory of unification between the strong force and the electromagnetic force, as there is between the electromagnetic and weak forces. But the strength of these three forces seem to approach one another at a rather high energy, (unlike gravity, which is part of the reason why quantum theories of gravity often have extra dimensions, where this "missing force" leaks into). The strong force also holds the nucleus together, via interactions between protons and neutrons, thus dominating the electromagnetic force at these small scales.

Hopefully, this answered some of your questions.

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Re: Common Questions

Postby Tchebu » Fri May 02, 2008 9:30 pm UTC

Just one thing.

Another interesting aspect of the strong force is that it gets stronger as particles move farther apart, up to a certain point, after which it basically disappears


This isn't right. The force doesn't stop at a certain point, what happens is if you try to rip apart a meson, for example, the potential energy between the quarks will increase, since the force increases with distance. When that energy becomes high enough, it forms two new quarks and you get back to where you started, just with two mesons instead of one. This is why you'll never get free quarks.
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Re: Common Questions

Postby thoughtfully » Fri May 02, 2008 9:37 pm UTC

I've read that the force doesn't increase, it just doesn't decrease, in other words, it is constant at any distance. The article is on wikipedia, and a little hand-wavey, so I'm not sure what to think of it. Anyone care to clarify?
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Re: Common Questions

Postby zenten » Wed May 07, 2008 7:38 pm UTC

capella wrote:Here are some astronomical tidbits - enjoy:
1 Astronomical Unit (AU) = approx. 93 million miles = approx. 150km


That's looking like a typo there :)

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Re: Common Questions

Postby Rippy » Thu May 08, 2008 2:59 am UTC

Here's one to that isn't physics!

How come human abdominal muscles are bumpy instead of being a smooth curve like any other muscle? (technically that's science, isn't it?)

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Re: Common Questions

Postby ian » Thu May 08, 2008 11:21 am UTC

Rippy wrote:Here's one to that isn't physics!

How come human abdominal muscles are bumpy instead of being a smooth curve like any other muscle? (technically that's science, isn't it?)


Are they? I'm pretty sure they aren't.

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Re: Common Questions

Postby Turambar » Sat May 10, 2008 9:53 pm UTC

Well, I looked it up, and it's because the abdominal muscles are crossed by three different tendons, which divide it into a "six-pack".

http://en.wikipedia.org/wiki/Linae_transversae
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Re: Common Questions

Postby Rippy » Mon May 12, 2008 1:46 am UTC

Ah, well, that would explain everything wouldn't it. I have another non-physics one which I kind of know the answer of, but I don't think I quite fully understand: why is water thought to be so critical to life? I mean, the bodily uses for it (for humans at least) that I know of are:
- regulating body temperature (perspiration)
- digesting food (salivation, and probably more factors I don't know of)
- flushing out excess substances (urination)

But none of those seem like things that only water can do. My suspicion is that it's something to do with how fats and other nutrients are broken down during digestion, but I've never seen it explained before. It's surprisingly hard to google. (can't think of any better keywords than "why water critical life")

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Re: Common Questions

Postby Klotz » Mon May 12, 2008 2:45 am UTC

How do ferromagnets attract each other? It looks like they just go directly towards each other coulomb-style, but that seems like it violates the del dot B=0 Maxwell equation.

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Re: Common Questions

Postby Tchebu » Mon May 12, 2008 3:22 am UTC

Water is essential to life because it's almost a universal solvant when liquid, and the most abundant one in the universe at that, which allows all the chemistry in you to work.
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Re: Common Questions

Postby BlochWave » Mon May 12, 2008 3:31 am UTC

Water is also important to life because

1)It has a very high specific heat compared to most any other liquid you can think of. We're mostly water. Put that together!

2)Frozen water is less dense than liquid water. This isn't normal for liquids. The result is that as a body of water freezes the ice ends up on top insulating the water and keeping it liquid. This is vital to aquatic life surviving in cold climates

3)Excellent properties when it comes to acids and bases. Been too long since chem 2 to be specific.

4)It's high surface tension is important too but I forget why

Try googling *shudder* astrobiology

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Re: Common Questions

Postby btarlinian » Mon May 12, 2008 10:12 pm UTC

Rippy wrote:Ah, well, that would explain everything wouldn't it. I have another non-physics one which I kind of know the answer of, but I don't think I quite fully understand: why is water thought to be so critical to life? I mean, the bodily uses for it (for humans at least) that I know of are:
- regulating body temperature (perspiration)
- digesting food (salivation, and probably more factors I don't know of)
- flushing out excess substances (urination)

But none of those seem like things that only water can do. My suspicion is that it's something to do with how fats and other nutrients are broken down during digestion, but I've never seen it explained before. It's surprisingly hard to google. (can't think of any better keywords than "why water critical life")


The short answer to that question is hydrogen bonds. Water forums very strong hydrogen bonds with itself, which leads to ice being less dense than water due its cyrstalline structure, the hydrophobic effect, which is key to protein folding, the deprotonation of acids, and basically a million other things.

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Re: Common Questions

Postby BlochWave » Tue May 13, 2008 4:29 am UTC

How do ferromagnets attract each other? It looks like they just go directly towards each other coulomb-style, but that seems like it violates the del dot B=0 Maxwell equation.


This may help
http://farside.ph.utexas.edu/teaching/3 ... ode77.html

Keep in mind that a permanent ferromagnet(a bar magnet in other words)is painfully roughly approximately a magnetic dipole. As you can see, it possessing a magnetic moment tells you do in fact have moving charges, like a current carrying loop
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Re: Common Questions

Postby Rippy » Wed May 14, 2008 10:50 pm UTC

Thanks for all the "Re: Water" responses. I didn't realize that water was crucial for a bazillion different reasons and not just one or two of them.

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Re: Common Questions

Postby Baza210 » Sun May 18, 2008 5:43 pm UTC

When a neutron decays <or so they say> to form a proton and an electron, why is the electron emitted from the nucleus rather than being attracted to the positive nucleus?



Strong Nuclear Force being repulsive as well as attractive? I haven't really studied particle Physics :|
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Re: Common Questions

Postby Turambar » Mon May 19, 2008 8:04 am UTC

Baza210 wrote:When a neutron decays <or so they say> to form a proton and an electron, why is the electron emitted from the nucleus rather than being attracted to the positive nucleus?

Because when a neutron decays a lot of energy is released, and much of it goes into kinetic energy for the electron and proton. So despite the strong attraction, the electron's velocity is so great that it easily escapes the nucleus.

Strong Nuclear Force being repulsive as well as attractive? I haven't really studied particle Physics :|

It is not, so far as I understand, actively repulsive, but becomes very weak and approaches zero at arbitrarily close distances. At these distances, similar electric charges of the quarks may cause the net force to be repulsive.

Essentially, the Strong Force interacts between quarks (and, by extension, between neutrons and protons, which are composed of quarks) and is carried by gluons, which themselves are also affected by the strong force. The gluons act to amplify the color charge of the quarks (color charge can be thought of as the Strong Force's analogue of electric charge), but very close to the quarks, the gluon's influence is weaker. So when quarks are very close together, there's not much room for the gluons to interact, so they don't contribute very much. This decreases the strength of the Strong Force at very close distances, preventing it from becoming infinite as distance approaches zero. As distances increase, however, the room for the gluons to act increases, and so the strength of the Strong Force increases as well, which is probably why single quarks are never seen by themselves.
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Re: Common Questions

Postby quintopia » Mon May 19, 2008 8:34 am UTC

Although I've heard that a message cannot be transmitted faster than light speed, I have also heard it said that in some models of the universe, the definition of "message" includes the knowledge of the location of the sender. Thus, there is some way to transmit message content at superluminal speed if there is very high doubt as to the origin of the message. Is this true? In which models is it true, if so?

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Re: Common Questions

Postby Turambar » Mon May 19, 2008 10:46 pm UTC

quintopia wrote:Although I've heard that a message cannot be transmitted faster than light speed, I have also heard it said that in some models of the universe, the definition of "message" includes the knowledge of the location of the sender. Thus, there is some way to transmit message content at superluminal speed if there is very high doubt as to the origin of the message. Is this true? In which models is it true, if so?


I think the concept behind those models has less to do with the sender's location being the content of the message than with the idea that if the sender's location is uncertain, then the distance the message is sent is also uncertain. That's my suspicion. But people have been speculating at ways to send things faster-than-light ever since Einstein told us we couldn't, and so far nobody has had any success in coming up with a reasonable mechanism for such communication. String theory's hypothesized tachyons are one example: not impossible, theoretically speaking, provided that they are extremely unstable, but also not exceptionally well supported.
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Re: Common Questions

Postby Baza210 » Wed May 21, 2008 8:56 pm UTC

Thanks Turambar. I'm guessing the electron gets most of the kinetic to satisfy CofM.
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Re: Common Questions

Postby Turambar » Thu May 22, 2008 8:27 am UTC

Baza210 wrote:Thanks Turambar. I'm guessing the electron gets most of the kinetic to satisfy CofM.

Yar. Wikipedia says that in some cases the electron can have "ultrarelativistic" velocities. My calculator is up two flights of stairs, so I'm not going to try and speculate on numbers.

This is why I love these forums: they cause me to waste hours on Wikipedia reading about W- bosons and other random things.
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Re: Common Questions

Postby Soralin » Sat May 24, 2008 9:44 pm UTC

eternauta3k wrote:Free-falling objects experience the same acceleration no matter their mass.


Not true, say for example you have a heavy object and a light one. Say, for object #1 you have a bowling ball, and for object #2 you have.. Mars. Now if you were to drop Mars (neglecting air resistance), it would hit the ground before the bowling ball did. Because, while the instant gravitational acceleration of the earth is the same on both the bowling ball and Mars at a given distance, Mars has more mass, and so it produces a greater gravitational force on the Earth then the bowling ball does. So Mars cheats, it hits the ground first through pulling the ground closer to it. But not only does it hit the ground sooner, it also accelerates faster over the whole fall, since gravitational acceleration is inversely proportional to the square of the distance between the objects, and the distance between Mars and the Earth would close faster then between the bowling ball and Earth, that means the rate of acceleration increase(from the increased gravitational acceleration from being closer) would be greater for Mars then the bowling ball.

So all else being equal, heavy objects do accelerate faster then light ones. ;)

(Note, orbital mechanics may have an impact with some tests, it may be recommended to do your tests in deep space, and to remove any atmosphere for a more reliable result. You may also wish to structurally reinforce your planets or planetoids to prevent them being pulled apart by tidal forces during the test)

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Re: Common Questions

Postby Mettra » Sat May 24, 2008 10:54 pm UTC

Soralin wrote:
eternauta3k wrote:Free-falling objects experience the same acceleration no matter their mass.


Not true, say for example you have a heavy object and a light one. Say, for object #1 you have a bowling ball, and for object #2 you have.. Mars. Now if you were to drop Mars (neglecting air resistance), it would hit the ground before the bowling ball did. Because, while the instant gravitational acceleration of the earth is the same on both the bowling ball and Mars at a given distance, Mars has more mass, and so it produces a greater gravitational force on the Earth then the bowling ball does. So Mars cheats, it hits the ground first through pulling the ground closer to it. But not only does it hit the ground sooner, it also accelerates faster over the whole fall, since gravitational acceleration is inversely proportional to the square of the distance between the objects, and the distance between Mars and the Earth would close faster then between the bowling ball and Earth, that means the rate of acceleration increase(from the increased gravitational acceleration from being closer) would be greater for Mars then the bowling ball.

So all else being equal, heavy objects do accelerate faster then light ones. ;)

(Note, orbital mechanics may have an impact with some tests, it may be recommended to do your tests in deep space, and to remove any atmosphere for a more reliable result. You may also wish to structurally reinforce your planets or planetoids to prevent them being pulled apart by tidal forces during the test)


All you've done is obfuscated the problem. From the frame of reference of the earth, it would appear that Mars is accelerating harder, but that's now a non-inertial frame of reference since earth is being accelerated noticeably towards Mars. From an inertial frame of reference, Mars will experience the same acceleration as the bowling ball.
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Re: Common Questions

Postby Soralin » Sun May 25, 2008 3:35 pm UTC

Mettra wrote:All you've done is obfuscated the problem. From the frame of reference of the earth, it would appear that Mars is accelerating harder, but that's now a non-inertial frame of reference since earth is being accelerated noticeably towards Mars. From an inertial frame of reference, Mars will experience the same acceleration as the bowling ball.


Actually, it should work in an inertial frame as well. Take an inertial frame at the position and velocity of the earth at the start of the experiment. Say that the Earth's pull is 1000 units/second2 at a distance of 100 units. And Mar's pull is 100 units/second2 at a distance of 100 units. And the bowling ball's gravitational pull is negligible. Start the objects 1000 units away from Earth, in two separate trials. I'm just going to use some crude discrete calculations for demonstration. Since the gravitational pull of the earth at 100 units away is 1000 units/second2, the pull at 1000 units away is 10 units/second2 (gravity inversely proportional to the square of the distance). So after the first second, both the bowling ball and Mars are moving toward Earth at 10 units/second, and let's call that 10 units closer as well. But in the Mars drop trial, the Earth moves as well, the pull on it is 1 unit/second2 at a distance of 1000 units, and so it's at 1 unit/second, and say one unit closer to Mars.

Now here's where the situation changes. The bowling ball is 990 units away from Earth, but Mars is 989 units away from Earth. That means the gravitational acceleration for the bowling ball at that distance is now 10.2030405 units/second2, whereas Mars, being closer, has a gravitational pull at it's distance of 10.223684 units/second2. So the bowling ball in the next second, has a speed of 20.2030405 units/second from our inertial reference point, and Mars has a speed of 20.223684 units/second from our initial reference point. Earth would be up to 2.0223684 units/s for the Mars trial, and stationary still for the bowling ball. So Mars would then be at a distance of 966.7539 units, whereas the bowling ball would be at a distance of 969.7969 units. So then the gravitational acceleration of the Earth on the bowling ball at that distance would be 10.63257 units/second2. And the acceleration of Mars, being closer, would be 10.6996 units/second2.

And so on and so forth if I got the math roughly close. And so Mars, even from an inertial reference point, would be seen to have a greater acceleration over the whole trip, as can be seen looking at the speeds of both throughout the trip or the derivative thereof, because it's instant acceleration is increasing faster then the bowling ball, since it's getting closer sooner, and closer = more acceleration. :)

Note that this only works if you drop the bowling ball and Mars on two separate trials, since if you dropped them at the same time, the bowling ball would also be affected by Mars drawing Earth closer.

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Re: Common Questions

Postby Mettra » Sun May 25, 2008 4:59 pm UTC

Soralin wrote:And so on and so forth if I got the math roughly close. And so Mars, even from an inertial reference point, would be seen to have a greater acceleration over the whole trip, as can be seen looking at the speeds of both throughout the trip or the derivative thereof, because it's instant acceleration is increasing faster then the bowling ball, since it's getting closer sooner, and closer = more acceleration. :) [1]

Note that this only works if you drop the bowling ball and Mars on two separate trials, since if you dropped them at the same time, the bowling ball would also be affected by Mars drawing Earth closer. [2]


[1] That's just displacement. It most definitely is not acceleration. When you're talking about acceleration, you're talking about a force. The force of gravity is not dependent on the mass of the falling object.

Fg = (Gm1m2)/r2 = m1a

The m1's cancel out.

= (Gm2)/r2 = a

You can put a bowling ball or a sun there, and they will have the same acceleration.

/edit accidentally hit tab+enter


[2] If we magically nullify the gravitation forces between Mars and the bowling ball, and their centers of mass are exactly the same distance with the same orientation away from Earth, then they will both fall at exactly the same rate, even relative to the earth's surface.
zenten wrote:Maybe I can find a colouring book to explain it to you or something.

Soralin
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Re: Common Questions

Postby Soralin » Sun May 25, 2008 6:02 pm UTC

[1] That's just displacement. It most definitely is not acceleration. When you're talking about acceleration, you're talking about a force. The force of gravity is not dependent on the mass of the falling object.

Fg = (Gm1m2)/r2 = m1a

The m1's cancel out.

= (Gm2)/r2 = a

You can put a bowling ball or a sun there, and they will have the same acceleration.


You're right that the force of gravity isn't dependent on the mass of the falling object, however, it is dependent on the distance of the falling object from the center of mass of the other object. And the distance closes more rapidly between two massive objects then it does between a massive object and a small object. And so therefore acceleration should be greater, or really, that the rate of increase of the acceleration is greater. The key isn't the m in those equations, it's the r (or I suppose it should be d for distance or such because radius would just be for surface gravity), r is not constant, therefore the force is not constant. The dr/dt for Mars is a greater negative then the dr/dt for the bowling ball is, and since a = (Gm2)/r2, and r starts out positive, that means that the da/dt is greater. And since the da/dt is greater for mars, and both start out with the same a, then a must be greater for Mars over time. Or maybe I'm just saying the wrong thing, the rate of increase of acceleration is greater for Mars, the average acceleration over a given time between the start and impact of Mars, is greater for Mars. The instant acceleration at a given time after the start is greater for Mars.

I agree that the instant acceleration of any object, no matter it's mass, at the same distance from the object they're falling toward, is the same. However, the acceleration of an object as it falls is not constant, the closer it gets to the object it's falling toward, the greater it's acceleration is, due to being proportional to 1/r2. And so while the acceleration of any object at a given distance is the same, mars and the bowling ball will both experience the same acceleration at the same distance, since the heavy object moves Earth more in it's direction, the distance between the two decreases at a faster rate for the heavier object (all else being equal, and dropped on separate trials), and since the distance decreases faster, the acceleration increases faster, since gravitational acceleration is dependent on the distance between the objects.

Basically, while the instant acceleration at any given point is always the same for any object, if you graphed the speed over the course of the whole fall, and took the derivative of it, the graph of acceleration over time should have Mars as slightly greater at any given time, due to the distance closing faster, due to the pull of the object moving Earth closer to it.

[2] If we magically nullify the gravitation forces between Mars and the bowling ball, and their centers of mass are exactly the same distance with the same orientation away from Earth, then they will both fall at exactly the same rate, even relative to the earth's surface.


Agreed if they're dropped at the same time, what I mentioned only works out if they're dropped in different trials, due to the gravitational effect of the objects on the Earth.

Mettra
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Re: Common Questions

Postby Mettra » Sun May 25, 2008 6:37 pm UTC

Soralin wrote:Basically, while the instant acceleration at any given point is always the same for any object, if you graphed the speed over the course of the whole fall, and took the derivative of it, the graph of acceleration over time should have Mars as slightly greater at any given time, due to the distance closing faster, due to the pull of the object moving Earth closer to it.


I think I see what you mean now. But it is the derivative of acceleration you are talking about and not acceleration. You are saying that the rate of acceleration (commonly called the jerk) is higher for Mars in a problem where the Earth isn't nailed down since the Earth will be at a smaller radius in a given dt (so the force will be higher) to Mars than it would be to a bowling ball in the same experiment.
zenten wrote:Maybe I can find a colouring book to explain it to you or something.

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Re: Common Questions

Postby Soralin » Sun May 25, 2008 7:40 pm UTC

Mettra wrote:I think I see what you mean now. But it is the derivative of acceleration you are talking about and not acceleration. You are saying that the rate of acceleration (commonly called the jerk) is higher for Mars in a problem where the Earth isn't nailed down since the Earth will be at a smaller radius in a given dt (so the force will be higher) to Mars than it would be to a bowling ball in the same experiment.


Yeah, the acceleration at a given time is higher for the mars drop, but the acceleration at a given distance isn't. da/dt is greater for Mars, and da/dr is the same for all objects. It would be the rate of acceleration, but it would also affect the acceleration, the increase of velocity over time, dv/dt, is larger as well, as I was trying to show in my example.

Mettra
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Re: Common Questions

Postby Mettra » Sun May 25, 2008 8:27 pm UTC

Soralin wrote:Yeah, the acceleration at a given time is higher for the mars drop, but the acceleration at a given distance isn't. da/dt is greater for Mars, and da/dr is the same for all objects. It would be the rate of acceleration, but it would also affect the acceleration, the increase of velocity over time, dv/dt, is larger as well, as I was trying to show in my example.


The only thing I take issue with is that you seem to be slightly stretching the meaning of acceleration but are trying to say something else altogether.

The statement 'massive bodies fall at the same rate' does not mean that two objects with different masses will complete their journey at the same time. There is a huge multi-lecture-sized context in which this simple statement needs to be taken. Yes, Mars will collide with Earth before the bowling ball would, given two identical experiments. But that isn't saying anything about acceleration. The reason this happens is that the jerk of one is higher than the other.

The statement 'massive bodies fall at the same rate' is talking about a particular kind of experiment (one on the earth) in which the earth is nailed down. But the statement itself isn't of importance, it's the consequences of the statement given the context of the experiments it's talking about. It says that if you drop any two objects on a nailed down earth, they will arrive at the same time. But this means that the objects experience exactly the same force (and therefore acceleration) independent of their mass at any given distance r. All of that is what people say in short by saying 'massive bodies fall at the same rate'.

At t=0, both objects start at a distance r. In a time dt, they would both feel the same force (at distance r) and be accelerated the same amount. However, the earth would also experience a force (and acceleration) from each of them. It just so happens that the force on Earth from Mars is higher (therefore the acceleration is higher). So in the next dt, Mars would be at a smaller r than the bowling ball. This means that the force would be higher (and that the acceleration would be higher). This entire paragraph is equivalent to 'the jerk of Mars is higher than the jerk of the bowling ball'.

You are trying to state the problem in terms of acceleration, but you could just as well say it in terms of velocity or position. But none of those causes the phenomenon of Mars meeting Earth before the bowling ball. The difference in jerk is what causes it. Putting it in terms of acceleration, velocity, or position confuses the semantics of what's going on. You already had it when you said da/dt is bigger for Mars.
zenten wrote:Maybe I can find a colouring book to explain it to you or something.

Soralin
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Re: Common Questions

Postby Soralin » Sun May 25, 2008 9:03 pm UTC

Sounds good. :) Yeah, my terminology was a bit confused while I was writing it as well. I basically just wanted to cover the sort of secondary effects, that if you were sitting in the inertial frame where Earth started at and pointed a laser rangefinder at the falling object, or measured the velocity (or acceleration) or such of the object falling, that you wouldn't necessarily get the same result on two trails for two different falling objects of different masses.


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