Why the weight falls and the volumes do not decrease

ROBERT KNESCHKE/123RF

Continue taking up new activities as you get older to keep you brain healthy.

As we reach adulthood, we notice changes in our bodies at every stage of ageing. We might find we need glasses when we hit our thirties, we can’t keep weight off as easily into our forties, we mightn’t feel as strong playing sport with the kids in our fifties, and we can’t hear a conversation across a crowded dinner table in our sixties.

All of these occur because the cells and processes in our bodies have existed for longer and longer periods of time. There are many theories as to why our body ages, but two main explanations are that the DNA within our genes determine how long we will live; the other is that over time, our body and DNA are damaged until they can no longer function as before, often referred to as “wear and tear”.

THE AGEING BRAIN

As we age, the volume of the brain declines. There are many explanations for this, including cell death, in which the brain cells’ structure declines over time.

Although the precise reasons for the decline in brain volume remain unclear, some research indicates it may be due to hormone levels, and wear and tear.

READ MORE:
* People in their 90s reveal the secrets to ageing well
* What’s an ageing mind to do?
* Aging naturally: I’ve always been glad to be grey

Some also believe that the volume of blood reaching the brain decreases due to conditions within the blood vessels and associated systems. However, this doesn’t have a great impact on a person’s ability to remember, as the brain has the ability to compensate for these changes.

You may have heard of neuroplasticity. This is the term used to explain how the brain can rewire itself by creating new pathways within the nerve cells to compensate for damage to an area. These new pathways are created when new experiences occur. So doing crosswords all of your life won’t increase the number of pathways, but if you add a new activity that you need to learn and practise, then new pathways can form.

While the risk of dementia increases with age due to many of the hundreds of causes being more present as we age, it is not a normal part of the ageing process. It is a result of damage to the brain. The reason why it is more likely to occur as we age is simply because the longer we live, the longer we expose ourselves to possible damage to the body through disease or injury, which are the main causes of dementia.

Alzheimer’s Disease occurs when there is plaque build-up in the brain. This is as a result of protein build-up over time that inevitably causes tangles in the neurons (brain cells).

CHANGES IN MUSCLE STRENGTH

As we age, there’s a decrease in the amount and strength of muscle tissue, due mostly to the influence of decreasing hormones. To make up for the muscle mass lost during each day of strict bed rest, older people may need to exercise for up to two weeks.

However, additional decreases in muscle occur due to a decrease in activity, not just as part of the normal ageing process.

DECREASE IN BONE DENSITY

As the body ages it absorbs less calcium from food, a vital mineral for bone strength. At the same time, changes in hormone levels affect the density of the bones.

Ageing people also often spend less time in the sun, thereby reducing their Vitamin D intake. This in turn reduces calcium absorption.

It is important people continue to exercise as they age. Exercise will not only help to maintain muscle strength, but also assist in combatting the decrease in bone density that occurs as the body ages, thereby reducing the risk of falls and hip fractures.

CHANGES TO OUR SENSES

Changes that occur directly as a result of ageing include those to vision, hearing, taste and smell. Impacts of the changes in vision are usually the first things noticed, making a person feel that they are ageing.

Changes to the eye that occur as part of the ageing process include stiffening and colouring of the lens, a reduction in the number of nerve cells, and a decrease in fluid in the eye. These lead to difficulty in focusing on close objects, seeing in low light becomes more difficult, and the ability to adapt to changes in light decline.

Some people appear clumsy, as their ability to judge the distance between objects – a cup and table, for example, or the height of stairs – becomes a problem. Many people do not realise their spills and trips are occurring as a result of shifts in their vision, known as depth perception changes. Eyes can also become drier, making them feel irritated. This can be treated with lubricating drops.

Changes in hearing include changes in registering high-pitched sounds, and words may become difficult to understand. Speaking more loudly to someone in this circumstance does not help, as the pitch is the problem, not the volume. Instead speaking slightly slower and concentrating on complete words can be helpful.

Taste and smell often decrease as part of the normal ageing process, as the cells responsible decrease in number and the ability to regenerate worn out cells decreases with age. The results make food less tasty and people less likely to eat. In addition, people’s taste can change altogether, so people who loved chocolate as a young person may prefer chilli as they age.

Overall there are many changes to the body as part of the normal ageing process as well as many that occur as a result of lifestyle factors. We are not all fated to age in a negative spiral. Many lifestyle choices made earlier in life can assist us in the future. With proactive decisions and community understanding, we can look forward to adapting to a positive ageing process.

Lisa Hee, Director of Healthy Ageing and Dementia Programs School of Nursing and Midwifery, PhD candidate in ?, CQUniversity Australia.

This article was originally published on The Conversation. Read the original article.

www.stuff.co.nz

Most of the time, people ask this question with the idea of a Newtonian “feather vs. bowling ball” concept in mind. Based on those terms, the typical answer is correct: two objects will fall at the same speed in a vacuum, and air resistance can appear to make an object fall slower. However, there is a surprising, but more complicated nuance to this problem.

Every action has an equal and opposite reaction. This means that, just as the Earth is exerting a gravitational force on the objects, the objects are exerting a gravitational force on the Earth. Just as much as the objects fall onto the Earth, the Earth falls onto the objects as well. It’s just the fact that the Earth is so much larger and more massive that we default to viewing things from the first perspective and not the latter. Nevertheless, the gravitational force exerted on the Earth by the objects cannot be ignored.

Gravitational force is determined by the Universal Gravitation law:

`F = (GmM)/r^2`

where m and M are the two masses involved in the interaction. If we do two separate calculations, one for the mass of the lesser object, and one for the mass of the greater object, we can see that there will actually be a larger gravitational force involved with the more massive object.

This is where most people would interject that, well, yes, the larger mass needs a larger force in order to achieve the same acceleration. But reverse the frame of reference; now let’s consider this from the point of view of the objects doing the pulling, instead of the Earth. Now we can see that the force exerted by the larger mass is doing more pulling than the smaller mass. The Earth will “hit” the larger mass first.

Mind you, the scale that this takes place on is smaller than we can actually measure with our current technology. However, it makes sense if you consider it in a different way; If you held a brick and the Moon at the same height and dropped them, which would hit first?

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  1. Say you compress a closed container full of gas (you reduce its volume). You are not holding the pressure constant or anything.

    As you do this, the temperature increases, but why? My best guesses are:

    – some of the energy you use for pressing down on the container is transferred to heat energy and thus increasing the temperature (?)
    – the force exerted on pushing the container down is passed onto colliding particles, thus increasing their kinetic energy

    But these two explanations would only increase the average kinetic energy by a small amount, if at all.

    Is there an explanation for this using kinetic theory?

  2. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations If you compress a gas (say with a piston) the piston will be moving inwards. The molecules that bounce against it will rebound with a higher velocity (however slowly you do it, you will still get the same answer). This means they will transfer this increased kinetic energy to all the other molecules. They will then be striking the walls of the container faster. There is more change of momentum at each collision – so more force – so more pressure.

    Now – the molecules are travelling faster (average speed) so this implies a rise in temperature. If you cool the container down to its original temperature there is STILL a different situation, despite the fact that the molecules have the same average speed as before. There is less distance for the molecules to travel between collisions with the walls so there will still be more collisions per second. This means that there will STILL be an increase in pressure.

    The “small amount” in your post is Just Enough to produce the right answer.

  3. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations

    If you compress a gas (say with a piston) the piston will be moving inwards. The molecules that bounce against it will rebound with a higher velocity (however slowly you do it, you will still get the same answer). This means they will transfer this increased kinetic energy to all the other molecules. They will then be striking the walls of the container faster. There is more change of momentum at each collision – so more force – so more pressure.

    Now – the molecules are travelling faster (average speed) so this implies a rise in temperature. If you cool the container down to its original temperature there is STILL a different situation, despite the fact that the molecules have the same average speed as before. There is less distance for the molecules to travel between collisions with the walls so there will still be more collisions per second. This means that there will STILL be an increase in pressure.

    The “small amount” in your post is Just Enough to produce the right answer.

    Surely the speed of the compressing piston is negligible compared to the speed of the molecules in the gas?

    I would have thought that the increase in temperature is more likely due to the increased rate of collisions between the molecules…

    When the molecules are travelling freely between collisions, they are unlikely to radiate infra-red radiation but can absorb infra-red radiation. When the molecules collide, they are more likely to release infra-red radiation.

    When the gas is compressed and the molecules are closer together, their mean time between collisions is less, so there is more infra-red radiation being released than before the compression.

    The opposite happens when a gas is expanded – the molecules are further apart and their mean time between collisions increases, so there is more infra-red radiation being absorbed than before the expansion.

  4. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations

    I would have thought that the increase in temperature is more likely due to the increased rate of collisions between the molecules…

    When the molecules are travelling freely between collisions, they are unlikely to radiate infra-red radiation but can absorb infra-red radiation. When the molecules collide, they are more likely to release infra-red radiation.

    You get an increase in temperature even for an ideal gas, in which you assume either that the molecules don’t interact at all, or that they collide completely elastically without losing kinetic energy. Remember, PV = nRT is for an ideal gas!

  5. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations

    You get an increase in temperature even for an ideal gas, in which you assume either that the molecules don’t interact at all, or that they collide completely elastically without losing kinetic energy. Remember, PV = nRT is for an ideal gas!

    How can that be true – that ideal gases collide completely elastically without losing kinetic energy?

    For in that case, how would an ideal gas ever lose heat? Since an ideal gas atom (as they are typically mono-atomic) can always absorb an infra-red photon, but by what mechanism would the ideal gas atom emit an infra-red photon?

  6. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations An ideal gas does not interact with radiation.

    The additional energy comes from elastic collisions with the compressing wall. Even if the wall moves very slowly, it is far more massive than an atom and the elastic collision will increase the atom’s speed quite a lot (momentum conservation). Since the temperature of a gas is proportional to the square of the rms speed of the molecules, this compression leads to a very noticeable increase in temperature.

    eg. for an adiabatic compression, (T’/T) = (V/V’)^(gamma – 1)

    So if you halve the volume (V/V’ = 2) of a diatomic gas (gamma = 7/5), the temperature will increase by a factor of 2^0.4 = 1.32. In terms of Kelvin that’s the equivalent of going from room temperature to about 125 C!

  7. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations

    Surely the speed of the compressing piston is negligible compared to the speed of the molecules in the gas?

    “Surely”????
    It may seem counter-intuitive but you won’t be able to show that the statement is wrong. Remember that every molecule that strikes the piston will have its speed increased by the massive piston. This can happen quickly or slowly, depending on the speed of the piston and, however quickly or slowly the change is made, the KE is redistributed amongst all the molecules to produce a different velocity distribution.
    The argument to justify Boyle’s Law (constant temperature situation) is fairly easy to grasp because it just depends on the reduced amount of space and the resulting frequency of collisions. To derive the full Gas Law is a bit more long winded and I recommend that you hunt around on the web for a website that presents it at a level you can cope with. Just think of the actual work done on a gas to compress it to half its volume. All that energy has to go somewhere and the only way it can be transferred for an ideal gas is by speeding up the molecules by contact with the piston.

  8. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations It has more to do with quantum mechanics, if you really want to talk about it in a way that gets at the fundamental reasons behind it all.

    Temperature is a measure of how “spread out” the particles are over all possible energy levels. At low temperatures, the particles are concentrated mostly in the lowest available energy levels, where as at higher temperatures they’re more spread out.

    If when you compress a volume, you decrease the spacing between energy levels – this is is a result from quantum mechanics.

    If you decrease the spacing between energy levels, but don’t change the total energy, then the particles have to spread out and occupy higher energy levels in order to keep everything conserved, and by definition this is a higher temperature.

    I think this is really the best way to think about it.

  9. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations

    It has more to do with quantum mechanics, if you really want to talk about it in a way that gets at the fundamental reasons behind it all.

    Temperature is a measure of how “spread out” the particles are over all possible energy levels. At low temperatures, the particles are concentrated mostly in the lowest available energy levels, where as at higher temperatures they’re more spread out.

    If when you compress a volume, you decrease the spacing between energy levels – this is is a result from quantum mechanics.

    If you decrease the spacing between energy levels, but don’t change the total energy, then the particles have to spread out and occupy higher energy levels in order to keep everything conserved, and by definition this is a higher temperature.

    I think this is really the best way to think about it.

    You are right, of course but it may not be necessary to understand this in depth as long as you can accept that there will be some sort of energy distribution amongst the molecules. That is a reasonable intermediate step in getting a handle on this, I feel. I realise that QM is necessary to deal with the ‘ultraviolet catastrophe’ but it’s a huge amount extra to take on board all in one go.

  10. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations Quote by robinpike

    Surely the speed of the compressing piston is negligible compared to the speed of the molecules in the gas?

    “Surely”????
    It may seem counter-intuitive but you won’t be able to show that the statement is wrong. Remember that every molecule that strikes the piston will have its speed increased by the massive piston. This can happen quickly or slowly, depending on the speed of the piston and, however quickly or slowly the change is made, the KE is redistributed amongst all the molecules to produce a different velocity distribution.
    The argument to justify Boyle’s Law (constant temperature situation) is fairly easy to grasp because it just depends on the reduced amount of space and the resulting frequency of collisions. To derive the full Gas Law is a bit more long winded and I recommend that you hunt around on the web for a website that presents it at a level you can cope with. Just think of the actual work done on a gas to compress it to half its volume. All that energy has to go somewhere and the only way it can be transferred for an ideal gas is by speeding up the molecules by contact with the piston.

    Hi I may be off base but I see some questions here.
    I understood that ideally slow compression or expansion was specifically to remove the momentum of the piston from consideration. Equivalent to ideally slow clock transport to remove time dilation as a factor.
    SO for expansion; no work is done by the gas to remove kinetic energy through transference of momentum to the piston. Or vise versa with compression
    Temperature is purely a function of internal kinetic energy so internal collisions are zero sum events and their increase in frequency through decreasing spatial relationships should have no effect on total energy, although it does have an affect on pressure which is dependent on number of collisions with the container walls.
    As I remember it the increase in internal temperature is related to the Van der Walls force.
    As such is a result of spatial reduction and the decrease in the mean distance between nuclei .
    I think for some monatomic gases, expansion for some pressure ranges actually results in temperature increase. Or reciprocally compression results in temperature decrease which seems to contradict any concept of piston imparted increased velocities.
    This force imparts an acceleration to proximate gas molecules dependent on distance and so does result in an overall increase in the mean probable velocity.
    If I am incorrect in any of these assumptions I will be happy to learn of it..

  11. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations I think you may be thinking in terms of isothermal changes or non-ideal gases. It has to be true that, if you insulate a mass of an ideal gas and do work in compressing it – and there is work involved in moving a piston against pressure (force times distance), however slowly you do it – then conservation of energy must apply (no?). The only place the energy can go must be into the internal energy of the gas. In an ideal gas, this must result in an increase in average K.E. – that is an increase in temperature.

    When Van der Waall’s forces are involved (non-ideal gases), you can get some of the work done transferred to potential energy and that will modify the temperature change – in either direction, I seem to remember.

  12. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations Look at the Wiki article on Joule Kelvin Effect. They make the distinction nicely between volume changes with and without work being done.

  13. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations

    Look at the Wiki article on Joule Kelvin Effect. They make the distinction nicely between volume changes with and without work being done.

    Thanks for the reference . In the meantime I had done some calculation with the increase in gas velocity being 2x the piston velocity per collision.
    Doing even a rough quesstimate of the number of collisions based on initial gas velocity and the average length of the container during compression, it was quite clear that no matter how negligible the piston velocity the net increase must be a significant percentage of the initial average velocity, even without considering the exponential increase in collision frequency with increasing velocity.
    SO I was badly mistaken in my idea of the effect of slow transport and the relative effects of the Van der Wall force.
    It makes me wonder about the conceptual basis of slow clock transport???
    Can you fool mother nature??
    Like a photon that can pop into existence out of nothing because it happens to quick for the conservation cops to take action 😉

    Thanks

  14. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations

    Thanks for the reference . In the meantime I had done some calculation with the increase in gas velocity being 2x the piston velocity per collision.

    Doing even a rough quesstimate of the number of collisions based on initial gas velocity and the average length of the container during compression, it was quite clear that no matter how negligible the piston velocity the net increase must be a significant percentage of the initial average velocity, even without considering the exponential increase in collision frequency with increasing velocity.

    SO I was badly mistaken in my idea of the effect of slow transport and the relative effects of the Van der Wall force.

    It makes me wonder about the conceptual basis of slow clock transport???

    Can you fool mother nature??

    Like a photon that can pop into existence out of nothing because it happens to quick for the conservation cops to take action 😉

    Thanks

    Glad your sums have convinced you about the reasonableness of that. Of course, the actual distribution of velocities after the change in volume needs the application of Quantum Theory to avoid the high energy problem.
    I think the slow clock transport thing with light speed is a different matter – possibly to do with the fact that one involves Energy transfer(?).

  15. A.T.

    Science Advisor

    Re: Why does temperature increase when volume decreases? (Kinetic theory explanations

    Surely the speed of the compressing piston is negligible compared to the speed of the molecules in the gas?

    The faster the molecules are, the more bounces with the moving wall will occur per time.

  16. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations

    The faster the molecules are, the more bounces with the moving wall will occur per time.

    That’s why both volume and temperature account for the pressure – according to the gas laws.

  17. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations A way to reconcile intuition with sophiecentaur’s good explanation is to imagine a container of gas at absolute zero, i.e. molecules absolutely at rest. Inserting the piston to compress the gas leaves particles with motion (increased temp) due to their encounter with the inward moving piston. Expansion cannot lower temp below absolute zero because the piston will not interact with the stationary gas molecules as it moves away.

    Interesting, it is possible to “cheat” Charle’s Law in the expansion case if the piston moves very fast, fast enough that no gas molecules collide with it while it is in motion.

    In this (impractical) case, the expansion would be simultaneously isothermal and adiabatic.

    Last edited: Nov 13, 2012

  18. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations

    A way to reconcile intuition with sophiecentaur’s good explanation is to imagine a container of gas at absolute zero, i.e. molecules absolutely at rest. Inserting the piston to compress the gas leaves particles with motion (increased temp) due to their encounter with the inward moving piston. Expansion cannot lower temp below absolute zero because the piston will not interact with the stationary gas molecules as it moves away.

    Interesting, it is possible to “cheat” Charle’s Law in the expansion case if the piston moves very fast, fast enough that no gas molecules collide with it while it is in motion.

    In this (impractical) case, the expansion would be simultaneously isothermal and adiabatic.

    That’s the equivalent of opening the side into a vacuum. No work is done then so no temperature drop for an ideal gas, I think.

  19. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations

    Look at the Wiki article on Joule Kelvin Effect. They make the distinction nicely between volume changes with and without work being done.

    Actually I first encountered this material in the past while researching the basis of compressive cooling. All the literature seemed to agree that such systems worked because gases cooled through expansion. This seemed to me to be a misconception equivalent to water as ice cooling through melting. In this case the ice has not only less KE than water at the same temp 0 deg C but greatly less internal energy.
    So a system designed to cool the gas itself would be totally adiabatic except for the extraction interface in the compressed phase. It seemed to me that if the energy extracted was only equal to the energy added by compression that the system would not work.
    Clearly in the case of gases where compression brought about a state transition this made available for extraction a significant amount of internal energy which could then leave the system as KE or radiation. SO the gas would have a much lower energy content even before the expansion phase.In other cases I understood that extra energy was available for extraction through actualization of Van der Waals potential.
    SO if we start with a volume of gas, say nitrogen, at environmental temp and bring it down to liquid temperature there is a huge net loss of energy.
    If this energy has not been extracted and now residing in the environment where in fact has it gone???
    The ideas that it was somehow “disappeared” through internal throttling seems like energy down the rabbit hole.
    Or if there are two equal volumes with equivalent PT that are expanded into twice the volume, one through throttling and one through free expansion , in the first case there is a reduction of temp but not in the second case.(ignoring Van der Waals effect).
    In the first case it is stated that there is work done even though there is no exchange with the outside. But if there is no work done on the valve, no transference of momentum, and the final condition is identical to free expansion as far as displacement of the gas itself where is the result of this work. I.e., where did the energy go??
    Thanks

  20. Re: Why does temperature increase when volume decreases? (Kinetic theory explanations I didn’t get the details of all that but when you add all the Kinetic Energies and all the Potential Energies and the Work in or out, the sum will be zero. It’s just a matter of modelling the particular substance right. The devil must be in the detail of the changes of Potential Energy as the volume changes and the work done. I don’t think you can ignore Van der Vaal because that blanket term accounts for the departure from idea l behaviour.

    Similar Discussions: Why does temperature increase when volume decreases? (Kinetic theory explanations)

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S represents the light source, while r represents the measured points. The lines represent the

flux

emanating from the source. The total number of

flux lines

depends on the strength of the source and is constant with increasing distance, where a greater density of flux lines (lines per unit area) means a stronger field. The density of flux lines is inversely proportional to the square of the distance from the source because the surface area of a sphere increases with the square of the radius. Thus the strength of the field is inversely proportional to the square of the distance from the source.

The inverse-square law, in physics, is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be understood as geometric dilution corresponding to point-source radiation into three-dimensional space (see diagram).

Radar energy expands during both the signal transmission and also on the reflected return, so the inverse square for both paths means that the radar will receive energy according to the inverse fourth power of the range.

In order to prevent dilution of energy while propagating a signal, certain methods can be used such as a waveguide, which acts like a canal does for water, or how a gun barrel restricts hot gas expansion to one dimension in order to prevent loss of energy transfer to a bullet.

Formula

Mathematically notated :

intensity ∝ 1distance2{displaystyle {text{intensity}} propto {frac {1}{{text{distance}}^{2}}},}

It can also be mathematically expressed as :

intensity1intensity2=distance22distance12{displaystyle {frac {{text{intensity}}_{1}}{{text{intensity}}_{2}}}={frac {{{text{distance}}_{2}}^{2}}{{{text{distance}}_{1}}^{2}}}}

or as the formulation of a constant quantity :

intensity1×distance12=intensity2×distance22{displaystyle {text{intensity}}_{1}times {{text{distance}}_{1}}^{2}={text{intensity}}_{2}times {{text{distance}}_{2}}^{2}}

The divergence of a vector field which is the resultant of radial inverse-square law fields with respect to one or more sources is everywhere proportional to the strength of the local sources, and hence zero outside sources. Newton’s law of universal gravitation follows an inverse-square law, as do the effects of electric, magnetic, light, sound, and radiation phenomena.

Justification

The inverse-square law generally applies when some force, energy, or other conserved quantity is evenly radiated outward from a point source in three-dimensional space. Since the surface area of a sphere (which is 4πr2 ) is proportional to the square of the radius, as the emitted radiation gets farther from the source, it is spread out over an area that is increasing in proportion to the square of the distance from the source. Hence, the intensity of radiation passing through any unit area (directly facing the point source) is inversely proportional to the square of the distance from the point source. Gauss’ law is similarly applicable, and can be used with any physical quantity that acts in accord to the inverse-square relationship.

Occurrences

Gravitation

Gravitation is the attraction of two objects with mass. Newton’s law states:

The gravitational attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation distance. The force is always attractive and acts along the line joining them.

If the distribution of matter in each body is spherically symmetric, then the objects can be treated as point masses without approximation, as shown in the shell theorem. Otherwise, if we want to calculate the attraction between massive bodies, we need to add all the point-point attraction forces vectorially and the net attraction might not be exact inverse square. However, if the separation between the massive bodies is much larger compared to their sizes, then to a good approximation, it is reasonable to treat the masses as point mass while calculating the gravitational force.

As the law of gravitation, this law was suggested in 1645 by Ismael Bullialdus. But Bullialdus did not accept Kepler’s second and third laws, nor did he appreciate Christiaan Huygens’s solution for circular motion (motion in a straight line pulled aside by the central force). Indeed, Bullialdus maintained the sun’s force was attractive at aphelion and repulsive at perihelion. Robert Hooke and Giovanni Alfonso Borelli both expounded gravitation in 1666 as an attractive force (Hooke’s lecture “On gravity” at the Royal Society, London, on 21 March; Borelli’s “Theory of the Planets”, published later in 1666). Hooke’s 1670 Gresham lecture explained that gravitation applied to “all celestiall bodys” and added the principles that the gravitating power decreases with distance and that in the absence of any such power bodies move in straight lines. By 1679, Hooke thought gravitation had inverse square dependence and communicated this in a letter to Isaac Newton. Hooke remained bitter about Newton claiming the invention of this principle, even though Newton’s Principia acknowledged that Hooke, along with Wren and Halley, had separately appreciated the inverse square law in the solar system, as well as giving some credit to Bullialdus.

Electrostatics

The force of attraction or repulsion between two electrically charged particles, in addition to being directly proportional to the product of the electric charges, is inversely proportional to the square of the distance between them; this is known as Coulomb’s law. The deviation of the exponent from 2 is less than one part in 1015.

Light and other electromagnetic radiation

The intensity (or illuminance or irradiance) of light or other linear waves radiating from a point source (energy per unit of area perpendicular to the source) is inversely proportional to the square of the distance from the source; so an object (of the same size) twice as far away, receives only one-quarter the energy (in the same time period).

More generally, the irradiance, i.e., the intensity (or power per unit area in the direction of propagation), of a spherical wavefront varies inversely with the square of the distance from the source (assuming there are no losses caused by absorption or scattering).

For example, the intensity of radiation from the Sun is 9126 watts per square meter at the distance of Mercury (0.387 AU); but only 1367 watts per square meter at the distance of Earth (1 AU)—an approximate threefold increase in distance results in an approximate ninefold decrease in intensity of radiation.

For non-isotropic radiators such as parabolic antennas, headlights, and lasers, the effective origin is located far behind the beam aperture. If you are close to the origin, you don’t have to go far to double the radius, so the signal drops quickly. When you are far from the origin and still have a strong signal, like with a laser, you have to travel very far to double the radius and reduce the signal. This means you have a stronger signal or have antenna gain in the direction of the narrow beam relative to a wide beam in all directions of an isotropic antenna.

In photography and stage lighting, the inverse-square law is used to determine the “fall off” or the difference in illumination on a subject as it moves closer to or further from the light source. For quick approximations, it is enough to remember that doubling the distance reduces illumination to one quarter; or similarly, to halve the illumination increase the distance by a factor of 1.4 (the square root of 2), and to double illumination, reduce the distance to 0.7 (square root of 1/2). When the illuminant is not a point source, the inverse square rule is often still a useful approximation; when the size of the light source is less than one-fifth of the distance to the subject, the calculation error is less than 1%.

The fractional reduction in electromagnetic fluence (Φ) for indirectly ionizing radiation with increasing distance from a point source can be calculated using the inverse-square law. Since emissions from a point source have radial directions, they intercept at a perpendicular incidence. The area of such a shell is 4πr 2 where r is the radial distance from the center. The law is particularly important in diagnostic radiography and radiotherapy treatment planning, though this proportionality does not hold in practical situations unless source dimensions are much smaller than the distance. As stated in fourier theory of heat “as the point source is magnification by distances , its radiation is dilute proportional to the sin of the angle, of the increasing circumference arc from the point of origin”

Example

Let the total power radiated from a point source, for example, an omnidirectional isotropic radiator, be P. At large distances from the source (compared to the size of the source), this power is distributed over larger and larger spherical surfaces as the distance from the source increases. Since the surface area of a sphere of radius r is A = 4πr 2, the intensity I (power per unit area) of radiation at distance r is

I=PA=P4πr2.{displaystyle I={frac {P}{A}}={frac {P}{4pi r^{2}}}.,}

The energy or intensity decreases (divided by 4) as the distance r is doubled; measured in dB it would decrease by 6.02 dB per doubling of distance.

Sound in a gas

In acoustics, the sound pressure of a spherical wavefront radiating from a point source decreases by 50% as the distance r is doubled; measured in dB, the decrease is still 6.02 dB, since dB represents an intensity ratio. The pressure ratio (as opposed to power ratio) is not inverse-square, but is inverse-proportional (inverse distance law):

p ∝ 1r{displaystyle p propto {frac {1}{r}},}

The same is true for the component of particle velocity v{displaystyle v,} that is in-phase with the instantaneous sound pressure p{displaystyle p,}:

v ∝1r {displaystyle v propto {frac {1}{r}} ,}

In the near field is a quadrature component of the particle velocity that is 90° out of phase with the sound pressure and does not contribute to the time-averaged energy or the intensity of the sound. The sound intensity is the product of the RMS sound pressure and the in-phase component of the RMS particle velocity, both of which are inverse-proportional. Accordingly, the intensity follows an inverse-square behaviour:

I = pv ∝ 1r2.{displaystyle I = pv propto {frac {1}{r^{2}}}.,}

Field theory interpretation

For an irrotational vector field in three-dimensional space, the inverse-square law corresponds to the property that the divergence is zero outside the source. This can be generalized to higher dimensions. Generally, for an irrotational vector field in n-dimensional Euclidean space, the intensity “I” of the vector field falls off with the distance “r” following the inverse (n − 1)th power law

I∝1rn−1,{displaystyle Ipropto {frac {1}{r^{n-1}}},}

given that the space outside the source is divergence free.

History

John Dumbleton of the 14th-century Oxford Calculators, was one of the first to express functional relationships in graphical form. He gave a proof of the mean speed theorem stating that “the latitude of a uniformly difform movement corresponds to the degree of the midpoint” and used this method to study the quantitative decrease in intensity of illumination in his Summa logicæ et philosophiæ naturalis (ca. 1349), stating that it was not linearly proportional to the distance, but was unable to expose the Inverse-square law.

In proposition 9 of Book 1 in his book Ad Vitellionem paralipomena, quibus astronomiae pars optica traditur (1604), the astronomer Johannes Kepler argued that the spreading of light from a point source obeys an inverse square law:

Original: Sicut se habent spharicae superificies, quibus origo lucis pro centro est, amplior ad angustiorem: ita se habet fortitudo seu densitas lucis radiorum in angustiori, ad illamin in laxiori sphaerica, hoc est, conversim. Nam per 6. 7. tantundem lucis est in angustiori sphaerica superficie, quantum in fusiore, tanto ergo illie stipatior & densior quam hic.

Translation: Just as spherical surfaces, for which the source of light is the center, from the wider to the narrower, so the density or fortitude of the rays of light in the narrower , towards the more spacious spherical surfaces, that is, inversely. For according to 6 & 7, there is as much light in the narrower spherical surface, as in the wider, thus it is as much more compressed and dense here than there.

In 1645 in his book Astronomia Philolaica …, the French astronomer Ismaël Bullialdus (1605 – 1694) refuted Johannes Kepler’s suggestion that “gravity” weakens as the inverse of the distance; instead, Bullialdus argued, “gravity” weakens as the inverse square of the distance:

Original: Virtus autem illa, qua Sol prehendit seu harpagat planetas, corporalis quae ipsi pro manibus est, lineis rectis in omnem mundi amplitudinem emissa quasi species solis cum illius corpore rotatur: cum ergo sit corporalis imminuitur, & extenuatur in maiori spatio & intervallo, ratio autem huius imminutionis eadem est, ac luminus, in ratione nempe dupla intervallorum, sed eversa.

Translation: As for the power by which the Sun seizes or holds the planets, and which, being corporeal, functions in the manner of hands, it is emitted in straight lines throughout the whole extent of the world, and like the species of the Sun, it turns with the body of the Sun; now, seeing that it is corporeal, it becomes weaker and attenuated at a greater distance or interval, and the ratio of its decrease in strength is the same as in the case of light, namely, the duplicate proportion, but inversely, of the distances .

In England, the Anglican bishop Seth Ward (1617 – 1689) publicized the ideas of Bullialdus in his critique In Ismaelis Bullialdi astronomiae philolaicae fundamenta inquisitio brevis (1653) and publicized the planetary astronomy of Kepler in his book Astronomia geometrica (1656).

In 1663–1664, the English scientist Robert Hooke was writing his book Micrographia (1666) in which he discussed, among other things, the relation between the height of the atmosphere and the barometric pressure at the surface. Since the atmosphere surrounds the earth, which itself is a sphere, the volume of atmosphere bearing on any unit area of the earth’s surface is a truncated cone (which extends from the earth’s center to the vacuum of space; obviously only the section of the cone from the earth’s surface to space bears on the earth’s surface). Although the volume of a cone is proportional to the cube of its height, Hooke argued that the air’s pressure at the earth’s surface is instead proportional to the height of the atmosphere because gravity diminishes with altitude. Although Hooke did not explicitly state so, the relation that he proposed would be true only if gravity decreases as the inverse square of the distance from the earth’s center.

See also

  • Flux
  • Gauss’s law
  • Kepler’s first law
  • Telecommunications, particularly:
    • William Thomson, 1st Baron Kelvin
    • Power-aware routing protocols
  • Inverse proportionality
  • Multiplicative inverse
  • Distance decay

References

 This article incorporates public domain material from the General Services Administration document “Federal Standard 1037C”.

  1. ^ Hooke’s gravitation was also not yet universal, though it approached universality more closely than previous hypotheses: See page 239 in Curtis Wilson (1989), “The Newtonian achievement in astronomy”, ch.13 (pages 233–274) in “Planetary astronomy from the Renaissance to the rise of astrophysics: 2A: Tycho Brahe to Newton”, CUP 1989.
  2. ^ Thomas Birch, The History of the Royal Society of London, … (London, England: 1756), vol. 2, pages 68–73; see especially pages 70–72.
  3. ^ Giovanni Alfonso Borelli, Theoricae Mediceorum Planetarum ex Causius Physicis Deductae of the Medicean planets deduced from physical causes] (Florence, (Italy): 1666).
  4. ^ Koyré, Alexandre (1952). “An Unpublished Letter of Robert Hooke to Isaac Newton”. Isis. (4): 312–337. doi:10.1086/348155. JSTOR 227384. 
  5. ^ Newton acknowledged Wren, Hooke and Halley in this connection in the Scholium to Proposition 4 in Book 1 (in all editions): See for example the 1729 English translation of the Principia, at page 66.
  6. ^ In a letter to Edmund Halley dated June 20, 1686, Newton wrote: “Bullialdus wrote that all force respecting ye Sun as its center & depending on matter must be reciprocally in a duplicate ratio of ye distance from ye center.” See: I. Bernard Cohen and George E. Smith, ed.s, The Cambridge Companion to Newton (Cambridge, England: Cambridge University Press, 2002), page 204.
  7. ^ Williams, Faller, Hill, E.; Faller, J.; Hill, H. (1971), “New Experimental Test of Coulomb’s Law: A Laboratory Upper Limit on the Photon Rest Mass”, Physical Review Letters, (12): 721–724, Bibcode:1971PhRvL..26..721W, doi:10.1103/PhysRevLett.26.721 
  8. ^ Millerson,G. (1991) Lighting for Film and Television – 3rd Edition p.27
  9. ^ Ryer,A. (1997) “The Light Measurement Handbook”, ISBN 0-9658356-9-3 p.26
  10. ^ John Freely, Before Galileo: The Birth of Modern Science in Medieval Europe (2012)
  11. ^ Johannes Kepler, Ad Vitellionem Paralipomena, quibus astronomiae pars optica traditur (Frankfurt, (Germany): Claude de Marne & heir Jean Aubry, 1604), page 10.
  12. ^ Translation of the Latin quote from Kepler’s Ad Vitellionem paralipomena is from: Gal, O. & Chen-Morris, R.(2005) “The Archaeology of the Inverse Square Law: (1) Metaphysical Images and Mathematical Practices,” History of Science,  : 391–414 ; see especially p. 397.
  13. ^ Note: Kepler’s notion of “gravity” was not the modern notion: Kepler believed that the Sun exerted a force on the planets which propelled them in their orbits around the Sun. Like beams of light from a light house, this force rotated with the Sun as it turned.
  14. ^ Ismail Bullialdus, Astronomia Philolaica … (Paris, France: Piget, 1645), page 23.
  15. ^ Translation of the Latin quote from Bullialdus’ Astronomia Philolaica … is from: O’Connor, John J. and Roberson, Edmund F. (2006) “Ismael Boulliau” Archived 30 November 2016 at the Wayback Machine., The MacTutor History of Mathematics Archive, School of Mathematics and Statistics, University of Saint Andrews, Scotland.
  16. ^ (Gal & Chen-Morris, 2005), pp. 391–392.
  17. ^ Robert Hooke, Micrographia … (London, England: John Martyn, 1667), page 227: “”

External links

  • Damping of sound level with distance
  • Sound pressure p and the inverse distance law 1/r
  • Inverse Square Law & Radiation Protection by Ionactive (Animation)

en.wikipedia.org

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