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.

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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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www.physicsforums.com

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 4π*r*2 ) 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 4π*r* 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* = 4*πr* 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”.

**^**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.**^**Thomas Birch,*The History of the Royal Society of London*, … (London, England: 1756), vol. 2, pages 68–73; see especially pages 70–72.**^**Giovanni Alfonso Borelli,*Theoricae Mediceorum Planetarum ex Causius Physicis Deductae*of the Medicean planets deduced from physical causes] (Florence, (Italy): 1666).**^**Koyré, Alexandre (1952). “An Unpublished Letter of Robert Hooke to Isaac Newton”.*Isis*. (4): 312–337. doi:10.1086/348155. JSTOR 227384.**^**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.**^**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.**^**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**^**Millerson,G. (1991)*Lighting for Film and Television – 3rd Edition*p.27**^**Ryer,A. (1997) “The Light Measurement Handbook”, ISBN 0-9658356-9-3 p.26**^**John Freely,*Before Galileo: The Birth of Modern Science in Medieval Europe*(2012)**^**Johannes Kepler,*Ad Vitellionem Paralipomena, quibus astronomiae pars optica traditur*(Frankfurt, (Germany): Claude de Marne & heir Jean Aubry, 1604), page 10.**^**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.**^**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.**^**Ismail Bullialdus,*Astronomia Philolaica*… (Paris, France: Piget, 1645), page 23.**^**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.**^**(Gal & Chen-Morris, 2005), pp. 391–392.**^**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