杏吧原创

On the pull

Question: If you could journey to the centre of the Earth, what would be the
sensation of gravity at various points on the way down, and at the centre?

Answer: This problem piqued the curiosity of no less a physicist than Isaac
Newton, who of course solved it in his Principia (Book 1, theorem 33).
If you are at the centre of the Earth you are pulled equally in all directions,
so you are in fact weightless. Higher up, at radius R from the centre,
Newton found that the attractions of the materials in the hollow spherical shell
of radius greater than R will all cancel one another out鈥攁
beautiful mathematical consequence of the fact that gravity decreases as the
square of the distance. You feel only the pull of the mass in the sphere below
you.

Newton showed that its combined pull is simply proportional to the inverse
square of the distance R from the centre. The mass of this sphere is
proportional to its volume, that is, R³. So, the weight you would feel,
if you were foolhardy enough to descend through a homogeneous planet, would
decrease in direct proportion to R³/R²
(which is equal to R) as you moved inwards, reaching zero at the centre.

In fact, the central parts of the Earth are much more massive than the outer
parts, mostly dense iron, so your weight would decrease a bit more gradually at
first and more rapidly as you penetrated the core.

Spencer Weart

Maryland

Answer: As you descended you would find the pull of gravity continuously
decreasing as the centre of the Earth approached, and at the centre you would be
almost completely weightless, but not quite.

First, suppose the Earth is perfectly spherical (even though it isn鈥檛 quite).
Then at any interior point all the matter lying outside your position (that is,
towards the surface of the Earth) makes no contribution to the pull of
gravity鈥攊t all cancels out to zero鈥攍eaving just the pull from the
matter inside your position (all the matter between you and the Earth鈥檚 centre).
So gravity gets even weaker as you descend, and would be zero at the centre.

However, the Earth is slightly pear shaped. Think of it as an extra 鈥渞ing鈥� of
matter on the surface just south of the equator. At the centre of the Earth,
there will be a very tiny net pull towards all the parts of that ring鈥攖he
overall effect of which will be an extremely tiny net pull roughly towards the
South Pole.

Incidentally, if you could slide down a frictionless tube through the centre
to your antipodal (opposite) point on the Earth鈥檚 surface and back, the
round-trip would take you 90 minutes鈥攅xactly the same time as it takes to
go round Earth in a low orbit.

Robin Clegg

Swindon, Wiltshire

Gene pooling

Question: Where there are areas containing isolated populations of threatened
species it is generally accepted that it is important to maintain corridors of
access between the areas to minimise genetic impoverishment and the building up
of harmful mutations in those populations.

Red squirrels in Britain are a case in point. However, there are other
species, such as grey squirrels, which have been introduced into new and
isolated habitats in very small numbers and within decades have exploded to
thousands.

Why do they not suffer the effects of inbreeding? Do they possess something
denied to the threatened groups and could it be used to shore up the threatened
groups?

(continued)

Answer: In your previous answers to this question, two replies mentioned that
grey squirrels were less susceptible to disease than red squirrels and that this
susceptibility was an important reason for the red squirrel鈥檚 decline.

One reply specifically mentioned parapoxvirus infection in this context.
Unfortunately, the situation is not so clear-cut. It is true that only one case
of parapoxvirus has been confirmed in grey squirrels but the effect of the
disease on the red squirrel populations is by no means certain. The idea that
the disease has led to the demise of the red squirrel population comes from
circumstantial evidence from epidemics of disease of unknown cause early this
century and a few further epidemics noted after the red squirrel parapoxvirus
was isolated in the 1970s.

Additionally, the replies stated that grey squirrels have a more diverse diet
than red squirrels and that male reds have stopped breeding because they are
surrounded by larger male greys. These statements are not correct.

Tony Sainsbury

Institute of Zoology, London

Myopic mammals

Question: I would estimate that about 40 per cent of people that I know need
glasses or contact lenses for distance vision. Assuming that this sample is
typical of the human race, I would like to know why it is that eye problems
prevalent in humans such as myopia (short-sightedness) seem very rare in wild
animals?

As far as I know, myopia is a genetic condition and so is not usually
acquired by habits such as reading small print (otherwise one would expect
recovery after stopping the habit).

Obviously, it is not easy to test the eyesight of an animal, but if the
incidence of myopia is as high in wild animals as it is in humans then how can
the animals survive?

(continued)

Answer: The simple answer is that most other animals that are born with or
develop myopia die quickly and are therefore incapable of passing on this trait
to their offspring. Humans can correct for, or at least mitigate, the problems
associated with many 鈥渘atural鈥� defects and thus we are not under the same
natural selection pressures that influence most other creatures.

I dare say that among the mammals there are not only more myopic humans but
also a greater percentage of people who have broken limbs, survived accidental
poisoning or had other such misfortunes.

Our technology and ability to cooperate in societies allows us to overcome
many of the things that kill other mammals. So relatively minor genetic defects
such as poor eyesight tend to accumulate in our gene pool because natural
selection cannot act against those individuals that have them.

Mark Farmer

by e-mail, no address supplied

This week鈥檚 question

Head start: When pigeons walk they move their heads rhythmically and
horizontally a considerable distance, I would estimate around 5 centimetres back
and forth. Is there a biological advantage associated with his movement and, if
not, why do they do it?

William Grut

Vancouver, Canada