Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: MoBiJo on 15/11/2006 02:58:33
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When I moved from Europe to New Zealand I noticed that the moons face is upside down. Not suprising of course, but it raised another question:
Why does the moon actually always show us the same face, why do we never see the so called "dark side" of the moon, which of course also gets sunlight, so it's not dark.
Anyway, it means that the moon has to make exactly one rotation around its own axis in the time it rotates around the earth. Conincidence or physically explainable?
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Hi MoBiJo, and welcome to the forum.
YAYYYYYYYYYYYY !!
Well, I wish i knew the answer...but someone will post you some words with more meaning than mine !!..
It IS quite an amazing coincidence isn't it....it's the same extraordinarily amazing coincidence that the moon is something like 400 times smaller...well..here's Wikipedias quote.....
............ " The Earth's distance from the Sun is about 400 times the Moon's distance from the Earth. The Sun's diameter is about 400 times the diameter of the Moon...........That is kind of bizarre isn't it ?
It certainly makes for eclipse joy !!
I suspect the answer to your original question will be found in how the moon came to be in existence...I gather the most favoured explanation is that it was formed when a Mars sized object collided with the earth early in the earths formation.............
I'll leave the rest up to an expert to answer for you.
WELCOME !!
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Good Question I would never have thought about it Like that!
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The size thing is as far as I know coincidence, however the showing the same face is not.
It is all to do with the tides. If you think think of all the energy that goes into sloshing water around the earth, where is it coming from. As the earth spins near the earth different bits of water are attracted to the moon at different times, so because the earth is spinnign faster than the mon is orbiting the energy is actually coming from the spinning of the earth, hence the earth is slowing down and days are getting longer - 200 million years ago there were 400 days in a year.
Now the earth is 80 times heavier than the moon, so the tides would be 80 times stronger (they actually act on the rock of the moon) and the moon being smaller is easier to slow down, so in a rough calculation I think the moon will slow down 10000 times faster than the earth, so much so it has pretty much stopped now - it does swing back and forth slightly like a pendulum now but shows the same face to the earth all the time - which means rotating once a month)
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With regards to the moon being upside down viewed from New ZeaLand people often remark on Whirpools etc rotating in the opposite way down under, but of course they don't they still rotate in the same way relative to the Earths rotation but they just look different because you are upside down
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The moon at it's present stage is almost "tidally locked". This occurs when the gravity pulling on the closer side of the moon is stronger than the gravity pulling on the far side of the moon. Because the moon no longer makes complete spins, we can no longer see the "dark" side of the moon. Although the Moon is almost tidally locked, it is not quite close enough to be completely still in what angle it faces the earth. hence the Pendulum effect.
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The moon is still rotating quite happily relative to the Sun and the remote galaxies it just so happens that its orbital period around the Earth and its rate of rotation are the same
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The moon is still rotating quite happily relative to the Sun and the remote galaxies it just so happens that its orbital period around the Earth and its rate of rotation are the same
Yes, but why this? daveshorts has given an explanation of it.
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Although the moon is now tidally locked with the Earth, as has been pointed out, the tidal interaction of the two bodies continues. The net effect is to reduce the rotational speed of the Earth. Since angular momentum must be conserved the moon acquires the angular momentum lost by the Earth. This moves it into a more distant orbit. It is retreating at a rate of around 1cm per annum. (I think I have that right.)
So the coincidence by which we can observe solar eclipses is exactly that - a time relaated chance. In several million years we shall glimpse only annular solar eclipses.
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With regards to the moon being upside down viewed from New ZeaLand people often remark on Whirpools etc rotating in the opposite way down under, but of course they don't they still rotate in the same way relative to the Earths rotation but they just look different because you are upside down
LOL !
[:D]
Actually there were some rather careful experiments done some years ago into the corriolis effect.
The experiments used a very large tray of water that was isolated from vibration and allowed to stabilise for several days before the experimental run.
I'm trying to remember the name of the chap who ran the experiments.
Anyway, the effect was, as expected, found.
And indeed the water did rotate in different directions.
The strength of the effect however was extremely small indeed.
So I'm afraid Michael Palin and his bowl of water is rather more romanticism than experiment.
You have absolutely no chance of observing the effect in a hotel bathroom.
I know, I tried for long enough.
[:D]
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I have visited Australia several times and have noticed that the water spirals down the waste pipe the the same way relative to the earths rotation as it doe's in Britain.
The water does not rotate in a different direction it is just that you are viewing it from a different perspective
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No, this is not true.
Water swirls around wash basins, baths and toilets predominantly due to local effects - the off-centre taps for instance - which introduce a spin to the water entering the receptacle. Faced with little resistance to its motion the water continues to turn for some time. Pulling out the plug exaggerates the visible motion.
BUT - conducted correctly you can see the effect of the turning earth on the direction in which water goes down the plughole. This coriolis effect is very weak and requires special apparatus to demonstrate it, but it has been done, both in the southern and northern hemispheres in the 50s and 60s respectively.
We conducted our own experiment on the radio to show how variable this observation can be, and then asked Australia's Dr Karl to explain it all. Here's a link to that show and transcript:
http://www.thenakedscientists.com/HTML/shows/2005.12.18.htm#3
Chris
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I would point out that I referred whirpools that are less subject to geometric influences than wash basins,the point I was making that as one is upside down compared to what one is in the northern hemisphere ones perspective is distorted.
In the outback one often hears tales of hikers getting lost and I am sure that the sun going round in an anti clockwise manner and being at its zenith in the north is a contributary factor
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Upside down ?
No you aren't.
Gravity pulls in toward the centre of the planet not from the top to the bottom.
We're all the same way up.
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Everybody's "down" is the same as eveyrone else's "down".
Down only has meaning if you're in a gravity well anyway.
Floating out in space there is no down.
There are downs on other planets but to get to them you have to go up and then float around a bit in directionless space before you fall down into another gravity well. The Moon's for example.
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I am certainly correct in saying I am upside down (why else would the moon appear to be inverted, see post 1), but on further reflection I realise that my conception of what is clockwise and anti clockwise would not alter , the Sun still rises in the East!.
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You're not upside down when you're in New Zealand.
Down is defined as the direction in which objects fall when acted upon by gravity.
You drop the ball and it falls towards your feet.
Towards the centre of the planet.
Down the gravity well.
It doesn't matter where on a sphere you try this the results are the same.
The ball falls down towards your feet.
Down is towards the centre of the planet.
Everyone has the same down.
Everyone has the same up.
No one on a sphere is upside down relative to anyone else.
Assuming they're not standing on their head of course.
If you happen to be floating out in space where you can see the people in the UK standing at an angle relative to you then the people in New Zealand will be at the opposite angle. Approximately 180 degrees from those in the UK.
It looks to you floating out there that the peeps in NZ are upside down relative to those in the UK but they are not.
It's all relative.
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If I board the elevator that travels from the antipodeon islands via the centre of the Earth to the UK, I start with my feet pointing towards the centre of the earth but after 42 minutes when I arrive in the UK my head points towards the centre of the earth, I call this being converted from rightway up to upsidedown.
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The reasin that the moon has settled down with one side facing the earth is that it although it is approximately spherical it has slight asymmetries and mass concentrations with in it that make it settle down in one position. It has probaly been this way for quite a long time because its back side shows more signs of recent collision damage than the side facing us which hase the well known Maria or flattish plains on it. this is what you would expect to hapen for a body that is rotation locked to its orbital period. I have however read papers suggeting that shorthly afer it was formed it wass probably in a 3 to 2 resonance with the earth like the planet Mercury is with the sun.
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If I board the elevator that travels from the antipodeon islands via the centre of the Earth to the UK, I start with my feet pointing towards the centre of the earth but after 42 minutes when I arrive in the UK my head points towards the centre of the earth, I call this being converted from rightway up to upsidedown.
Duh !
Sorry.
I forgot about the elevator.
I don't get out much. What can I say ?
[:D]
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An interesting question [???] I was wondering how Earth looks from the moon?
see:
http://www.smeter.net/propagation/views/earth-from-moon.php
I [;D]t appears to have phases as it revolves around the Moon once a year--relative to the Sun.
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You're not upside down when you're in New Zealand.
I think he was referring to a plane perpindicular to the equator where "up" equals north. You are upside down relative to where you are now when you are in New Zealand.
Agreements, disagreements, death threats?
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If I board the elevator that travels from the antipodeon islands via the centre of the Earth to the UK, I start with my feet pointing towards the centre of the earth but after 42 minutes when I arrive in the UK my head points towards the centre of the earth, I call this being converted from rightway up to upsidedown.
This brings to my mind an other question : what happens to your weight (not your mass) if you penetrate as deep as 1000 km (not meters), or to make things easier to 1/4 of the earth's diameter ? You distance to the earth's center of gravity will be halved, does that mean that your weight (force of attraction from the earth) will be 4 times higher ? What is the influence of the part of the earth above you ?
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Inside the earth the gravitational field goes down linearly with your distance from the centre of the earth. At the centre of the earth your weight is zero. This is because the gravitational field inside a uniform thick spherical shell is zero at all points inside the shell.
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Am I correct that in free fall your trip would take 21 minutes down to the centre and at that point your speed would be the same as if you were doing a ground level orbit (84 mins)(7.937KM/s),
I notice that if you accelerated at 1 G for 21 mins your speed would be 12.36KM/s does this confirm there is some reduction in G as you go down.
I think to calculate the reduction of velocity due to a linear reduction in G with distance would need a knowledge of calculus which I do not have but I could probably do a numerical approximation
P.S
I am puzzled by your assertion that that G falls off in a linear manner as one descends, this I could understand for a cubic or cylindrical body but for sphere it does not seem logical!!!
This post seems to have arrived on the scene rather late due to some technical problem, I have tried to calculate how the varying gravitational field affects the transit time but it is rather beyond my GSE level maths the only thing I worked out was the average value of G for the descent was 8.02/Ms/s which is reasonable as the elevator travel relatively slowly through the regions of high G but zips through the low G regions
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This is because the gravitational field inside a uniform thick spherical shell is zero at all points inside the shell.
Is this what you really wanted to say?
I know this isn't a model we can recreate in a lab. Plus, the "Inverse/Squares Law" totally fails for resolving gravitation of two masses in contact, (denominator goes to Zero) but to make such a counter-intuitive statement seems against the spirit of this forum.
(Forgive my being so blunt.)
I think that as random points within the Earth are considered, the mass of material radiating out from all sides of each random point has an associated piece of "Acceleration Due To Gravity" to consider, one that is unique in every direction surrounding that point.
Arguably, there is one single point somewhere within the planet where g = 0, (And that point is not at the Earth's geometric centre) but since I've begun this sentence, that point of g = 0 has repositioned itself due to Tectonics.
My first question on the subject is; Can Newtonian mechanics be modified to reason out this model? Or is it more of a Quantum Mechanics model?
Mike
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This is because the gravitational field inside a uniform thick spherical shell is zero at all points inside the shell.
This is actually a fairly standard result of newtonian gravity and vector calculus. I will see if I can work out how to derive, it and then if I can derive it in a comprehensible manner.
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Ok right here we go.
There is a theorem in mathematics called stokes theorem which like all the best maths is bloody obvious when you think about it but has profound consequences.
This says that for a substance that is conserved
Inside a closed surface - one that joins up like a sphere
The sum of the amount produced - the sum of the amount destroyed = the amount going through the surface.
If you think of the stuff as water this is saying, it has to go somewhere.
Gravitational field is a conservative field - it is conserved
and it is created by mass so we can rewrite the above as:
Sum of gravitational flux over a surface = Mass within this surface.
gravitational flux is just the field times the area you are looking at.
[diagram=32_0]
or in the terms of the above diagram - where g = the gravitational field at a point
ds = the bit of surface you ar looking at
sum the flux over the surface = sum of g x dS over the surface [prop] M
there is a constant in there we will call G the gravitational constant
s
Now if we consider a sphere everything is beautifully symmetric
so the field must be symmetric so g must be constant.
[diagram=33_0]
This is great because it means all we need to know to work out the gravitational field produced by a uniformly distributed mass in a sphere is it's Mass and the surface area
g [prop] Total mass/ Surface area
the area of a sphere is 4πr2 so:
g [prop] M / 4πr2
Oh look if M is constant eg if we are outside the body we appear to have derived the inverse square law, which is reassuring.
This means that outside of a spherical body we can consider the field produced by it is identical to a point mass - which makes calculations far far easier.
Now if we consider a hollow sphere:
the field produced by the shell inside it inside must again be uniform:
[diagram=34_0]
Now the flux leaving outwards + the flux leaving inwards = Mass of the shell
We can work out the flux leaving outwards:
We worked out earler that a spherically symmetric body's field is the sum of it's symmetrically symmetric parts so:
flux leaving a solid sphere = flux leaving a sphere the size of the hole + affect of the shell
as the flux leaving the shell inwards will make no difference to the big shpere
fluxsolid = fluxhole + flux leaving shell outwards
this can be rearranged to:
flux leaving the shell outwards = fluxsolid - fluxhole
[diagram=36_0]
flux leaving the shell outwards [prop] Msolid - Mhole
We know that the
mass of the shell = mass of a solid sphere - mass of a sphere the size of the hole
[diagram=35_0]
So
Total flux leaving the shell [prop] mass of a solid sphere - mass of a sphere the size of the hole
Total flux leaving the shell = flux leaving the shell outwards
so there is none left to leave inwards so the field inside the hollow spherical shell must be zero!
I hope that makes some sense I apologise for using = & [prop] interchageably, if you did it all properly it would have the same result
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Due to your elegant exposition I now understand how mass of residual part of the earth varying according with a third power and Newtons inverse square law combine to give a value of G that varies in a linear manner with distance from the centre.
Could you please now turn your attention to the transit time which I am surprised to learn depends solely on the density.
I am saddened to learn that my tunnel from the UK to the Antipodeon islands would not work due to the rotation of the earth it would have to run from North to South Pole which would involve rather a lot of air travel
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If the force varies linearly with distance from the centre of the earth this is the same relationship as force has with movement away from equilibrium in a spring.
A mass on a spring's period is constant as long as you don't change the spring or the mass. - it is a form of simple harmonic motion, you probably did it at school.
In this case changing the mass won't help you as the force is proportional to the mass. Changing the size of the planet is just like changing the starting amplitude of a mass on a spring. So the only thing you can change which will have an effect is the density of the planet, or of course G.
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As I see it, the earth was struck, then a small planet, by a Mars sized object, or so I heard. Then a mass was sent out that had been part of the earth and was in motion with it and so it left with a similar motion and hence rotates facing the earth, slowly turning. It spun off, the earth didn't quite divide in two. All the solar system rotates on the same plane and the smaller planes of the sattellites are aligned too.
All from one disc which was originaly all dust from another star which exploded. Then gravity caused the formation of a centre, the sun, and then planets and then sattelites and comets and there were a lot of collisions. Look at the moon. Venus was knocked backwards and Uranus lost it's axis. Pluto was detached from it's planet.
The earth's rotation must have changed by this impact and over time it slowed down because of the seas and the moon tides.
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Thank you for your explanation Daveshorts
Mike
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The linear fall off is a bit counter intuitive, but it is true it results in the motion of the body through the center of the earth being a classical simple harmonic motion. In fact you can think of it as a completely flattened orbit if you looked at a circular orbit going round the earth from the side a linear "orbit" through the middle would look just the same.
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Many points of this strange business become progressively more clear the path of a straight down and up trip is of course elliptical but with one axis reduced to zero, I would still like to calculate the transit time on the basis of how G varies as you go down and up if you have any idea how it could be done?
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Do you want to work out the transit time for any variation of g or for a linear change. If the first have you done any calculus?
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The Hole Through the Earth Problem with some practicalities and simplifications.
This is an interesting thought experiment and involves being dropped through a hole drilled between the North and South Poles. (If you take any other journey, you would bash into the sides as the Earth rotated.)
Let's assume, for a minute, that the hole is completely empty and ignoring the incredibly high temperatures and pressures down there (probably 5000 degrees and about 5 million times atmospheric pressure).
We start to fall down the hole; accelerating under 'normal gravity'. Newton tells us that only the bits of the Earth that are nearer to the centre than we are would have any effect on us. The bits nearer the surface than we are have no net effect; their attractions would all cancel out.
This force on us is, in fact, proportional to our distance from the centre. When half way down, we would weigh half as much as at the surface. This means that we exhibit what is known as Simple Harmonic Motion (just like a pendulum or a weight on a spring). We would oscillate backwards and forwards, from pole to pole for ever, if it weren't for friction.
The period of this motion is fairly easy to calculate. It's about 90 minutes for the return journey; exactly the same as the time for a satellite in a low Earth orbit to go round the Earth once.
To be a bit practical; what would be the effect of the hole being open to the air? Well, we know that, as we go up in the air, the atmospheric pressure halves every 5.5km. As we went down the hole, the reverse would happen; every 5.5 km downwards, the pressure would double. After only 110km (only 2% of the way down) the pressure would have doubled 20 times! That corresponds to a million times atmospheric pressure. The air molecules would have long since been squeezed together and this simple calculation runs out of steam. But, in any case, the atmosphere would become a highly compressed liquid and we would never get through,
We could do this experiment though, if we went out into space and found ourselves a nice, spherical asteroid or tiny planetoid of the same density as the Earth - say it was a couple of hundred km across and made of Granite If our planetoid were in an orbit near to Earth, it would be warm enough so that any atmosphere would have boiled away so the hole would be completely empty all the way through.
It would work.
But here is the interesting bit. Because we are dealing with simple harmonic motion, the return trip would still take 90 minutes and this would also be the orbit time of a tiny satellite in orbit just above its surface. It must also be true for bits of dust orbiting close to rocks. I wonder if astronauts have ever observed it outside their window. .
[:)]
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Do you want to work out the transit time for any variation of g or for a linear change. If the first have you done any calculus?
I had about three months of calculus lessons in 1944 but we were only spoonfed various formulae with lille idea of practical applications.
I wanted to calculate the the time of descent to the centre allowing for the fact that G was decreasing in a linear manner in accordance with how far we have travelled.
If I know G and either the time or the distance I can easily calculate the other but when two things are varying simultaneously I am defeated
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g = GM/r^2 G being the universal gravitational constant and M the mass of the
portion of the earth which is active, which is that contained inside a sphere having a radius equal to the distance from the center to the traveler (assumed inside the earth). Thus, the force upon the traveler is proportional from the distance to the center, and what you have here is a simple harmonic oscillator, like a mass connected to a linear spring.
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It is simple to calculate the down-up time on the basis that it equal to the orbital time, what I was hoping was that someone with the necessary mathematical skills would show how it can be calculated in an alternative manner by allowing how the velocity of the elevator varies under the influence of the steadily decreasing gravitational force as it travels towards the centre of the Earth
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To calculate it you just need to do the same bit of bookwork that you use for normal simple harmonic motion. You solve the second order differential equation which gives you a sinusoidal answer for the motion.
Of course, it is only sinusoidal for a sphere of uniform density. Any random old planet would need the calculation to be done step by step, using numerical methods (a fast computer) - but then what would that prove unless you actually NEEDED to know the answer in detail? Calculus is much more satisfying.
lyner
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I have visited Australia several times and have noticed that the water spirals down the waste pipe the the same way relative to the earths rotation as it doe's in Britain.
The water does not rotate in a different direction it is just that you are viewing it from a different perspective
"viewing it from a different perspective" doesn't makes sense. clockwise is still clockwise and counterclockwise is still counterclockwise, even on the southern hemisphere ;)
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Thank you daveshorts and Soul surfer,
your two explanations have completly satisfied me as to the original question, why we always see the same face of the moon.