Couple of Hypotheticals re: gravity

1)

Suppose that you were able to core the Earth, like you would an apple, i.e. theres a cylindrical tube going right through the centre from pole to pole with nothing in the centre. From the surface, it looks like a hole all the way through to the other side.

Assuming that the atmospheric conditions in this cylinder were the same as on the surface (pressure, temp. etc were all normal), if you fell into this 'hole' would you fall towards the centre of the earth, pass a point at the exact centre, and then begin to slow down as gravity was now pulling in the opposite direction?

If yes, would you then reach a point where you would begin falling back towards the centre of the earth again, only to pass it and begin to slow down again? Would this then keep happening (slingshot-ing about the centre of Earth) until you were finally suspended in the middle?

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2)

If you had a mountain tall enough, and were able to trow some projectile fast enough (lets say a sliotair from a hurley) would the curvature of the earth dictate that this projectile would be 'falling' constantly i.e. by the time the sliotar reaches the point where it would normally hit the ground, the earth has curved so that the sliotar has remained at an almost constant height.

Is this, basically, how objects orbit the earth? Does it also mean that different objects of differing weight (mass?) orbit at higher altitudes? Also, can the same object orbit at different altitudes depending on their speed/velocity?

Just something I thought of one day while er, under the influence.

Thoughts?

ceejay

Deleted User wrote: »

Suppose that you were able to core the Earth, like you would an apple, i.e. theres a cylindrical tube going right through the centre from pole to pole with nothing in the centre. From the surface, it looks like a hole all the way through to the other side.

Assuming that the atmospheric conditions in this cylinder were the same as on the surface (pressure, temp. etc were all normal), if you fell into this 'hole' would you fall towards the centre of the earth, pass a point at the exact centre, and then begin to slow down as gravity was now pulling in the opposite direction?

Yes, though you would have to assume other things too such as the distribution of matter in the Earth is even enough that the centre of gravity is at the centre of the Earth, and also that no other significant masses such as the Moon would affect your motion, etc.

If yes, would you then reach a point where you would begin falling back towards the centre of the earth again, only to pass it and begin to slow down again? Would this then keep happening (slingshot-ing about the centre of Earth) until you were finally suspended in the middle?

Yes, based on the same assumptions. Note that there would be a similar, but minute, motion of the Earth based on the force of gravity exerted by your mass on it, and the oscillations would happen about your common centre of gravity.

If you had a mountain tall enough, and were able to trow some projectile fast enough (lets say a sliotair from a hurley) would the curvature of the earth dictate that this projectile would be 'falling' constantly i.e. by the time the sliotar reaches the point where it would normally hit the ground, the earth has curved so that the sliotar has remained at an almost constant height.

Is this, basically, how objects orbit the earth? Does it also mean that different objects of differing weight (mass?) orbit at higher altitudes? Also, can the same object orbit at different altitudes depending on their speed/velocity?

Yes, you're essentially talking about escape and orbital velocities here. You have to reach a certain velocity known as escape velocity before you will be able to get into orbit. Once in orbit your orbital velocity will be determined by the altitude you want to orbit at. Lower altitudes typically require higher velocities. In geostationary orbit, the orbital velocity matches the rotational velocity of the Earth, so the satellite remains above the same point on the Earth. You can use the analogy of an ice skater spinning on the spot - to spin quicker they bring their arms in (lower altitude), slower they spread their arms out (higher altitude).

But fundamentally you're right, it's the combination of the forward velocity of the satellite - or sliotar - and the downward velocity due to the gravitational pull from the Earth that produces the circular path of the orbit. Take away the pull from the Earth and the object would then fly off in a straight line - think of swinging a yoyo over your head in a flat circle, and suddenly letting go of the string. Conversely, slow down and you will start to fall inwards - the string wraps around your head and you get a yoyo in the eye

However, mass should not be an issue, since the accelleration due to gravity is the same - think of the experiment of dropping a feather and a cannonball in a vacuum, they both fall at the same speed. We don't see this normally due to air resistance acting more on the feather resulting in a lower terminal velocity for the feather. Mass affects how much force you need to accellerate the object to the required velocity, but once at the same velocity two satellites of different masses will orbit at the same altitude.

Ciarán.

Perfect answer.

That's exactly what i was looking for. I was unaware that there were different 'types' of orbit. I just assumed that "in orbit" meant that something was x number of miles above the ground and once you reached that height, you'd automatically be 'in orbit' so to speak.

When i thought it through one day, it suddenly dawned on me.

One last question,......assuming, then, that there wasn't anything in the way nor any other outside influences, and that the earth was perfectly spherical, could something orbit the earth at any height/altitude, even, say, a few inches off the ground, provided it was travelling fast enough?

JoeB-

Yes, I reckon for a perfect spherical object with no atmosphere it would be possible to orbit at huge speeds only an inch off the ground. Possibly things orbit very small black holes at very close distances.

For the Earth,.. I thought that when inside a sphere there is no gravational attraction to the mass that is outside... i.e when 15 miles from the center the gravational attraction will be the same as a 15mile radius Earth, the rest will cancel out. It still produces the same result... i.e an oscilation... probably simple harmonic motion where the force is in the opposite direction and preportional to your distance from a point.)

(Another way of putting this is that if you were inside a huge hollow metal football type object there would be no gravatational attraction... because it will cancel out... even if very close to one edge, or at any point in the interior... this is one situation when considering the mass to be concentrated at the center of gravity produces the wrong results... I could be wrong but I seem to remember this)

Delphi91

Deleted User wrote: »

1)

Suppose that you were able to core the Earth, like you would an apple, i.e. theres a cylindrical tube going right through the centre from pole to pole with nothing in the centre. From the surface, it looks like a hole all the way through to the other side.

Assuming that the atmospheric conditions in this cylinder were the same as on the surface (pressure, temp. etc were all normal), if you fell into this 'hole' would you fall towards the centre of the earth, pass a point at the exact centre, and then begin to slow down as gravity was now pulling in the opposite direction?

If yes, would you then reach a point where you would begin falling back towards the centre of the earth again, only to pass it and begin to slow down again? Would this then keep happening (slingshot-ing about the centre of Earth) until you were finally suspended in the middle?

I remember this question being on a Uni physics paper last century (literally!!) and the question asked you to calculate the frequency of the resulting oscillating motion.

Mike

Podge_irl

Delphi91 wrote: »

I remember this question being on a Uni physics paper last century (literally!!) and the question asked you to calculate the frequency of the resulting oscillating motion.

Mike

Takes 42 minutes assuming no air resistance, assuming spherical earth etc.

gondorff

Down, down, down. Would the fall never come to an end? 'I wonder how many miles I've fallen by this time?' she said aloud. I must be getting somewhere near the centre of the earth. Let me see: that would be four thousand miles down, I think-' (for, you see, Alice had learnt several things of this sort in her lessons in the schoolroom and although this was not a very good opportunity for showing off her knowledge, as there was no one to listen to her, still it was good practice to say it over) '-yes, that's about the right distance - but then I wonder what Latitude or Longitude I've got to?' (Alice hadn't the slightest idea what Latitude was, or longitude either, but she thought they were nice grand words to say.)
Presently she began again. 'I wonder if I shall fall right through the earth! How funny it'll seem to come out among the people who walk with their heads downwards! The antipathies, I think -' (she was rather glad there was no one listening, this time, as it didn't sound at all the right word) - 'but I shall have to ask them what the name of the country is, you know. Please, Ma'am, is this New Zealand or Australia?' (and she tried to curtsey as she spoke - fancy, curtseying as you're falling through the air! Do you think you could manage it?) 'And what an ignorant little girl she'll think me for asking! No, it'll never do to ask: perhaps I shall see it written up some-where.'
Down, down, down.

Alice's Adventures In Wonderland


'They run their railway-trains without any engines - nothing is needed but machinery to stop them with. Is that wonderful enough, Miladi?'
'But where does the force come from?' I ventured to ask.
Mein Herr turned quickly around, to look at the new speaker. Then he took off his spectacles, and polished them, and looked at me again, in evident bewilderment. I could see he was thinking - as indeed I was also - that we must have met before.
'They use the force of gravity', he said. 'It is a force known also in your country, I believe?'
'But that would need a railway going down-hill,' the Earl remarked. 'You can't have all your railways going down-hill?'
'They all do, said Mein Herr.
'Not from both ends?'
'From both ends.'
'Then I give it up!' said the Earl.
'Can you explain the process?' said Lady Muriel. 'Without using that language, that I ca'n't speak fluently?'
'Easily,' said Mein Herr. 'Each railway is in a long tunnel, perfectly straight: so of course the middle of it is nearer the centre of the globe than the two ends: so every train runs half-way down-hill, and that gives it force enough to run the other half up-hill.'
'Thank you. I understand that perfectly,' said Lady Muriel. 'But the velocity, in the middle of the tunnel, must be something fearful!'

Sylvie and Bruno Concluded.