Gravity escape: Daughters homework.
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From: The center of the earths surface
Gravity escape: Daughters homework.
Hope the right forum for a science Q.
My 9 yr old Daughter bought home a school science book, Titled Kingfisher encyclopedia.
She was asking about gravity, and how it works? I went to my technical reference library and dusted off Mechanics of Flight by A C Kermode.
She then asked me why to escape earths gravity the speed has to be 11.2 KM/s, then showed me the book and the bit about gravity.
Enter my 12yr old (going on 30) Daughter and after listening to the two of us says " that can't be right Dad?????" If you built a really really huge ladder, a really really Humungous ladder ( Her words)and had some oxygen, you could climb like Jack and the Bean Stalk???I guess you would get tired though???
( quote)
50 mumble yr's old, 22yrs of commercial aviation behind me, and always thought of Kermode as the Principles of flt bible?
The Q why not? the raw theory I mean, disregarding the practicality of such, I think it's a beaut?
I need enlightening as much as she needs the Q answered.
My 9 yr old Daughter bought home a school science book, Titled Kingfisher encyclopedia.
She was asking about gravity, and how it works? I went to my technical reference library and dusted off Mechanics of Flight by A C Kermode.
She then asked me why to escape earths gravity the speed has to be 11.2 KM/s, then showed me the book and the bit about gravity.
Enter my 12yr old (going on 30) Daughter and after listening to the two of us says " that can't be right Dad?????" If you built a really really huge ladder, a really really Humungous ladder ( Her words)and had some oxygen, you could climb like Jack and the Bean Stalk???I guess you would get tired though???
( quote)
50 mumble yr's old, 22yrs of commercial aviation behind me, and always thought of Kermode as the Principles of flt bible?
The Q why not? the raw theory I mean, disregarding the practicality of such, I think it's a beaut?
I need enlightening as much as she needs the Q answered.
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From: TBC
Kermode as the Principles of flt bible
It can be calculated by equating the kinetic energy of an object to the gravitational potential energy of the point in the field which the object is in. It turns out to be independent of the mass of the object and is equal to twice the gravitational constant times the mass of the Earth, divided by the distance from the centre of the Earth to the object. This is all then square rooted.
As for the ladder idea, of course it would work in theory. Build the ladder 36,000 km high and you'll be in a geostationary orbit anyway and won't have to worry about gravity.
Ginger
Ecce Homo! Loquitur...
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From: Peripatetic
Escape velocity is the speed at which an object must be propelled in order not to return to another object under their mutual gravitational attraction. Alternatively, it is the speed required to propel the object into a orbit about that body. But that assumes a one time acceleration and then coast, with the gravitational attrition gradually eroding the speed. Too little, you stop and fall back. Enough, and you continue to coast, at a small speed, untill attracted to another body or Lagrange point.
However,assuming you have a variable thrust engine with enough impulse, you could balance your thrust against gravity and climb out of the gravity well at a foot a second if you wished, though it might take a while and be very inefficient. Similarily, a space elevator would allow slow climb out of the well.
The difference is in how the power is supplied. The same case can be made for the velocity required to fire an artillery shell 20 miles, but the same shell can be carried the same distance in the back of a truck at 20mph....
However,assuming you have a variable thrust engine with enough impulse, you could balance your thrust against gravity and climb out of the gravity well at a foot a second if you wished, though it might take a while and be very inefficient. Similarily, a space elevator would allow slow climb out of the well.
The difference is in how the power is supplied. The same case can be made for the velocity required to fire an artillery shell 20 miles, but the same shell can be carried the same distance in the back of a truck at 20mph....
Last edited by ORAC; 29th June 2006 at 11:00.
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From: Norfolk UK
Depends how high and where you built it!
If you built one on the equator, standing at the top you'd be whizzing around at a fair old rate as you'd be following the earth's rotation, so in theory, yes it's possible.
If you built one on one of the poles you'd have to get a veeeeery long way away as earth's gravity would still be pulling you down, albeit with a tiny amount of force, but given long enough you'd eventually get pulled back to earth. (unless you were so far away that another planet/star was pulling harder)
The key is to have a rotational velocity, which in turn will give you the acceleration to overcome gravity.
(apologies for not necessarily using the correct terms, it's been a few years since physics!)
If you built one on the equator, standing at the top you'd be whizzing around at a fair old rate as you'd be following the earth's rotation, so in theory, yes it's possible.
If you built one on one of the poles you'd have to get a veeeeery long way away as earth's gravity would still be pulling you down, albeit with a tiny amount of force, but given long enough you'd eventually get pulled back to earth. (unless you were so far away that another planet/star was pulling harder)
The key is to have a rotational velocity, which in turn will give you the acceleration to overcome gravity.
(apologies for not necessarily using the correct terms, it's been a few years since physics!)
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From: TBC
So the escape velocity deals with objects that once released have nothing to exert a force on them. With the truck/ladder examples you still have something to push against to propel you forward. If you're firing something into space that doesn't have propulsion, that's when you need the escape velocity.
Consider also that the space shuttle, despite being an impressive feat of engineering (and physics!
) does not reach 11.2km/s on the launch pad, but still manages to go up.
Consider also that the space shuttle, despite being an impressive feat of engineering (and physics!
) does not reach 11.2km/s on the launch pad, but still manages to go up.
Last edited by Gingerbread Man; 29th June 2006 at 12:53.
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Escape velocity is a bit of a fictional construct. Essentially it works like this:
- Consider the earth to be a body in a universe of it's own.
- To increase height, you need to give a body more potential energy.
- To do this, you must initially give it kinetic energy (move it upwards)
- The faster you push it, the higher it'll go.
Escape velocity is the speed at which, in an otherwise empty universe, the object would theoretically reach zero speed, at an infinite distance from the earth. But it ignores certain things:-
- We don't fire spacecraft out of a gun and give them all their speed in one go, we apply continuous thrust, so they never need to see escape velocity near the surface.
- If you want to, say, fly to Mars in any sensible time then escape velocity may be much too slow and you actually want to go much faster.
In practice, there are all sorts of other factors that apply to spaceflight. For example, between any two bodies in space (say the Earth and Moon) there are points in space called the "Lagrange points" where the two gravities balance out, so an object placed there, with no speed, will in theory stay put forever, a tiny nudge either way and it'll eventually hit (or orbit) the earth or moon.
An orbit is a different thing. To put a spacecraft into orbit, you need to give it:
(a) enough potential energy that it'll get that high
(b) enough additional kinetic energy that it's speed when it gets there gives it a centrifugal force equal to the pull of gravity at that height.
In practice, a lower orbit needs less energy than a higher orbit, because the potential energy is the biggest player. So if a spacecraft wants to orbit higher, it pushes itself forward faster, and if it wants to go lower, pushes itself backwards / slower (not unlike an aeroplane).
In all of this you can use the spin of the earth. If you launch at or near the equator, you can use the energy from the spin to give you "free" kinetic energy, hence most space-launch sites are near the equator.
At a certain height, around 35,000,000 metres, the speed you need to stay at constant height, takes you around the earth once per day (23 hours and 56 minutes to be exact). This means that you stay over one spot on the equator, since the speed matches the spin of the earth. This is where the biggest communications satellites are, and is either called "geostationary orbit" or "Clarke orbit", named after Arthur C Clarke, the British scientist and writer who first suggested putting satellites there (in a paper in "practical mechanics" magazine in 1949).
Arthur C Clarke also wrote a novel "Fountains of Paradise" which is all about building a "space elevator", essentially the very long ladder that was talked about. He is always very careful to get his science right, and to explain it clearly - I'd recommend reading it.
G
- Consider the earth to be a body in a universe of it's own.
- To increase height, you need to give a body more potential energy.
- To do this, you must initially give it kinetic energy (move it upwards)
- The faster you push it, the higher it'll go.
Escape velocity is the speed at which, in an otherwise empty universe, the object would theoretically reach zero speed, at an infinite distance from the earth. But it ignores certain things:-
- We don't fire spacecraft out of a gun and give them all their speed in one go, we apply continuous thrust, so they never need to see escape velocity near the surface.
- If you want to, say, fly to Mars in any sensible time then escape velocity may be much too slow and you actually want to go much faster.
In practice, there are all sorts of other factors that apply to spaceflight. For example, between any two bodies in space (say the Earth and Moon) there are points in space called the "Lagrange points" where the two gravities balance out, so an object placed there, with no speed, will in theory stay put forever, a tiny nudge either way and it'll eventually hit (or orbit) the earth or moon.
An orbit is a different thing. To put a spacecraft into orbit, you need to give it:
(a) enough potential energy that it'll get that high
(b) enough additional kinetic energy that it's speed when it gets there gives it a centrifugal force equal to the pull of gravity at that height.
In practice, a lower orbit needs less energy than a higher orbit, because the potential energy is the biggest player. So if a spacecraft wants to orbit higher, it pushes itself forward faster, and if it wants to go lower, pushes itself backwards / slower (not unlike an aeroplane).
In all of this you can use the spin of the earth. If you launch at or near the equator, you can use the energy from the spin to give you "free" kinetic energy, hence most space-launch sites are near the equator.
At a certain height, around 35,000,000 metres, the speed you need to stay at constant height, takes you around the earth once per day (23 hours and 56 minutes to be exact). This means that you stay over one spot on the equator, since the speed matches the spin of the earth. This is where the biggest communications satellites are, and is either called "geostationary orbit" or "Clarke orbit", named after Arthur C Clarke, the British scientist and writer who first suggested putting satellites there (in a paper in "practical mechanics" magazine in 1949).
Arthur C Clarke also wrote a novel "Fountains of Paradise" which is all about building a "space elevator", essentially the very long ladder that was talked about. He is always very careful to get his science right, and to explain it clearly - I'd recommend reading it.
G
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Genghis has very well described the forces at play, but just to emphasise - most of the energy required to reach orbit needs to be applied to accelerate an object AROUND the earth, not AWAY from it.
A SUBORBITAL spaceflight, as performed by the early Mercury missions, merely flung the spacecraft (moreorless) straight up, and unless you go really really far away from earth in one go, this will not be good enough - you will eventually fall back to earth as gravity still acts.
For ORBITAL sapceflight, the force provided by gravity must equal that required for centripetal acceleration of an obejct in orbit around the earth. This requires fairly massive speeds, hence this is where the bulk of the energy goes.
This is why, after they get a good amount of seperation from the ground, you see spacecraft turning to accelerate horizontally.
Hope that makes sense!
A SUBORBITAL spaceflight, as performed by the early Mercury missions, merely flung the spacecraft (moreorless) straight up, and unless you go really really far away from earth in one go, this will not be good enough - you will eventually fall back to earth as gravity still acts.
For ORBITAL sapceflight, the force provided by gravity must equal that required for centripetal acceleration of an obejct in orbit around the earth. This requires fairly massive speeds, hence this is where the bulk of the energy goes.
This is why, after they get a good amount of seperation from the ground, you see spacecraft turning to accelerate horizontally.
Hope that makes sense!
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From: uk
Have a look (and download) the free 'Orbiter' Sim from here:
http://orbit.medphys.ucl.ac.uk/orbit.html
- it models such physics as described here in exceptional detail and can get quite addictive (and complicated)!
http://orbit.medphys.ucl.ac.uk/orbit.html
- it models such physics as described here in exceptional detail and can get quite addictive (and complicated)!
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From: The center of the earths surface
Thanks to all:
Chaps thanks, I have printed it all off,after showing the girls the reply's,
The 9 yr old says its all very interesting but very complicated (Quote).
The 12 yr old, says why do people complicate a very simple process, like climbing a ladder? told you it could be done Dad (quote).
Genghis I will source a copy of the book, and will read it myself before I pass it on to either of these two.
H'snort
The 9 yr old says its all very interesting but very complicated (Quote).
The 12 yr old, says why do people complicate a very simple process, like climbing a ladder? told you it could be done Dad (quote).
Genghis I will source a copy of the book, and will read it myself before I pass it on to either of these two.
H'snort
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A couple of oddments come to mind.
Firstly, you can assure your daughters that nobody knows how gravity works, some of the cleverest people in the world are still trying to work it out. All anybody really knows is what gravity does does, which is pull things together - the bigger and closer they are, the more it pulls.
Secondly, whilst Fountains of Paradise is really for grown-ups, Arthur C Clarke wrote two excellent science fiction books for children. The first is called Dolphin Island which is about people living in the sea in the future, whilst Islands in the Sky is all about living on a space station. He explains the science quite well in both, and I *think* that a 12 year old would enjoy both, although the first is slightly easier reading (and with pictures!).
G
Firstly, you can assure your daughters that nobody knows how gravity works, some of the cleverest people in the world are still trying to work it out. All anybody really knows is what gravity does does, which is pull things together - the bigger and closer they are, the more it pulls.
Secondly, whilst Fountains of Paradise is really for grown-ups, Arthur C Clarke wrote two excellent science fiction books for children. The first is called Dolphin Island which is about people living in the sea in the future, whilst Islands in the Sky is all about living on a space station. He explains the science quite well in both, and I *think* that a 12 year old would enjoy both, although the first is slightly easier reading (and with pictures!).
G
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From: England
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This is my two cents on it. It's been a while since i did physics like this, so I'm not up to speed on formulas etc.
1. Rotational velocity is irrelevant in theory. The fact that the earth does spin may be seen as the fact that the universe spins about the earth - perfectly reasonable. One might argue that the sun in what the universe spins about - the sun is merely just another star. True, the planets in our solar system moves around the sun, but then again our solar system is only a part of a galaxy, which is part of space, and there is relative movement everywhere.
2. Let's first make som statements:
a) The further you are away from Earth, the less the force of gravity becomes, but at no point will the force of gravity become zero.
b) Because it takes work (i.e. an addition of energy) to escape the Earth's gravity field, the potential energy must increase when distance is increased.
c) The datum from potential energy may be placed anywhere. An object may be above or below it.
3. Then let's think about those for a while.
d) Because of a) and b) the rate at which the potetial energy increases, decreases as distance increases. This will then be a function which tends to increase to a certain specific number as it's operator, the distance from earths, tends to infinity. It will never reach this number however (if this puzzles you, read on convergent sequences). This matches our second part of the statement a).
e) Because of d) and c), we will put the datum for the potetional energy, Ep=0, at this number. As our "normal" datum usually refers to the surface or earth, this datum will refer to the position where an object would stand still, and not be affected by Earth's gravity. Referring to a), this would be imaginary. However, and this is the biggie, if we can give an object more total energy (Ek+Ep) than this number, it will be able to escape gravity.
f) Newton's Law of Gravity implies that Ep = -(GMm/r), where G is a universal gravitational constant, M is the mass of the Earth in this case, m is the mass of the propelled object, and r is the distance between the two. We know that Kinetic and Potential Energy is interchangable in an ideal system, so Ek would have to be at least equal to than Ep. I.e. Ek=Ep, or (1/2)mv^2 = -(GMm/r). We rearrange the formula to (1/2)mv^2 - GMm/r = 0. Further we can say that m((1/2)v^2 - GM/r)=0, so the mass of the propelled object is irrelevant. By solving for v, we see that v=(2GM/r)^(1/2).
This shows us that the escape speed is dependant upon the following: the mass of the body to escape and the distance between the two objects' centers of gravity at start.
With G=6,67E-11, the earth mass= 5,97E24kg and the earth's radius at equator r=6378E3m, we are able to compute the escape velocity: type in (2*6,67E-11*5,97E24/6378E3)^(1/2) into google and see for yourself. The answer comes out to approximately 11 km/s.
3.
You are implying that a (rotational) velocity will produce acceleration. If this acceleration is other than gravity, you will have to add energy somehow - speed does not add energy by itself. And for gravity, that's what we are trying to escape, right?
4.
Very true indeed, and a good point to make! We do however need to keep in mind that even though we do not know why gravity works, we do know, fairly accurate, how it behaves. These physics are well-researched, and the math appratus around this has been there for a long time.
5. Kudos to Genghis for a, as i now see, much simpler explanation
---
About convergent sequences: Try to add 1 + 0,5 + 0,25 0,125.... You can go on as long as you want to, without ever reaching 2. The sum of the sequence is always increasing, but will only reach 2 in infinity, which of course never exists in practice. Still confused? Find a 2-meter rope. Cut it in half. Cut one half in half. Take the one quarter you get and cut that in half. Go on, make as many cuts you can. How many cuts does it take before all your pieces is exactly two meters, again?
1. Rotational velocity is irrelevant in theory. The fact that the earth does spin may be seen as the fact that the universe spins about the earth - perfectly reasonable. One might argue that the sun in what the universe spins about - the sun is merely just another star. True, the planets in our solar system moves around the sun, but then again our solar system is only a part of a galaxy, which is part of space, and there is relative movement everywhere.
2. Let's first make som statements:
a) The further you are away from Earth, the less the force of gravity becomes, but at no point will the force of gravity become zero.
b) Because it takes work (i.e. an addition of energy) to escape the Earth's gravity field, the potential energy must increase when distance is increased.
c) The datum from potential energy may be placed anywhere. An object may be above or below it.
3. Then let's think about those for a while.
d) Because of a) and b) the rate at which the potetial energy increases, decreases as distance increases. This will then be a function which tends to increase to a certain specific number as it's operator, the distance from earths, tends to infinity. It will never reach this number however (if this puzzles you, read on convergent sequences). This matches our second part of the statement a).
e) Because of d) and c), we will put the datum for the potetional energy, Ep=0, at this number. As our "normal" datum usually refers to the surface or earth, this datum will refer to the position where an object would stand still, and not be affected by Earth's gravity. Referring to a), this would be imaginary. However, and this is the biggie, if we can give an object more total energy (Ek+Ep) than this number, it will be able to escape gravity.
f) Newton's Law of Gravity implies that Ep = -(GMm/r), where G is a universal gravitational constant, M is the mass of the Earth in this case, m is the mass of the propelled object, and r is the distance between the two. We know that Kinetic and Potential Energy is interchangable in an ideal system, so Ek would have to be at least equal to than Ep. I.e. Ek=Ep, or (1/2)mv^2 = -(GMm/r). We rearrange the formula to (1/2)mv^2 - GMm/r = 0. Further we can say that m((1/2)v^2 - GM/r)=0, so the mass of the propelled object is irrelevant. By solving for v, we see that v=(2GM/r)^(1/2).
This shows us that the escape speed is dependant upon the following: the mass of the body to escape and the distance between the two objects' centers of gravity at start.
With G=6,67E-11, the earth mass= 5,97E24kg and the earth's radius at equator r=6378E3m, we are able to compute the escape velocity: type in (2*6,67E-11*5,97E24/6378E3)^(1/2) into google and see for yourself. The answer comes out to approximately 11 km/s.
3.
The key is to have a rotational velocity, which in turn will give you the acceleration to overcome gravity.
4.
you can assure your daughters that nobody knows how gravity works
5. Kudos to Genghis for a, as i now see, much simpler explanation
---
About convergent sequences: Try to add 1 + 0,5 + 0,25 0,125.... You can go on as long as you want to, without ever reaching 2. The sum of the sequence is always increasing, but will only reach 2 in infinity, which of course never exists in practice. Still confused? Find a 2-meter rope. Cut it in half. Cut one half in half. Take the one quarter you get and cut that in half. Go on, make as many cuts you can. How many cuts does it take before all your pieces is exactly two meters, again?
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From: England
In theory you could go straight up at 1mph but you would have to run your engine for a long time. That would use a lot of fuel and that means lots of weight = more fuel needed to lift the fuel etc etc.
The point about escape velocity is that once you reach that velocity you can switch off your motor and you will still escape.
The point about escape velocity is that once you reach that velocity you can switch off your motor and you will still escape.
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From: Australia
Ghengis/hoggs,
You may tell your daughters, that as a result of around 15,000 hours of empirical testing using all sorts of aircraft from small to Humungous, the answer is:
Gravity Sucks !
Dents in runways around the world will testify to my research.
Regards F88
edited for speling
You may tell your daughters, that as a result of around 15,000 hours of empirical testing using all sorts of aircraft from small to Humungous, the answer is:
Gravity Sucks !
Dents in runways around the world will testify to my research.
Regards F88
edited for speling
Joined: Aug 1999
Posts: 1,050
Likes: 4
From: England
Have a look (and download) the free 'Orbiter' Sim from here:
http://orbit.medphys.ucl.ac.uk/orbit.html
- it models such physics as described here in exceptional detail and can get quite addictive (and complicated)!
http://orbit.medphys.ucl.ac.uk/orbit.html
- it models such physics as described here in exceptional detail and can get quite addictive (and complicated)!
CPB
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From: The center of the earths surface
Fraggs Quote's: Gravity suck's?
Fraggs I have never dented any runways 
so can't say I agree with you, as I only have 12500 hrs of testing:
But wait until the sphere stops spinning and see if you still think it sucks?
Here's to the long standing practice of "PISSING ON VELVET"
"May you discover this art form" Fraggs.
Capt Pit Bull, thanks.
HSnort
so can't say I agree with you, as I only have 12500 hrs of testing:But wait until the sphere stops spinning and see if you still think it sucks?
Here's to the long standing practice of "PISSING ON VELVET"
"May you discover this art form" Fraggs.Capt Pit Bull, thanks.
HSnort
