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Author Topic: Gravity as an accelerating acceleration?  (Read 6567 times)

Offline Supercryptid

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Gravity as an accelerating acceleration?
« on: 21/08/2006 03:26:44 »
I'm a bit confused about gravity here. The acceleration of gravity at the surface of Earth is 9.8 m/s^2, which is fine and dandy. But, depending on their distance, not all objects fall to Earth at that rate. At about 8,000 kilometers from the Earth's center, the rate of free fall is about 6 m/s^2. 1 lightyear away, and it's going to be way smaller than even that. So gravitational acceleration decreases as you farther from Earth.

But, as an object falls from 8,000 kilometers above the Earth's center, it's getting closer to the Earth every moment. That means that you can't use ~6 m/s^2 to calculate its time for freefall, because even its rate of acceleration would increase as it got closer to Earth. By the time it gets to the Earth's surface, it's not going to still be accelerating at ~6 m/s^2, it's going to be accelerating at 9.8 m/s^2. It seems to me, that gravity is therefore an accelerating acceleration, and not just a simple acceleration. But I can't find much information about this. Is my reasoning correct?


 

Offline lightarrow

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Re: Gravity as an accelerating acceleration?
« Reply #1 on: 21/08/2006 10:51:18 »
So, where is the problem? Of course the force of gravity, and hence the acceleration, varies with the distance! The same is for all kinds of forces. F = -k*M1*M2/r^2; where M are the masses and R is the distance between them. What is constant is k, not the acceleration.
 

Offline Soul Surfer

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Re: Gravity as an accelerating acceleration?
« Reply #2 on: 22/08/2006 18:00:12 »
The acceleration due to gravity also decreases linearly to zero as you go downwards below the surface of the earth.  The reson for this is that only the part of the earth inside the sphere from the centre of gravity to your position contributes to the attraction.  The gravitational force inside a spherical shell is zero.

The total velocity of an object falling from stationary with respect to the earth from a long way away to the surface of the earth is equal to the escape velocity which is about 7 miles per second

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Offline syhprum

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Re: Gravity as an accelerating acceleration?
« Reply #3 on: 24/08/2006 19:35:30 »
when  I was at school we were taught a rather simplified form of Newtonian physics that said that an object shot up moved in and parabolic path until it returned to earth.
This of course would be true if the earth was flat and of infinite extent but it is not!
The path taken is of course eliptical albeit that one of the foci is within the earth.
as the velocity is increased both foci are outside the earth and the object is in orbit
I have never been able to get anyone to admit the path taken is other than parabolic.

syhprum
 

Offline Soul Surfer

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Re: Gravity as an accelerating acceleration?
« Reply #4 on: 22/08/2006 18:00:12 »
The acceleration due to gravity also decreases linearly to zero as you go downwards below the surface of the earth.  The reson for this is that only the part of the earth inside the sphere from the centre of gravity to your position contributes to the attraction.  The gravitational force inside a spherical shell is zero.

The total velocity of an object falling from stationary with respect to the earth from a long way away to the surface of the earth is equal to the escape velocity which is about 7 miles per second

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Offline Soul Surfer

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Re: Gravity as an accelerating acceleration?
« Reply #5 on: 22/08/2006 18:00:12 »
The acceleration due to gravity also decreases linearly to zero as you go downwards below the surface of the earth.  The reson for this is that only the part of the earth inside the sphere from the centre of gravity to your position contributes to the attraction.  The gravitational force inside a spherical shell is zero.

The total velocity of an object falling from stationary with respect to the earth from a long way away to the surface of the earth is equal to the escape velocity which is about 7 miles per second

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Offline syhprum

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Re: Gravity as an accelerating acceleration?
« Reply #6 on: 24/08/2006 19:35:30 »
when  I was at school we were taught a rather simplified form of Newtonian physics that said that an object shot up moved in and parabolic path until it returned to earth.
This of course would be true if the earth was flat and of infinite extent but it is not!
The path taken is of course eliptical albeit that one of the foci is within the earth.
as the velocity is increased both foci are outside the earth and the object is in orbit
I have never been able to get anyone to admit the path taken is other than parabolic.

syhprum
 

Offline syhprum

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Re: Gravity as an accelerating acceleration?
« Reply #7 on: 24/08/2006 19:35:30 »
when  I was at school we were taught a rather simplified form of Newtonian physics that said that an object shot up moved in and parabolic path until it returned to earth.
This of course would be true if the earth was flat and of infinite extent but it is not!
The path taken is of course eliptical albeit that one of the foci is within the earth.
as the velocity is increased both foci are outside the earth and the object is in orbit
I have never been able to get anyone to admit the path taken is other than parabolic.

syhprum
 

Offline Soul Surfer

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Re: Gravity as an accelerating acceleration?
« Reply #8 on: 29/08/2006 09:50:02 »
True but one of the foci is always centered on the earth the object just misses the earth but for most practical purposes the parabolic approximation is good enough.  If you go into enough detail most familiar equations are approximations.  I remember one university physics homework calculation I was set in which we were asked to describe EXACTLY where "compared to a plumb line" an object would land when dropped from a tallish tower  (neglecting all effects caused by the atmosphere).  It's amazingly complicated.

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Re: Gravity as an accelerating acceleration?
« Reply #8 on: 29/08/2006 09:50:02 »

 

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