Can the Change in Gravitational Field Strength Exceed Its Original Value?

In summary, the conversation revolves around the formula g-g'=(2h/R)g which explains the change in gravitational field strength when h<R. It is noted that if h=3R/4, the change in gravitational field strength will be 1.5g, which seems to be bigger than the original strength. The conversation also touches upon the proof of F=GMm/R2 and where to find more information on gravitational field. It is mentioned that F=-GMm/r² is considered the axiom of Newton's theory of gravitation and cannot be proven absolutely. Additionally, it is mentioned that the local difference in gravity strength at different heights is only approximately equal to 2g(h/R) and this can be proven using
  • #1
ngkamsengpeter
195
0
I come across this formula :
g-g'=(2h/R)g ; h<R
However , if I substitute h =3R/4 the change in gravitational will be 1.5g .
How can the change of gravitational field strength is bigger than its original gravitaitonal field strength ?

Besides , how can I prove F=GMm/R2 ?

Besides this , where can I find the details explanation on gravitational
 
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  • #2
?! Where did you find this formula?

P.S. You can't prove F = -GMm/r². Newton defined force as F = ma and then calculated that a grav. force of the form F = -GMm/r² would explain both the motion of the planets and the falling of apples at the surface of earth. From there, we can only make observations that will either agree with his theory of gravitation, or disprove it. But never prove it.

Edit: What I meant to say is that F = -GMm/r² is like THE axiom of Newton's theory of gravitation. Historically, this was the mother equation, and all the other flowed from it. Of course, starting from different axioms, you could manage to derive, and thus "prove" F = -GMm/r². But it would only be a proof in the mathematical sense of the word, meaning that F = -GMm/r² is true provided your axioms are true. But since no axioms on which a physical theory is built are absolutely provable, nothing is absolutely provable, including F =-GMm/r².
 
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  • #3
The local difference in gravity strength at different heights
(g_lo - g_hi) is only APPROXIMATELY equal to 2g(h/R) , and
only if h be MUCH smaller than R : h << R .

We START with g = GM/R^2 . If we move to a higher elevation,
R becomes [tex] R_{hi} = R_{lo} + h [/tex] ; [tex] {R_{hi}}^{2} = {R_{lo}}^{2} + 2 h R_{lo} + h^{2} [/tex] .
We ignore h^2 compared to R.
Now, the fractional "%" difference [tex]({R_{lo}}^2 - {R_{hi}}^2) / {R_{lo}}^2 \approx 1 - 2h/R \approx \frac{1}{1+2h/R}[/tex]
So g_old , at low elevation , changes by the reciprocal of that factor,
[tex]\frac{g_{lo}-g_{hi}}{g} \approx 1 + 2h/R[/tex] .

(this is easier with derivatives)

You can "prove" that nested sperical shells (sort-of-like Earth)
are surrounded by a gravity field "as if" they were all at R = 0 ...
 
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1. What is gravity?

Gravity is a natural force that attracts objects with mass towards each other. It is responsible for keeping planets in orbit around the sun and objects on Earth from floating off into space.

2. How does gravity work?

Gravity works by the mass of an object creating a curvature in space-time. This curvature causes objects to move towards each other, creating the force we experience as gravity.

3. How was gravity discovered?

Gravity was first discovered by Sir Isaac Newton in the 17th century. He observed the motion of objects and developed the theory of gravity and the laws of motion.

4. What is the difference between mass and weight in relation to gravity?

Mass is the amount of matter an object contains, while weight is the measurement of the force of gravity acting on an object. The more mass an object has, the stronger its gravitational pull.

5. Can gravity be manipulated or controlled?

As far as we know, gravity cannot be manipulated or controlled. However, scientists are constantly studying and researching ways to understand and potentially harness gravitational forces for space travel and other applications.

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