Why is gravitational acceleration independent of test masses?

[Gazi]

how two objects hit the ground at same time regardless of their weight of masses.
what is the reason of Acceleration is always constant via gravitational force for both of them. F=mg
F1/m1=F2/m2

 

[pervect]

how two objects hit the ground at same time regardless of their weight of masses.
what is the reason of Acceleration is always constant via gravitational force for both of them. F=mg
F1/m1=F2/m2

When you phrase it in terms of forces, you are implicitly asking about Newtonian gravity and not General Relativity. According to Newtonian gravity, it's just a coincidence that all matter, regardless of what it's made of, falls at the same rate. Another way of saying this is that the inertial mass is always equal to the gravitational mass.

In terms of General Relativity, the theory is that the equivalence of gravitational and inertial mass is not just a coincidence, but it's postulated as part of the theory. One way of stating this is that gravity is an inertial force. Pursuing this line of thought eventually leads to the idea that falling objects are moving along special curves called geodesics, and that this motion is the natural force-free motion that all objects share.

 

[Gazi]

I took a look web site, it says, all freely-falling bodies experience the same acceleration, that is, a = -g
Mass of gravitational = Mass of inertial.
There is no obvious reason why the inertial mass m that governs the response of a body to an applied force... http://www.britannica.com/science/inertial-mass
i guess there is no brief explanation for the situation.

 

[Ibix]

In terms of Newton's theory of gravity, there is no explanation. It's just one of those things.

In terms of Einstein's theory of gravity, gravity isn't a force. Instead it is a curving of spacetime. Objects all act the same way because they're moving through the same curved spacetime. Their own mass doesn't come into it.

 

[A.T.]

how two objects hit the ground at same time regardless of their weight of masses.

Note that the definition of an "object" is arbitrary. You can consider two equal apples falling side by side as two objects, you might also consider them as just one object called "pair of apples", that has twice the weight of a single apple.

 

[MikeGomez]

how two objects hit the ground at same time regardless of their weight of masses.

Galileo would ask you to explain how it would make sense any other way. Let’s say the larger rock falls faster and the smaller rock falls slower. If we tie the two rocks together the small rock falling slower would slow down the large rock.

But another way to think about it is that the combination of the two rocks makes a rock that is larger than either of the original rocks, so the two rocks tied together should fall faster than the original rocks.

So should the (tied together larger rock) fall faster or slower than the original rocks?

What A.T. said in post #5 is correct. What you decide to call an object is arbitrary.

 

[DrStupid]

According to Newtonian gravity, it's just a coincidence that all matter, regardless of what it's made of, falls at the same rate. Another way of saying this is that the inertial mass is always equal to the gravitational mass.

I wouldn't call it a coincidence because Newton set inertial and gravitational mass equal because all bodies are falling identical.

 

[Gazi]

In terms of Newton's theory of gravity, there is no explanation. It's just one of those things.

In terms of Einstein's theory of gravity, gravity isn't a force. Instead it is a curving of spacetime. Objects all act the same way because they're moving through the same curved spacetime. Their own mass doesn't come into it.

if gravity isn't a force, how objects act the same way,... moving through curved space time? if there is no force, no motion

 

[Ibix]

if gravity isn't a force, how objects act the same way,... moving through curved space time? if there is no force, no motion

That's not true even in Newtonian physics. Things move in straight lines at constant speed.

The same is true in general relativity. The only difference is that near massive bodies, the concept of a straight line doesn't really make sense. Spacetime is curved and you can't move in a straight line through it without applying a force (if you can even define "straight line" unambiguously). Objects in free fall near massive bodies move along curved paths because massive bodies curve spacetime.

 

[pervect]

I wouldn't call it a coincidence because Newton set inertial and gravitational mass equal because all bodies are falling identical.

If you've got a ball of, say lead, and you split it into two parts, it's not a coincidence that the two parts fall at the same rate. But there's no a-priori reason that a ball of copper, a ball of lead, and a feather (ignoring air resistance, obviously) should all fall at the same exact rate according to Newton's theory. We observe that they do, and this leads to the principle of equivalence, one of the foundational principles of GR.

 

[DrStupid]

If you've got a ball of, say lead, and you split it into two parts, it's not a coincidence that the two parts fall at the same rate. But there's no a-priori reason that a ball of copper, a ball of lead, and a feather (ignoring air resistance, obviously) should all fall at the same exact rate according to Newton's theory.

Both, Newtonian mechanics and general relativity are designed to result in identical trajectories for all free falling objects and both Newton and Einstein did it for the same reason: because we observe that in nature.

 

[Gazi]

That's not true even in Newtonian physics. Things move in straight lines at constant speed.

The same is true in general relativity. The only difference is that near massive bodies, the concept of a straight line doesn't really make sense. Spacetime is curved and you can't move in a straight line through it without applying a force (if you can even define "straight line" unambiguously). Objects in free fall near massive bodies move along curved paths because massive bodies curve spacetime.

i need to fix my last sentence, it would be if there is no force, no acceleration which is gravity. Newton's first law says, if an object is moving along, untouched by a force of any kind, it will continue to move along in a perfectly straight line at a constant speed...

 

[Ibix]

Both, Newtonian mechanics and general relativity are designed to result in identical trajectories for all free falling objects and both Newton and Einstein did it for the same reason: because we observe that in nature.

Yes. But Newtonian gravity doesn't forbid some kind of Unobtanium whose "gravitational charge" is $\kappa m$ but whose inertial mass is $m$, and the fix to Newtonian gravity is easy. But you can't fix GR in the same way since the geodesic equation doesn't directly depend on the mass of the free falling particle, which means that "no Unobtanium" is a prediction of GR - at least that's my understanding.

 

[Ibix]

Newton's first law says, if an object is moving along, untouched by a force of any kind, it will continue to move along in a perfectly straight line at a constant speed...

Yes. But Newton made three assumptions that turned out to be incorrect - that time is a separate thing from space, that it is an absolute thing that everyone agrees on, and that space obeys the rules of Euclidean geometry. That last is why things move in straight lines when not accelerated. But in GR spacetime is non-Euclidean, so objects move along curves through spacetime. You may wish to search these forums for posts by @A.T. who has produced a nice animation describing this.

 

[PeroK]

i need to fix my last sentence, it would be if there is no force, no acceleration which is gravity. Newton's first law says, if an object is moving along, untouched by a force of any kind, it will continue to move along in a perfectly straight line at a constant speed...

All laws and formulas have a context in which they are true. Newton's. First law is, in fact, only valid in inertial reference frames. It's not valid in an accelerating reference frame. If you are accelerating then you see objects moving in curves not straight lines.

Someone at rest in a gravitational field is effectively in an accelerating reference frame. That is the approach of general relativity.

In classical mechanics, of course, gravity must be considered a force. But not in GR.

 

[Gazi]

What is GR. gravitational radiation?

 

[jbriggs444]

What is GR. gravitational radiation?

GR = General Relativity. Our best current model for gravitation.

 

[ZapperZ]

how two objects hit the ground at same time regardless of their weight of masses.
what is the reason of Acceleration is always constant via gravitational force for both of them. F=mg
F1/m1=F2/m2

https://www.physicsforums.com/insights/why-is-acceleration-due-to-gravity-a-constant/

Zz.

 

[Gazi]

F1/m1=F2/m2=F3/m3.....= gravity.
formulas don't explain the reason why all object fall at same time.

 

[ZapperZ]

F1/m1=F2/m2=F3/m3.....= gravity.
formulas don't explain the reason why all object fall at same time.

They don't! They only fall at almost the same time when the OTHER body has a mass significantly bigger than all the others.

Did you even read and understand the link I gave?

Zz.

 

[Gazi]

They don't! They only fall at almost the same time when the OTHER body has a mass significantly bigger than all the others.

Did you even read and understand the link I gave?

Zz.

yes. I checked the web site. The formula F=ma is a Newton's second law which is same formula with gravity. F=m g, gravitational force is 9.81m/s2 equal for all objects in world. thus proportion of F1/m1=F2/m2=F3/m3=F4/m4...= gravity. Mass of gravitational = Mass of inertial for any object . a = -g but it don't explain atomic scale approach... except GR which is about bending space time.

 

[ZapperZ]

yes. I checked the web site. The formula F=ma is a Newton's second law which is same formula with gravity. F=m g, gravitational force is 9.81m/s2 equal for all objects in world. thus proportion of F1/m1=F2/m2=F3/m3=F4/m4...= gravity. Mass of gravitational = Mass of inertial for any object . a = -g but it don't explain atomic scale approach... except GR which is about bending space time.

What "atomic scale approach"?

At the atomic scale, Gravity is irrelevant!

Zz.

 

[A.T.]

Newton's first law says, if an object is moving along, untouched by a force of any kind, it will continue to move along in a perfectly straight line at a constant speed

Note that this constant velocity, under no force, corresponds to a straight path in a space-time diagram. This is still true in General Realtivity were gravity is not a force: Free falling objects, have locally straight paths in a space-time (geodesics).

 

[Ibix]

yes. I checked the web site. The formula F=ma is a Newton's second law which is same formula with gravity. F=m g, gravitational force is 9.81m/s2 equal for all objects in world. thus proportion of F1/m1=F2/m2=F3/m3=F4/m4...= gravity. Mass of gravitational = Mass of inertial for any object . a = -g but it don't explain atomic scale approach... except GR which is about bending space time.

If you want to stick with Newton (which $F=ma$ and $F=GMm/r^2$ is) then there is no explanation. It's just the way it is. Newton does not say that we will never find a material that does not fall with the same acceleration; only that every material we have ever seen does so.

General Relativity does provide an explanation. Gravity is not a force. What you think of as the force of gravity is a misinterpretation of what is going on. Actually, spacetime is curved near massive bodies and the unaccelerated paths of bodies are curves (even things you think of as "not moving" are moving through time and the curvature means they don't stay only moving through time). Because an unaccelerated thing is an unaccelerated thing regardless of mass, their paths depend only on their velocity and position.

 

[Gazi]

Note that this constant velocity, under no force, corresponds to a straight path in a space-time diagram. This is still true in General Realtivity were gravity is not a force: Free falling objects, have locally straight paths in a space-time (geodesics).

height=1/2gt2= 4.9m 1st sec.
19.62m 2nd sec.
44.14m 3rd sec.
78.48m 4th sec.
bending space time parabolic is only way to provide motion to object at constant velocity, flow of time doesn't accelerate or decelerate via bending space-time. however video shows that time is bent with space as a sheet.

 

[Ibix]

height=1/2gt2= 4.9m 1st sec.
19.62m 2nd sec.
44.14m 3rd sec.
78.48m 4th sec.
bending space time parabolic is only way to provide motion to object at constant velocity,flow of time doesn't accelerate or decelerate via bending space-time. however video shows that time is bent with space as a sheet.

Taking your points in no particular order...

Clocks do tick at different rates at different heights and states of motion (see the general relativistic correction to the GPS clocks or the Pound-Rebka experiment). I think that's probably what you mean by "flow of time accelerating".

Don't get too hung up on the grid in the video - you can draw different grids. However, most of the spacetime curvature in the vicinity of the Earth is in the time-like direction so the space-like lines remain nearly straight. This must be the case or we would notice failures of Euclidean geometry in everyday life.

The curvature is approximately parabolic, yes. Higher order terms aren't significant near the Earth - however one of the first failures of Newtonian gravity was that it predicted the precession of the orbit of Mercury incorrectly - in fact this is because of those higher order terms which are present in reality and general relativity, but not Newton's theory.

 

[A.T.]

bending space time parabolic is only way to provide motion to object at constant velocity

Did you mean constant acceleration? Note that the parabolic world line is just an approximation, even in Newtonian mechanics. And the diagram in the video is not scaled naturally with 1second = 1lightsecond. However, on small scale in weak gravity gradient the difference between the two models becomes negligible.

flow of time doesn't accelerate or decelerate via bending space-time

Gravitational time dilation is described by space time geometry:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

 

[Gazi]

Taking your points in no particular order...

Clocks do tick at different rates at different heights and states of motion (see the general relativistic correction to the GPS clocks or the Pound-Rebka experiment). I think that's probably what you mean by "flow of time accelerating".

Don't get too hung up on the grid in the video - you can draw different grids. However, most of the spacetime curvature in the vicinity of the Earth is in the time-like direction so the space-like lines remain nearly straight. This must be the case or we would notice failures of Euclidean geometry in everyday life.

The curvature is approximately parabolic, yes. Higher order terms aren't significant near the Earth - however one of the first failures of Newtonian gravity was that it predicted the precession of the orbit of Mercury incorrectly - in fact this is because of those higher order terms which are present in reality and general relativity, but not Newton's theory.

curvature depends on height of object from ground thus parabolic curvature change for any height.?

 

[A.T.]

curvature depends on height of object from ground thus parabolic curvature change for any height.?

Parabolic world lines are an approximation, based on the assumption of a uniform, Newtonian gravity. In reality the field is neither exactly uniform nor Newtonian.

 

[Ibix]

curvature depends on height of object from ground thus parabolic curvature change for any height.?

I'm not sure what you mean.

 

[Mark Harder]

F₁ / m₁ = g. (Inertial masses and forces).
F₂ / m₂ = G M/r². (Gravitational masses and forces).
The quantities on the rh sides of both equations are all measurable quantities that don't depend on any assumptions about gravitational and inertial forces and masses. So we can equate the lh sides of both equations and we get F₁ / m₁ = F₂ / m₂ . Assuming that inertial mass = gravitational mass, i.e. m₁ = m₂ the m's cancel leaving the forces equal. So we can equate the rh sides of the first 2 equations:
g = G M/r ²,
which means that gravitational acceleration is independent of the test masses.