[Zer0 (OP)]

I've viewed graphs online showing the Dilation relationship between
" Time vs Velocity ".

As Velocity increases, Time ticks Slower.
(Unable to post a Graph Image due to Copyright claims on it)

But even Gravity affects the Rate of ticking of Time, Right?
More Gravity, the Slower Time ticks.

I just want to Know an approximation of how much Mass is required to slow Time by 25% 50% 75% & 100% respectively.

Can anyone post a
" Time vs Gravity " graph in here showing Dilation relationship.
(If it's Copyrighted, even a Link to the Website would work out Great)

P.S. - I Hope this is a Sensible question to have been asked...lol

[Halc]

More Gravity, the Slower Time ticks.

Gravity isn't a quantifiable thing. There's no such thing as 'there's twice as much gravity here as there is there'. There's no symbol or units for gravity.

What there is is mass, gravitational potential, and gravitational acceleration.
For Earth, these are respectively
mass: m = 6E24 kg
potential V = 60 MJ/kg
acceleration a = 9.8 m/sec

Your weight is due to the acceleration value, so you weigh about the same on Saturn as you do on Earth despite the vastly larger mass of it.

The middle one (V) determines the dilation.
Formula for dilation (relative to the absence of the mass) due to the potential at any point above the surface of some mass is 1 / √(1 - 2V/c²). Where V for a mass is GM/r.  It doesn't work for points below the surface.

I just want to Know an approximation of how much Mass is required to slow Time by 25% 50% 75% & 100% respectively.

It's not about mass. You can slow time over 80% with 1 kg if you get close enough to it, but it's very hard to get that close to the entirety of the 1 kg thing.

Can anyone post a  " Time vs Gravity " graph in here showing Dilation relationship.

I seem unable to find a graph of dilation vs potential. All the graphs seem to plot dilation vs radius. Those are all over the place. At least radius is positive. Potential is always negative.

[MikeFontenot]

But even Gravity affects the Rate of ticking of Time, Right?
More Gravity, the Slower Time ticks.

It is true that, for a uniform (constant in the direction of the field) gravitational field of strength "g", two clocks rigidly separated by distance "L" (in the direction of the field) will tic at different rates.  It is commonly believed that the clock farther from the source of the field will tic faster than the closer clock by the factor

  exp(L * g).

This equation has only been tested for very small fields (which are not quite uniform, and for which the argument [L * g] is so small that the exponential is tested only in its linear range when it has a value very near 1), and it gives reasonable results for that.  But I have shown, when the gravitational field  "g" is replaced by an acceleration "A" (via the equivalence principle), that for very large "A" (lasting only for a very short duration), the exponential equation gives results that contradict the outcome of the twin paradox.  In that dispute, the twin paradox outcome wins.  I have derived a new gravitational time dilation equation that agrees perfectly with the outcome of the twin paradox.

[paul cotter]

That's interesting, Halc. That formula is a close analogue of the Lorentz factor for speed related relativity effects- I had guessed the gravitational equation would be more complex. Does V have the same dimensionality as csquared?.PS: it cant have the same dimensionality, that was a premature question. Now i'm confused.

[alancalverd]

The "time versus gravity" physics is well described by the Wikipedia article on the Pound-Rebka experiment. The blue shift of photons travelling towards a lower gravitational potential is exactly analogous to the ground observer's measurement of received clock frequency from an elevated source. The experimental result was remarkably good, and the everyday importance of the analysis is embedded in satellite navigation.

[Zer0 (OP)]

I Appreciate all of you giving deep & detailed responses.

I just Forgot to mention " Plz explain as if you were trying to make a kid Understand " in my initial question.

Anyhow, I'll ask stuff which is relevant to my intellectual understanding on the Topic...

1) The Internet says Earth's Gravity is 1g.(small non capital g)
So small " g " is not a quantifiable symbol?

2) acceleration is 9.8 m/sec or 9.8 m/sec Squared?

3) I'm completely bowled over the Fact that my weight won't change considerably on Saturn.
(i need sum time to absorb this)

But Saturn has more Mass than Earth..is it bcoz all that mass is dispersed over a very very larger surface area?
Is Gravity not a Force?
If the Attraction Effect is due to simply " acceleration " then how come I'd weigh less on the Moon?
(lol dis is driving me Crazee)

4) If it ain't about Mass but only
" acceleration " then in what way is the Earth accelerating more than the Moon?

On the Internet it says Moon g = 1.625 m/s2.
So what Exactly is moving at the rate of 1.625 m/s2?
The surface of the Moon is moving Upwards at that Rate eh?

5) slow time by 80% by gettin Real close to 1kg...lol.
1kg of sum gud potent weed i suppose...hell yeah!
(Plz don't even try, don't waste your time explaining dis, i simply won't get it)

P.S. - i kinda feel a lil sad now, so much time spent on Science, n still im unable to understand Graviteee!
☹️
(sad face emoji)

[paul cotter]

Zero, I believe I could answer most of your questions. However i'm tired and ready to hit the sack. If you haven't got an answer in ~12hours I will respond.

[Halc]

I don't think they try to explain general relativity to 'a kid'. It's an unreasonable request.

1) The Internet says Earth's Gravity is 1g.(small non capital g)
So small " g " is not a quantifiable symbol?

The site you found should have called that gravitational acceleration. Many pop sites get the terminology wrong. g is a measure of acceleration due to gravity. This is the third thing on my list. Time dilation isn't due to that.

2) acceleration is 9.8 m/sec or 9.8 m/sec Squared?

This is the value of g on the surface of Earth: 9.8 m/sec².  Notice the little ² up there. It is one of the characters you can select on the green symbol choice above the post window. You're always posting shortcuts for people. Here's me returning the favor. There's also a couple fractions up there, one of which I use below.

Anyway, m/sec is a speed. m/sec² is an acceleration, meaning that absent other forces, velocity of an object relative to the surface of Earth changes by 9.8 m/sec every second. If you drop a dart off a cliff, and it takes 2 seconds to hit the ground, it will be moving around 19.6 m/sec when it hits, minus speed lost to air drag.

3) I'm completely bowled over the Fact that my weight won't change considerably on Saturn.
(i need sum time to absorb this)

Scalar gravitational acceleration is computed by g = GM/r². G is constant. M is almost 100x more for Saturn, but you're nearly 10x further from its center, so the /r² part nearly cancels the bigger M.

Is Gravity not a Force?

In Newtonian physics, gravity is a force, but you're asking about dilation, so Newtonian physics isn't where you should be looking. Under relativity, gravity is curvature of spacetime. In flat space or spacetime, parallel lines never meet, but in positively curved space like the surface of Earth, parallel lines meet more than once. The lines don't curve (a train on a straight track doesn't accelerate left or right), but two trains nevertheless might meet where the straight tracks must cross.

If the Attraction Effect is due to simply " acceleration " then how come I'd weigh less on the Moon?

It isn't. Your change in speed is defined by acceleration. You weigh less on the moon because it isn't very massive and you're not close enough to the center of mass to bring your weight up higher. Digging a hole doesn't work because only the mass beneath you contributes to your weight. Mass is the first thing on my list, and it doesn't cause dilation either.

4) If it ain't about Mass but only
" acceleration " then in what way is the Earth accelerating more than the Moon?

The Earth isn't accelerating. Well, OK, it is, mostly due to the sun's gravity, but by itself it would just sit there and not change speed at all. It is you that accelerates if you fall.

On the Internet it says Moon g = 1.625 m/s2.
So what Exactly is moving at the rate of 1.625 m/s2?[/quote]1.625 m/s² is an acceleration, not a rate of movement (speed). It is a free-falling object that accelerates at these various rates, so essentially nothing on the moon since all of it is sitting on the surface.

The surface of the Moon is moving Upwards at that Rate eh?

No. The surface of moon and Earth are both just sitting there, neither being in freefall. The ISS accelerates at about 7¾ m/sec² at all times because unlike you, it is in freefall. The 7¾ is less than 9.8 because it is farther from Earth (bigger r) than something on the surface.

You didn't comment on the 2nd thing in my list: gravitational potential. If two 'stationary' clocks are at the same gravitational potential, they'll tick at the same speed, regardless of the local gravitational acceleration and regardless of the amount of mass nearby. So for instance, a clock on Ganymede (g = about a 7th that of Earth) would tick nearly a the same rate as one on Uranus (g = 8.9 m/s², about 90% that of Earth). Those were the two objects I could find with the closest potentials at their respective surfaces.

[paul cotter]

Zero, Halc has made further comment by me redundant with one exception. The reference to 1kg and 80% is, I believe, as follows: if one were close enough to a POINT mass of 1kg the gravitational potential would be sufficient to cause 80% time dilation. I'm still confused by the dimensional analysis of the quoted equation for gravitational time dilatation and would be much obliged if someone could help me out.

[Zer0 (OP)]

Thank You for your inputs Mr Cotter...much appreciated!

If the Kidd is a savant & way ahead on the academic learning curve, then maybe it won't sound like an Unreasonable Request.
(I don't wanna play word salad with u, coz i already know, eventually in the end, u'll win lol)

1) i keep hearing & seeing that " g " thing almost everywhere.
From rollercoasters to jet planes to missiles n stuff.
But considering it's b'coz of Gravitational Acceleration is UnDeniable.
Maybe They just use a small " g " to make it easier to say n talk about.

2) ¹
Yep! Got it...Thanx!
(I kinda knew bout it, let's say i got fat buttery fingers & a cheap small screen chinese phone)
²
(ya ya save it, i know the forum page can be enlarged, it didn't use to work before when i enlarged it, but to my great luck, it's workin like a charm today)
³
" acceleration a = 9.8 m/sec "
(watch out, sumtims We click, but it doesn't register)

3) so then i seem to understand this one Right?
Saturn has more Mass but the Radius is very large, hence low Gravity.
If Saturn had same Mass, but half Radius, Gravity would have been More, Correct?
So then it isn't really about the Quantity of Mass, rather Gravity is dependent on the way in which that Mass is structured, concentrated, densely packed.
(that to me could help explain how Time could be slowed considerably(80%) just by a little amount of Mass(1kg))

U remember i said this in another OP...one thing leads to another, n then to the next...
Mass & Weight are Different.
For the first time ever in life, I'll be reading up on 9.81N(newtons)
(wish me luck)

Yes there seems to be a distinction between Newton's Gravity & Einstein's Gravity.
The Curvature of SpaceTime.
(I had watched an animated video on Utube showing an Apple detaching from the branch of the Tree. And it did not fall down, it stayed right there suspended in free Space. Then They explained that the Apple doesn't just Exist in only Space, but Time as well. Hence as it moves thru Time, it seems to be moving towards the bottom, but it's just stuck in the Curvature of SpaceTime.)

The Moon has less Mass, hence I'd Weigh less.
(Understandable, seems like common sense.)
But what if the Moon had 10x less Radius but same amount of Mass.
Then I'd surely Weigh More, Correct?
(g = GM/r²)

4) i think i get these points.
Seem like stupid questions to have asked now.
Glad to know the surfaces of both the Moon & Earth ain't going anywhere lol.

That " Gravitational Potential " & " Stationary Clocks " thingy was for Mee?
Perhaps You accidently posted that in here, isn't it.
(Anyways, I'll take that up as a challenge n provide U with an Answer, just gimme 3 days to figure out Gravitational Potential, Ganymede & Uranus)
lol have lil faith!
I'll crack it.

M is the First, V is Second & g is Third...now I'm Curious, what sort of a list is this anywhichways?

P.S. - I'd Really Appreciate if Someone could help out Paul by responding to his doubts, Thanks!

*Disclaimer - Marijuana usage is Harmful to Health & Damages the Brain.
😳
(If you're one of those who's already gifted with a very small intelligent quotient, then using weed/dope would be similar to committing intellectual suicide)

[MikeFontenot]

The "time versus gravity" physics is well described by the Wikipedia article on the Pound-Rebka experiment. The blue shift of photons travelling towards a lower gravitational potential is exactly analogous to the ground observer's measurement of received clock frequency from an elevated source. The experimental result was remarkably good, and the everyday importance of the analysis is embedded in satellite navigation.

But if you look closely at those confirmations, none of them test the nonlinear part of the exponential function where the argument L*g or L*A is very large (and THAT is what is important in the twin paradox scenario).  Except for my calculations, the exponential function has only been tested in the near-linear portion when L*g or L*A is very small.

If you do the sequence of finite calculations that I describe in my first paper, which involves always getting on each iteration the same (finite) velocity change (which determines the acceleration for different choices of the acceleration duration "tau"), you will find that the exponential function produces a limit, as "tau" gets closer and closer to zero, that is unbounded ... i.e., for "tau" equal zero and acceleration infinite (but such that the velocity change is the same finite value used in each iteration of the sequence of finite calculations), the home twin's age is INFINITE at the reunion, which contradicts the well known (and trustworthy) time dilation equation (TDE) for an inertial observer.

[alancalverd]

Beware of Zeno's Paradox!

[Zer0 (OP)]

I figured out the Ganymede vs Uranus stationary clocks thingy.
(I believe i did)

Ganymede is under the influence of Jupiter's gravitational well.

Took just a few minutes to figure it out, but spent rest of the days thinkin it's a " Trick Question ".
(bcoz the solution seemed so easy)

Soo...am i Right?

" But what if the Moon had 10x less Radius but same amount of Mass.
Then I'd surely Weigh More, Correct?
(g = GM/r²) "
?

P.S. - Has Paul become invisible to Others?