Newtonian Gravity: How GR Affects F=GMm/d^2

[Stratosphere]

What exactly was wrong with Newtons gravity. I understan that GR says that gravity is the curveture of space and time. However if Newton was wrong wouldn't that mean that F= GMm/d^2 is actualy wrong?

 

[ZapperZ]

What exactly was wrong with Newtons gravity. I understan that GR says that gravity is the curveture of space and time. However if Newton was wrong wouldn't that mean that F= GMm/d^2 is actualy wrong?

Newtonian mechanics is also "wrong" at speeds near c. Do you see us abandoning Newton's laws when we build houses and buildings?

You need to look at under what conditions the classical description are no longer accurate. It doesn't mean that they are wrong. It just means that they work very well, within the accuracy that we need, only within certain range of conditions.

Zz,.

 

[arildno]

What exactly was wrong with Newtons gravity. I understan that GR says that gravity is the curveture of space and time. However if Newton was wrong wouldn't that mean that F= GMm/d^2 is actualy wrong?

For all eternity, predictions made on basis of Newtonian mechanics will remain as precise as they always have been.

 

[Stratosphere]

So F= GMm/d^2 is correct?

 

[D H]

No. It is approximately correct in a limited domain (but a very useful domain to us).

 

[Stratosphere]

How limited are we talking?

 

[T.O.E Dream]

depends, we don't usually well actually we never travel anywhere near the speed of light maybe some pilots (usually military) travel past the speed of sound which is only a very and i mean very small fraction of the speed of light so in order for Newtonian physics to start to appear wrong is about 10 percent of C, though it's always wrong but very, very slightly at normal speeds. (that's only SR)

 

[T.O.E Dream]

again sound travels very, very, very slow compared to the speed of light

 

[xxChrisxx]

You have to remember that no physics equations are really 'right' per se. They are just models to describe what we see, some models are better then others others are valid in different circumstances.

Newtons model describes gravity in every day life well enough, but like TOE said at 0.1C things start to go wrong. This is where GR model takes over.

Neither are right or wrong, just valid in different circumstances.

 

[ImAnEngineer]

How limited are we talking?

How limited you're talking depends on how accurate you want to predict ;) .

 

[jtbell]

One of the first experimental tests of GR was its prediction of the rate of precession of the perihelion of Mercury. Newtonian gravity predicted a rate of 5557 seconds of arc per century. The actual measured value is 5600 seconds of arc per century, consistent with Einstein's prediction from GR.

http://phyun5.ucr.edu/~wudka/Physics7/Notes_www/node98.html

Differences between GR and Newtonian gravity are largest for Mercury's orbit because it's closest to the sun and experiences the strongest gravitational field. For the other planets, the differences are a lot smaller. If you don't need to deal with that level of precision, Newtonian gravity works fine on the scale of the solar system.

 

[D H]

One of the first experimental tests of GR was its prediction of the rate of precession of the perihelion of Mercury. Newtonian gravity predicted a rate of 5557 seconds of arc per century. The actual measured value is 5600 seconds of arc per century, consistent with Einstein's prediction from GR.

That was more of a post-diction than a prediction. That 43 arcsecond per century discrepancy was a known problem with Newtonian gravity at the end of the 19^th century. The first successful prediction of GR was the bending of a ray light from some remote star as the ray passed by the Sun. GR predicted this result before it was observed in solar eclipses.

That 43 seconds of arc per century discrepancy between prediction and measurement is a tribute to 19^th astronomers. First thing to note: 43 seconds of arc per century is an incredibly small number. It is equal to 0.00012 degrees per year. It would take three million years to accumulate an error of 360 degrees. That astronomers could even see such a discrepancy using 19^th technology is quite amazing.

Second thing to note: Calculating what Newtonian mechanics predicts for the precession requires a precise understanding of the Earth's rotation (~5026 arc seconds per century of Mercury's apparent precession arises from the precession of the Earth's rotation axis), precise estimates of the masses and orbits of the other planets (~531 arc seconds per century of Mercury's precession arises from interactions with other planets), and doing all of the hairy calculations with pencil and paper. Another tribute to 19^th astronomers and mathematicians.GR makes itself apparent much more readily in terms of time rather than position. Our GPS receivers would give incredibly bad positions if the special and general relativistic effects on clocks were not taken into account.

 

[Bob S]

Newtonian mechanics is also "wrong" at speeds near c. Do you see us abandoning Newton's laws when we build houses and buildings?
Zz,.

When experimenters (Pound and Rebka (Harvard), 1959) put a Mossbauer Effect experiment iron-57 14.4 keV photon source at the top of a 73.8 foot tower (roof of physics building) and a detector in the basement, the experiment showed that when the photons fall to the ground, their energy increases (doppler shift). Although the energy shift due to gravity was very small (about 1 part in 10^15), the measured energy shift agreed with GR predictions to about 1%. So both apples photons gain energy when falling from trees or tall buildings.