# Was Newton in Error?

ptabor
My philosophical prejudices lead me to believe that the necessity of dark matter/energy implies a shortcoming in our understanding of gravity.

Clearly, there are shortcomings at the quantum scale, but this is another matter entirely.

I ran across an article on physicsweb where a scientist proposes a test for a MOND theory.

http://physicsweb.org/articles/news/11/3/12/1

2) What are your educated opinions on MOND theories?

Staff Emeritus
Gold Member
Clearly, there are shortcomings at the quantum scale, but this is another matter entirely.

I disagree with this.

In quantum field theory, the vacuum is not like a classical vacuum, it is the ground state of the system. In classical physics, the zero for energy (think mgh) can be chosen arbitarily, but in general relativity, mass/energy is responsible for the spacetime curvature that is gravity, so establishing the zero is important. Many physicsts believe dark energy is the energy of the quantum vacuum, but naive calculations give what might be the worst disagreement between theory and experiment in the history of science.

Because of all this, I think that understanding the relationship between the quantum vacuum and (a possible modification of) general relativity is necessary (but maybe not sufficient) for an understanding of dark energy. Maybe dark matter too.

I think that MOND is too ugly to be correct, but this opinion is far from scientific. Experiments are important.

Ivan Alexander
Is there a MOND like ‘modifier’ for our solar system, but gentler?

Newton postulated that his gravity ratio between masses is a ‘universal constant’ G, and it had been used as such ever since. However, though we get good orbital results for our solar system, this ran into difficulty when orbital behavior for outer galaxy arms were observed, where they acted as if there was more massive matter there, invisible to us, so dubbed ‘dark matter’. Mordehai Milgrom’s MOND solution was to factor in an acceleration force, F = ma^2/ a_o, which translates using F = GMm/ r^2, into a = (GM a_o/ r^2)^1/2, where Milgrom calculated the value for a_0=1.2×10^−10 ms^−2 empirically. This does not invalidate Newton’s constant G, but it does indicate that over great astronomical distances, force from gravity may have a modifier in it.

Since the discovery of the Pioneer Anomally by Anderson, Nieto, Turyshev et al, there had been independent speculations that perhaps a similar modifier may be at work within our solar system to account for the anomalous acceleration towards the Sun by Pioneers, Galileo, and Ulysses space crafts, though non- gravitational systemic reasons were not fully disqualified. However, if the Pioneer Anomaly is telling us something about our solar system that is gravitational, ‘dark matter’ like, for our solar system (where the computed –a = ~8E^-10 ms^−2 approximates Milgrom’s a_0), then there may be cause to look for a gravitational anomaly within our solar system as well. Such an anomaly, for example, may account for the very large atmospheres of the outer gas giants, or some moons like Titan’s atmosphere, or Pluto’s atmosphere, where the masses of distant bodies calculated using a constant Newton’s G works for orbital dynamics, but may be giving us erroneous readings for planetary mass densities.

One possible indication of this is by using Milgrom’s MOND’s a = (GM a_o/ r^2)^1/2 and modifying it for our solar system, but to drop Newton’s assumption of a constant universal G, and give it a variable value instead. For example, if we ‘assume’ a variable G at the rate of 1G per 1AU with distance from the Sun (at present unsubstantiated empirically), we get an approximation of the Pioneer Anomaly, as follows:

-a = (GM a_o/ r^2)^1/2, which becomes modified with 1G per 1AU as:

-a = [G(AUn)M a_o/ r(AUr)]^1/2, where AUn is the number of AU distance, and AUr is the distance r for one AU, so with numbers, for Earth’s orbital:

-a = [(6.67E-11)(1)(1.98E+30)(1.2E-10) / (1.5E+11)(1.5E+11)]^1/2, gives us a value of:

-a = (15.8479E+9 / 2.25E+22)^1/2 = (70.435E-14)^1/2

-a = 8.3934E-7 m/s^2, which is three orders of magnitude greater than Pioneer’s –a = ~8E-10 m/s^2, too far out of ball park.

The same calculation for any distance in AU will yield the same result, i.e., at Saturn’s 9.5AU, where r = 1.429E+12 m, gets nearly same result, viz. –a = 8.38E-7 m/s^2

However, what Milgrom calculated for the outer galaxy flat rotation curves may not be the same as what is operable within the limits of our solar system, so that a ‘gentler’ MOND effect may be the case here, which can be calculated as follows, solving for a_os within our solar system:

-a = = [G(AUn)M a_o/ r(AUr)]^1/2, and plugging in known values for Pioneer Anomaly:

-8E-10 m/s^2 = [(6.67E-11)(1)(1.98E+30)(a_o) / 2.25E+22]^1/2, and solving for our solar system’s a_os we get:

-8E-10 m/s^2 = [13.2066E+19)(a_os) / 2.25E+22 ]^1/2

a_os = 1.0908E-16 m/s^2, which is a far lower, gentler value for our solar system then what was computed for the outer galaxy curves, viz. a_o = 1.2 E-10 m/s^2.

The purpose of this exercise, hypothetically, is to show that perhaps we do not have Newton’s gravity right for any distance away from Earth’s known value of G. Perhaps on this Equinox day, like trying to stand an egg on its end, there is cause to try to find what is the real value of Newton’s G for our solar system, away from Earth’s orbital? If we test for G on Mars, or Venus, where the Bouguer anomalies had been detected, we may be surprised. We may not need ‘dark matter’ after all, if so. Perhaps a better understanding of Newton’s G for the outer solar system can be tested empirically in the future?

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