Changes

The different effects predicted by special relativity, compared to classical formulations, are extremely tiny.  Most relativistic effects are negligible at the speeds of ordinary phenomena observed by humans.  The effects only become significant when the speeds involved are a significant fraction of the speed of light, which is <math>3 \times 10^8</math> meters per second&mdash;such speeds are called ''relativistic''.  (However, it's worth noting that ordinary magnetism can be considered an effect of relativity, dictated by the need for electrostatic theory to be correct under relativity.  The speed of light in fact appears in the formulas ([[Maxwell's Equations]]) governing electricity and magnetism, though these equations were developed long before relativity was proposed.)

The different effects predicted by special relativity, compared to classical formulations, are extremely tiny.  Most relativistic effects are negligible at the speeds of ordinary phenomena observed by humans.  The effects only become significant when the speeds involved are a significant fraction of the speed of light, which is <math>3 \times 10^8</math> meters per second&mdash;such speeds are called ''relativistic''.  (However, it's worth noting that ordinary magnetism can be considered an effect of relativity, dictated by the need for electrostatic theory to be correct under relativity.  The speed of light in fact appears in the formulas ([[Maxwell's Equations]]) governing electricity and magnetism, though these equations were developed long before relativity was proposed.)

Because the effects of relativity are so tiny, scientists have been devising sophisticated and sensitive tests ever since the theory was formulated in 1905.  In fact, at the end of Einstein's original 1905 paper [http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ "Does the Inertia of a Body Depend its Energy Content?"], he speculates on the possibility that the equation <math>E = m c^2</math>, which would normally be very hard to verify, could be verified with the extremely high energies of the newly-discovered phenomenon of radioactivity.<ref>This is perhaps the most famous, most widely quoted, and least understood equations ever written.  It is not related to [[quantum mechanics]].</ref>

Because the effects of relativity are so tiny, scientists have been devising sophisticated and sensitive tests ever since the theory was formulated in 1905.  In fact, at the end of Einstein's original 1905 paper [http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ "Does the Inertia of a Body Depend its Energy Content?"], he speculates on the possibility that the equation <math>E = m c^2</math>, which would normally be very hard to verify, could be verified with the extremely high energies of the newly-discovered phenomenon of radioactivity.<ref>This is perhaps the most famous, most widely quoted, and least understood equation ever written.  It is not related to [[quantum mechanics]].</ref>

Another prediction of special relativity was time dilation in rapidly moving objects.  Some have suggested that this effect is verified in the anomalously slow decay of relativistic cosmic muons, but other explanations are possible for this effect.  Similarly, the assertion that time dilation must be taken into account in all high-energy nuclear physics experiments is rarely backed up by specific examples with data.

Another prediction of special relativity was time dilation in rapidly moving objects.  Some have suggested that this effect is verified in the anomalously slow decay of relativistic cosmic muons, but other explanations are possible for this effect.  Similarly, the assertion that time dilation must be taken into account in all high-energy nuclear physics experiments is rarely backed up by specific examples with data.

While Newcomb's theory, and general relativity, don't lead to closed-form solutions, both theories can be solved numerically to as much precision as one desires.

While Newcomb's theory, and general relativity, don't lead to closed-form solutions, both theories can be solved numerically to as much precision as one desires.

General relativity was developed to predict this extra precession, in the amount of <math>3{}v^2/c^2</math> revolutions per planet's "year", where <math>v</math> is the planet's average orbital speed.<ref>That is a simple approximation, designed to relate the precession to the planet's speed relative to the speed of light.  A more accurate approximation is <math>\frac{3GM}{c^2 a(1-e^2)}</math>, where a is the semi-mahor axis and e is the eccentricity.</ref>  More accurate, modern measurements of Mercury's precession differ slightly from the calculated combined effects of planetary perturbation, equinoctial precession, solar oblateness, and general relativity.  The reason for this is not known.

General relativity was developed to predict this extra precession, in the amount of <math>3{}v^2/c^2</math> revolutions per planet's "year", where <math>v</math> is the planet's average orbital speed.<ref>That is a simple approximation, designed to relate the precession to the planet's speed relative to the speed of light.  A more accurate approximation is <math>\frac{3GM}{c^2 a(1-e^2)}</math>, where a is the semi-major axis and e is the eccentricity.</ref>  More accurate, modern measurements of Mercury's precession differ slightly from the calculated combined effects of planetary perturbation, equinoctial precession, solar oblateness, and general relativity.  The reason for this is not known.

The following table show some approximate parameters for the planets.  Note that Mercury has the smallest orbit, the fastest speed, and the highest gravitational pull.  Precession of planets other than Mercury is extremely hard to measure, but measurements of the actual anomalous precessions are in good agreement with the last column of the table.<ref>http://www.mathpages.com/rr/s6-02/6-02.htm</ref>

The following table show some approximate parameters for the planets.  Note that Mercury has the smallest orbit, the fastest speed, and the highest gravitational pull.  Precession of planets other than Mercury is extremely hard to measure, but measurements of the actual anomalous precessions are in good agreement with the last column of the table.<ref>http://www.mathpages.com/rr/s6-02/6-02.htm</ref>