Changes

[[Pioneer 10]] and [[Pioneer 11]] were space probes sent to study the planets [[Jupiter]] and [[Saturn]].  After following a [[hyperbolic]] trajectory around these planets, they had reached [[escape velocity]] for the solar system and were flying out.  While their main mission was now ended, NASA stayed in radio contact with the craft to study the outskirts of the solar system<ref name="Nieto">Michael Martin Nieto and John D Anderson.  "[http://www.iop.org/EJ/abstract/0264-9381/22/24/008 Using Early Data to Illuminate the Pioneer Anomaly]".  ''Classical and Quantum Gravity'', 2005</ref>.

[[Pioneer 10]] and [[Pioneer 11]] were space probes sent to study the planets [[Jupiter]] and [[Saturn]].  After following a [[hyperbolic]] trajectory around these planets, they had reached [[escape velocity]] for the solar system and were flying out.  While their main mission was now ended, NASA stayed in radio contact with the craft to study the outskirts of the solar system<ref name="Nieto">Michael Martin Nieto and John D Anderson.  "[http://www.iop.org/EJ/abstract/0264-9381/22/24/008 Using Early Data to Illuminate the Pioneer Anomaly]".  ''Classical and Quantum Gravity'', 2005</ref>.

Around the time of Pioneer 11's flyby of Saturn, it was found to be slightly off-course.  (Every spacecraft sent to the outer solar system is intended to follow a specific course, predicted by the theory of [[general relativity]].  Radio transmissions and radar are used to track spacecraft to ensure that they stay on course.)  While this in itself was within the range of error, astronomers continued tracking the craft to find that the anomalous sunward acceleration increased.  Currently, [[Pioneer 10]] and [[Pioneer 11]] are respectively over 30 and 70 [[Astronomical Unit|AU]] from the sun, the farthest any spacecraft has gone in near-free-fall.  By using [[Doppler effect|Doppler radar]], scientists have found that the courses for both the Pioneer spacecraft show a constant acceleration towards the sun of <math>8.74 \times 10^{-10} \frac{m}{s^2} \ </math> beyond theoretical preditions.<ref name="Nieto" />

Around the time of Pioneer 11's flyby of Saturn, it was found to be slightly off-course.  (Every spacecraft sent to the outer solar system is intended to follow a specific course, predicted by the theory of [[general relativity]].  Radio transmissions and radar are used to track spacecraft to ensure that they stay on course.)  While this in itself was within the range of error, astronomers continued tracking the craft to find that the anomalous sunward acceleration increased.  Currently, [[Pioneer 10]] and [[Pioneer 11]] are respectively over 30 and 70 [[Astronomical unit|AU]] from the sun, the farthest any spacecraft has gone in near-free-fall.  By using [[Doppler effect|Doppler radar]], scientists have found that the courses for both the Pioneer spacecraft show a constant acceleration towards the sun of <math>8.74 \times 10^{-10}\,\mathrm{m}/\mathrm{s^2} \ </math> beyond theoretical preditions.<ref name="Nieto" />

Although the [[Galileo Project|Galileo]] and Ulysses spacecraft showed some unexpected sunward acceleration, other unpredictable factors, such as the [[Yarkovsky effect]] and the thrust caused by radioactive material onboard, prohibit any accurate measurement of the effect on these two spacecraft.  The confounding effects are even more significant on the Voyager spacecraft, preventing even a discussion of whether the Pioneer Anomaly affects these craft at all.

Although the [[Galileo Project|Galileo]] and Ulysses spacecraft showed some unexpected sunward acceleration, other unpredictable factors, such as the [[Yarkovsky effect]] and the thrust caused by radioactive material onboard, prohibit any accurate measurement of the effect on these two spacecraft.  The confounding effects are even more significant on the Voyager spacecraft, preventing even a discussion of whether the Pioneer Anomaly affects these craft at all.

The Pioneer anomaly is about 1000 times bigger than the two effects contributing to the difference between the acceleration predicted by general relativity and that predicted by classical (Newtonian) gravity.  The effect of the increase in inertia due to the Lorentz transform is less than <math>10^{-12} \frac{m}{s^2} \ </math>, and the difference in acceleration due to the Schwarzschild metric is also less than <math>10^{-12} \frac{m}{s^2} \ </math>.

The Pioneer anomaly is about 1000 times bigger than the two effects contributing to the difference between the acceleration predicted by general relativity and that predicted by classical (Newtonian) gravity.  The effect of the increase in inertia due to the Lorentz transform is less than <math>10^{-12}\, \mathrm{m}/\mathrm{s^2} \ </math>, and the difference in acceleration due to the Schwarzschild metric is also less than <math>10^{-12}\, \mathrm{m}/\mathrm{s^2} \ </math>.

 

==Explanations==

==Explanations==