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In order to estimate the multipolar thermal conductance of a
In order to estimate the multipolar thermal conductance of a

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... • What is the magnitude of the centripetal force on the cart from the previous slide? __________ • If the mass of the cart is doubled, what happens to the centripetal force acting on the cart? • If the speed of the cart is doubled, what happens to the magnitude of the centripetal force of the on the ...
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Pioneer anomaly

The Pioneer anomaly or Pioneer effect was the observed deviation from predicted accelerations of the Pioneer 10 and Pioneer 11 spacecraft after they passed about 20 astronomical units (3×109 km; 2×109 mi) on their trajectories out of the Solar System. The apparent anomaly was a matter of tremendous interest for many years, but has been subsequently explained by an anisotropic radiation pressure caused by the spacecraft's heat loss.Both Pioneer spacecraft are escaping the Solar System, but are slowing under the influence of the Sun's gravity. Upon very close examination of navigational data, the spacecraft were found to be slowing slightly more than expected. The effect is an extremely small acceleration towards the Sun, of 6990874000000000000♠(8.74±1.33)×10−10 m/s2, which is equivalent to slowly accelerating to a velocity of 1 kilometre per hour (0.6 mph) over a period of ten years. The two spacecraft were launched in 1972 and 1973 and the anomalous acceleration was first noticed as early as 1980, but not seriously investigated until 1994. The last communication with either spacecraft was in 2003, but analysis of recorded data continues.Various explanations, both of spacecraft behavior and of gravitation itself, were proposed to explain the anomaly. Over the period 1998–2012, one particular explanation became accepted. The spacecraft, which are surrounded by an ultra-high vacuum and are each powered by a radioisotope thermoelectric generator (RTG), can shed heat only via thermal radiation. If, due to the design of the spacecraft, more heat is emitted in a particular direction—what is known as a radiative anisotropy—then the spacecraft would accelerate slightly in the direction opposite of the excess emitted radiation due to radiation pressure. Because this force is due to the recoil of thermal photons, it is also called the thermal recoil force. If the excess radiation and attendant radiation pressure were pointed in a general direction opposite the Sun, the spacecraft's velocity away from the Sun would be decelerating at a greater rate than could be explained by previously recognized forces, such as gravity and trace friction, due to the interplanetary medium (imperfect vacuum).By 2012 several papers by different groups, all reanalyzing the thermal radiation pressure forces inherent in the spacecraft, showed that a careful accounting of this explains the entire anomaly, and thus the cause was mundane and did not point to any new phenomena or need for a different physical paradigm. The most detailed analysis to date, by some of the original investigators, explicitly looks at two methods of estimating thermal forces, then states ""We find no statistically significant difference between the two estimates and conclude that once the thermal recoil force is properly accounted for, no anomalous acceleration remains.""
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