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There are some people who believe that Earth has a twin that orbits directly opposite the sun with exactly the same orbital elements and in the saem direction and thus unseen from Earth. The two planets are exactly 180 degrees opposed when they occupy ecliptic longitudes of 90 degrees and 270 degrees. Show how this scenario is not possible by doing the following:a. Determine the true anomalies for Earth 1 and Earth 2 when the difference in their orbital velocities is at maximum.b. Find the greatest elongation of Earth 2, as seen from Earth 1 (the planet we live on), in degrees as measured from the center of the sun's disk.
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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