Derive the governing equation of the Cartpole system. m M <1 5. Cart-pole>
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- A mood of a mass m and raduis a is orbiting a planet of mass M and if radius b at a distance d (center to center) in a circular orbit. Derive an expression for the speed of the mood v in terms of M,d and the gravitational constant G.At least a good four or five billion years from now the Sun will become a "dead" white st! to dwarf staC, shrinking to about 1% of its 1*% current radius. Assume it loses no mass in this process, If the sun currently rotates once every thirty days, then how many radians per second will it be rotating at after it changes into a white dwarf?Black holes are difficult to observewith telescopes because they, bydefinition, don’t emit or reflect any light. They can be found by look-ing for other nearby objects orbit-ing them, however. Here is a dia-gram of a star in a circular orbit around a black hole. a. The period of the star’s orbit is 90 days, and its orbital radius around the black hole isobserved to be 3.6 : ×10^11 m. Find the orbital velocity of the star in units of m/s. (You need to convert 90 days to seconds, first). The circumference of a circle is 2πr. b. The mass of the star is known to be 4 × 10^30 kg. Find the centripetal acceleration of thestar and the strength of the gravitational force on the star. c. Find the mass of the black hole.
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