Planet-X has a mass of 5.23×1024 kg and a radius of 7010 km. What is the First C
ID: 2062202 • Letter: P
Question
Planet-X has a mass of 5.23×1024 kg and a radius of 7010 km. What is the First Cosmic Speed i.e. the speed of a satellite on a low lying circular orbit around this planet? (Planet-X doesn't have any atmosphere.)
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What is the Second Cosmic Speed i.e. the minimum speed required for a satellite in order to break free permanently from the planet?
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If the period of rotation of the planet is 20.6 hours, then what is the radius of the synchronous orbit of a satellite?
Explanation / Answer
the gravitational force between planet-X and earth is F = GMm/r^2 --------(1) where G = 6.67 * 10^-11 Nm^2/kg^2,M is mass of earth,m is mass of planet-X and r is radius of orbit the centripetal force acting on planet-X is F1 = mv^2/r ---------(2) from (1) and (2) GMm/r^2 = mv^2/r or v^2 = GM/r or v = (GM/r)^1/2 where r = R + h R is radius of earth and h is altitutde above earth surface