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Planet-X has a mass of 3.62×1024 kg and a radius of 8400 km. What is the...

Planet-X has a mass of 3.62×1024 kg and a radius of 8400 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.) What is the Second Cosmic Speed i.e. the minimum speed required for a satellite in order to break free permanently from the planet? If the period of rotation of the planet is 19.9 hours, then what is the radius of the synchronous orbit of a satellite?

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Answer #1

Concept - for the revolution of the satellite around the planet, the gravitational force provides centripetal acceleration for the circular motion. We use this to find the relation between speed and radius of orbit of the satellite as shown below,

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