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Assume you have a planet of mass $M$ and radius $R$ and have a stationary spaceship at distance $4R$ from the center of the planet.If a projectile is launched from the spaceship of mass $m$ and velocity $v$ and just grazes the planet's surface, what will be the locus of the projectile?

I guess on Earth we take projectile path to be parabolic because of no variation in acceleration due to gravity. But in this case acceleration due to gravity will change with change in distance.

So in the end, will the trajectory be parabolic, elliptical, circular? Explain why with full proof.

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Hmmm... If I read correctly - Does your question ends at "... Explain with full proof ". More likely, it looks like an order (commanding) to me. – Ϛѓăʑɏ βµԂԃϔ Jan 5 at 14:49
Welcome to Physics.SE, Adeetya. Our FAQ is written so that we don't answer specific instances of question that look textbook assignments. Instead we prefer to address the onceptual underpinnings of the problems. If you would like to rewrite this in a conceptual form we would be happy to help. To point you in the right direction I would ask you to consider the combined kinetic and gravitational energy of falling bodies in a gauge where the potential energy is set to zero at infinite remove. – dmckee♦ Jan 5 at 16:54

closed as too localized by Ϛѓăʑɏ βµԂԃϔ, dmckee♦ Jan 5 at 16:51

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