If an object is thrown upwards with escape velocity, will it orbit the earth?
Think about it - If an object is thrown downwards with escape velocity, will it orbit the earth?
What does the word "escape" mean? Does that definition match the definition of "orbit"?
So now you have two questions, approaching the problem from two different directions, These are hints. What do you think the answer is?
escape velocity is the velocity by which any object overcomes the gravitational pull and flies away from planet.
ve = √2gr
Will a body projected with a speed less than the escape velocity may orbit the earth in circular path?
Of course. All elliptic paths are closed orbits, so all speeds less than escape can take any elliptic path (of which the circular is special case)
For a body launched from the surface of the earth the only possibility for a circular orbit is a horizontal launch with a speed equal to escape velocity divided by the square root of two. Any other direction and the orbit will intersect with the surface of the Earth. Any higher velocity and the orbit will fail to be circular. It will rise above the surface of the earth. Any lower velocity and the orbit will fail to be circular. It will fall below the surface of the earth.
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