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OP means "original post". For your last question, use conservation of energy. The object has ##-\frac{G\ m\ M_{earth}}{r_1}## mechanical energy at ##r_1## distance from the center of the earth when you "drop" it and ##\frac{1}{2}mv^2-\ \frac{G\ m\ M_{earth}}{R_{earth}}## mechanical energy when it hits the surface. Equate the two and solve for ##v##!How do I "fix the mistakle"? And BTW, what is an OP?

Escape Velocity = Freefall from Height of One Radius?

It was a question, not a declaration.

If I were to "drop" an object from a height of 4,000 miles what would its velocity be when it hit the earth? The force of gravitation at this altitude would be 1/4 that at sea level, and would increase as the falling object approached the surface. How would I calculate this?

edit: changed "conversation of energy" to "conservation of energy" although this is technically a conversation with energy as a topic.

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