Comments for blog.brightstartutors.com

Comment on Escape Velocity – Part 1 by curiousCharacter

curiousCharacter — Mon, 20 May 2013 04:57:03 +0000

Good question, David Rosen, and I see what you are thinking.
First consider the potential energy PE. It is zero at the Earth’s surface. At infinity, it is some positive amount given by the formula. At a finite distance, it has some intermediate value.
Say we launch with an initial kinetic energy KE1, and KE1 is is not enough to escape gravity. Conservation of energy requires that at all subsequent times we must have KE + PE = KE1. If the launch direction is directly away from the Earth’s center, it will reach a maximum distance when all the kinetic energy has been used up, and velocity is indeed zero, before it starts falling back. This is actually an infinitely flat elliptical orbit (eccentricity = 1).
If the launch direction is not directly outward, Newton’s mathematics show that it will follow an ordinary elliptical orbit, and will reach apoapsis before the velocity is zero. That is, for an ordinary orbit, the initial velocity is never entirely “used up”.
I hope this helps.

Comment on Escape Velocity – Part 1 by David Rosen

David Rosen — Sun, 19 May 2013 18:33:12 +0000

All of this assumes that for the object to escape, its kinetic energy must not reach zero before it reaches infinity. There is one point about this which is a bit confusing to me:

Let’s say the object is launched below escape velocity but fast enough to establish an elliptical orbit. We seem to be saying that it will reach zero kinetic energy at the furthest point of the orbit (apoapsis). However, it seems that its velocity would not be zero at that point. Only the component of the velocity directly away from the earth would be zero. But would still retain tangential velocity and so would still retain kinetic energy. Therefore kinetic energy would not in fact be zero.
What is the flaw in this reasoning?
Thanks for your help!

Comment on Bayes Formula by Thomas Chloe

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Comment on Bayes Formula by reed lily

reed lily — Sun, 12 May 2013 06:17:18 +0000

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Comment on Bayes Formula by Bailey Mason

Bailey Mason — Sun, 05 May 2013 13:44:22 +0000

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Comment on Where does pi R squared come from? by Jeff Broudde

Jeff Broudde — Tue, 02 Apr 2013 06:40:23 +0000

Good! Very good indeed! A clear, concise, easy to follow explanation.
And I like the way you tie it to integral calculus. Keep up the good work.