https://blogs.lotterypost.com/jadelottery/2013/6/the-blackhole-and-two-dark-moments.htm JADELottery's Blog: The Blackhole and Two Dark Moments. en-us Lottery Post RSS Generator https://blogs.lotterypost.com/jadelottery/2013/6/the-blackhole-and-two-dark-moments.htm https://blogs.lotterypost.com/jadelottery/2013/6/the-blackhole-and-two-dark-moments.htm Mon, 03 Jun 2013 20:29:02 GMT JADELottery There are two dark moments around a blackhole and their boundaries are at two different radii.

The first is the obvious escape velocity radius of no return.

If given the equation ve = 2 G m / re, where ve is the velocity and re is the distance from the center of blackhole mass, m, then we can set ve equal to the speed of light, c.

The equation becomes c = 2 G m / re; solve for re it becomes, re = 2 G m / c2.

The second might not be so obvious; it's the centripetal velocity radius of no return.

This is a balance between two forces; one centripetal: mo vc2 / rc and two gravitation: -G m mo / rc2, where mo is the mass of smaller object, m is the mass of the blackhole, vc is the centripetal velocity around the blackhole at radius rc.

The second equation becomes (mo vc2 / rc) - (G m mo / rc2) = 0, solve for rc it becomes, rc = G m / vc2.

Now set vc equal to the speed of light, c, it becomes rc = G m / c2.

As we can see, the two boundaries are different by only a factor of 2, re = 2 G m / c2 and rc = G m / c2, but the velocities are at 90 degrees of each other.

The escape velocity is pointing out from the center of the blackhole, normal or perpendicular to the circle swept out by the radius re.

The centripetal velocity is pointing on a tangent to the circle swept out by the radius rc.

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