Re: If the mass is 800 vs 700...
"The black hole left after the collapse of a giant star is so much smaller than the original star that the escape velocity increases from a few hundred kilometres per second to the speed of light. Less dense objects have a lower escape velocity than dense objects of the same mass."
Wrong on a number of levels.
Firstly, only a small amount of the mass of the original star actually forms the black hole. The rest blows off into space.
Which means that anything orbiting will see its escape velocity _at that orbit_ decrease dramatically.
But if you setup shop in orbit close to the event horizon, then yes your escape velocity will be high. That orbit will be well inside the diameter of the original star. (gravity follows the inverse square law of distance)
Fun quiz for the day: If you were to go straight up from earth to the distance of the moon's orbit, then you'll experience a gravitational pull from the earth of about 1/3 G - and start coming straight down again as soon as you stop counteracting that pull and lose any outward momentum you had. It's a long way to fall. At times like this, how long will you have to consider all those things your mother told you before you discover if the ground will be friendly?