Question

If the plain wanted to leave the Earth, how fast would it need to fly? a) Given the fallowing equation, derive the formula for escape velocity. 1/2mv2(power) - kgmMe/Re) A black hole is not just science fiction, it is a case where the mass of a star collapses inward. The “Radius” of this hole is from the center, known as the singularity, and the very edge of the black hole. That edge is called the Event Horizon. This is where the escape velocity equals the speed of light (C = 3.0 x 10^8 m/s). Use the answer from part a) to find the formula for the Radius of a black hole. You do not need to plug any numbers in, but you can if you want to know what the Radius of a black hole would be if it had the mass of the Earth.

Answer 1

For a planet to escape the gravitational field of the Earth, its initial kinetic energy has to equal the final potential energy at the Earth's Radius.

mu 'esc GMem RE 2GM Vesc VRE

Now, to find out the radius of such a blackhole, we take the mass as that of the Earth, and the escape velocity equal to light, $v_{esc}=3\times 10^8\mathrm{m/s}$ .

Putting in our values, we get

$\\3\times 10^8=\sqrt{\frac{2\times G\times (5.972\times 10^{24})}{R}} \\R=8.85\times 10^{-3}\mathrm{m}$