Black Holes, Gravity, and Escape Velocity

In earlier hubs on Satellites we went over some of the details on escape velocities. As was discussed, the velocity to attain Low Earth Orbit was around 17,000 mpg. To escape the gravitational pull of the earth all together, and travel to the moon and beyond requires considerably more velocity, some 25,000 mph. The velocity required is dependent on a few factors including the mass of the body being escaped from and the distance from the center of the body’s mass. It is not dependent ultimately upon the mass of the object trying to attain escape velocity since the escape velocity itself takes into consideration the energy necessary to move the escaping object. Put a little more concisely, the equation to determine escape velocity below does not include the mass of the escaping body, but rather the mass being escaped from.

So when thinking about how fast one would need to go to rocket away from a planet or star, think about how massive the planet or star is, and how far you are from it, as this is what really matters. So although escape velocity from the surface of the earth is some 25,000 mph, to escape from the surface of the sun requires 6 times that speed or around 150,000 mph. Now for those that are good at doing some math on the fly, you may notice a huge disparity. Why only 6 times the speed when the sun is some 300,000 times the mass of earth? This leads us to how important the distance from the center of the mass is when calculating escape velocity, and its curious implications.

So, the black hole. What is a black hole, why is it black, and why care?

Looking back again to the idea of velocity and mass, imagine for a second you took all the mass of the earth, some 5.9736×10²⁴ kg (yes..move the decimal 24 places to the right) and packed it into an area the size of a golf ball (something which is in principle possible) you would have an interesting phenomena. You see, for the equations above that provide the escape velocity you would plug in the same M or mass, but rather then a radius of some 4000 miles that the earth is currently, you would put in some 2 centimeters. This would cause the equation to spit out an enormous velocity necessary to escape from the surface of the hypothetically tiny earth. (Note of the earth was shrunk to the size of a golf ball, but you found yourself some 4000 miles away, your escape velocity from that location should be the same as when the earth had a radius of 4000 miles since the distance from the center of the mass is crucial) This enormous velocity would cause many strange phenomena, but the most obviously odd byproduct would be that it would be a greater velocity then the speed of light itself. So the escape velocity would be so enormous that light would not be able to escape the pull of gravity. (A statement that needs some qualification). The result would be that if one where a sufficient distance from this tightly packed immensely dense little golf ball and observed it intently they would see nothing at all. Any light going it would never get out. In fact anything getting close enough would never escape. To any observer it would be quite literally a black hole.

Now-a-days scientists believe that the occurrence of black holes in the universe is not entirely uncommon. One very famous example of what by all accounts “appears” to be a black hole is an object in the sky known as Cygnus X-1. This can be found in the summer night sky in the northern hemisphere toward the center of the Cygnus constellation, also known as the Northern Cross. In addition many believe that immense black holes exist and power the center of galaxies such as the Milky Way.

Some other interesting stats (taken from Wikipedia)

Sun, the Sun's gravity: 617.5 km/s

Mercury, Mercury's gravity: 4.3 km/s at

Venus, Venus' gravity: 10.3 km/s at

Earth, the Earth's gravity: 11.2 km/s at

Moon, the Moon's gravity: 2.4 km/

Mars, Mars' gravity: 5.0 km/

Jupiter, Jupiter's gravity: 59.5 km/s

Saturn, Saturn's gravity: 35.6 km/s

Uranus, Uranus' gravity: 21.2 km/

Neptune, Neptune's gravity: 23.6 km/s

Brain teaser I will answer in later Hubpages…

Light necessarily has a fixed speed of 186,000 miles a second. This is a constant. So light escaping from a black hole still travels away from a black hole, despite the escape velocity, at this speed. Light does not slow down, and if shot perpendicular to the surface of the black hole, it does not turn around and head back, it still travels out at light speed. So why don’t we see light escaping from a black hole at certain angles?