Black Holes

Black Holes are some of the most mysterious objects in the deep sky. Black holes are actually objects having huge mass concentrated in very little space. For example, a black hole having mass equal to that of earth (5.9742 × 10²⁴ kilograms) will have a diameter of just 1.8 cm!! Yeah it is one point eight centimeters, there's no mistake and I'm not kidding. Black holes have massive gravitational energy and nothing not even light can escape them.

If you grab your old CRT monitor and squash it to millionth of a millionth of its original size, you will end up with a black hole measuring a couple of picometers in diameter. But it won't have sufficient gravity to grab hold of light since gravity of an object is directly proportional its mass. A true black hole(I mean a powerful one), has 300,000 times the mass of earth!

Now a quick glance over what makes it impossible (Nothing is impossible? Give it a second thought before saying so again) for almost everything (even light included) to escape a black hole. Why can't even light not escape it?

Light is energy. And according to Albert Einstein, mass contains energy and energy has got mass i.e. mass and energy are different forms of the same thing

Now consider our earth. If you throw a ball up in the air (obviously using your very own hands), it will reach a certain height and ultimately fall back to the earth. This is due to earth's gravity. But if throw a ball with an acceleration greater than the acceleration due to gravity (9.8 m/s²) or in other words, with a velocity more than 9.8 m/s, the ball will overcome the earth's gravity and will not be influenced by it any more. Similarly, the black holes have a massive gravity that even objects moving as fast as that speed of light (299 792 458 m / s) are not able to dominate it. Hence even light is attracted towards black holes.

Calculating Time Dilation

Science is interesting and pretty weird too. Well I'll discuss how to calculate time dilation. For those who don't know, time dilation is a phenomenon wherein time appears to slow down with respect to a certain observer. Weird things happen as you approach the speed of light, very very weird things. one of them is the slowing down of time generally referred to as time dilation. It is incredible but true.

So, how do you proceed calculating by how much amount time slows down? There's a formula. It is somewhat like this:

Δt' = γΔt

where

γ =  1/√(1-v²/c²)

Δt is the time interval between two events happening at the same place as measured an observer in the same frame of reference. This is also called proper time.

Δt' is the time interval between those same events as measured by another observer moving at a certain velocity with respect to former observer.

v is the relative velocity between the former and later observers.

c is the speed of light.

Length Contraction

Another incredible phenomenon that can be experienced while traveling close to the speed of light is length contraction. It so happens that the closer you move to the speed of light, the shorter your length seems to be when viewed from a direction parallel to your motion. This amazing effect is called length contraction.

There is a simple formula to calculate length contraction. It is somewhat like this:

L' =   L/γ(v)

That is

L' = L√1-v²/c²

Where:

L is the actual length of the object.

L' is the length as observed by an observer who is in relative motion with respect to the object

v is the relative velocity between the observer and the moving object.

c is the speed of light.

Pretty simple.