Visualizing what would happen if the Sun was replaced by a black hole
A look into what black holes are and their source of gravity
TLDR version — No, we won’t be sucked into the black hole. Of course, without the Sun, all living things will freeze to death due to the absence of an energy source. But there will not be any changes in the orbits of the planets. They will continue to revolve around the black hole, just like they were doing around the sun. All this is under the assumption that we replaced the Sun with a black hole of the same mass (1 solar mass). Read on to understand what really happens!
What are black holes?
Let’s start with the basics and understand what black holes really are.
Gravitational Force: Newton’s law of gravitation tells us that two objects of mass m1 and m2 and at a distance r attract each other with a force F given by the below equation where G is the gravitational constant
Using this equation we can also find the Earth’s force of attraction by substituting Earth’s mass for m1 and the radius of Earth as r. Another concept to refresh here is the escape velocity which is the velocity required by an object to escape the force of attraction by another object. Escape velocity can be easily derived using the earlier equation and the concepts of kinetic and potential energy. The escape velocity from a massive body of mass M is given by the equation below.
If we substitute M and r with the mass and radius of the Earth, we get an escape velocity of 11.2 km/s. If we do the same for the Sun, we get an escape velocity of approximately 615 km/s (though it is unlikely that anything would survive the heat on the surface of the Sun to start with!). You can see from the equation that the escape velocity can be increased either by increasing the mass or by reducing the radius of an object. This intuition will come in handy later in this article!
I feel the easiest way to understand black holes is to think of them as an object whose escape velocity is equal to the speed of light. Now imagine, what if we could compress the Earth to a smaller radius, can we make the escape velocity equal to the speed of light? It turns out we can! Substitute speed of light c as the escape velocity and Earth’s mass as M in equation 2 and find out how much r should be. This radius to which any object should be compressed so that its escape velocity becomes the speed of light is known as the Schwarzschild radius.
There are several insights to be had from this equation. It shows that any object ( the Sun, the Earth, your smartphone, even you!) can be converted to a black hole if we can compress it to a specific size. Using equation 3, we get Schwarzschild of Sun as close to 3 km. That of the Earth? 9 mm! That of a human being? 1/10²³ cm, smaller than the nucleus of an atom! This is exactly the reason we do not find black holes easily because we simply do not have any way to compress objects to such smaller sizes. And this is also why black holes are formed where you have such immense forces — the stars.
Stellar Black Holes
Stellar black holes are the most common type of black holes which are formed when huge stars (more than 8 times the mass of the Sun) die. But what is a star’s death? Or even better what is a star’s life? Stars begin as just clouds (nebula) of gas (Hydrogen, the simplest element). Due to gravitational force, the clouds of gas accumulate, its mass increases and it starts attracting more gas clouds. This continues and the gas cloud grows to immense size and mass. Now you have a huge ball of a gas cloud, the size of the Sun or even bigger.
You can imagine how intense the pressure would be at the center of this gas cloud because of the weight of the huge gas cloud around it. This pressure pushes the hydrogen atoms together and they combine (fuse) to form helium. In chemical terms, this is an exothermic process - releases more energy than it takes to force the hydrogen nuclei together. The gas cloud lights up — a star is born! The energy released balances out the huge inward pressure of the gas cloud due to gravity. In other terms, the star burns just enough hydrogen to balance the weight of the gas cloud and now we have a stable star.
Death of a star
What happens when a star has burned/fused all its hydrogen to helium? Helium starts fusing and we get even heavier elements. This process continues and we get other elements like neon, carbon, oxygen, magnesium, etc. till we get iron. The fusion of iron is endothermic — it takes up energy rather than releasing it. The below table shows that elements up to iron can release energy by fusion whereas elements heavier than iron can release energy only by fission (splitting up).
Once all the lighter elements are burned up and the stars are left with iron, the equilibrium between gravity and fusion breaks down. The core of the star cannot produce energy to balance out the weight of the star and the entire mass comes crashing inwards. The atoms are pushed together there till there is no empty space between them. If the star is huge (more than 8 solar masses), the compression continues and the size of the star is compressed to its Schwarzschild radius — a black hole is born!
Source of immense gravity of a black hole
By now, it should be clear that black holes do not possess some mysterious force. It still has only the mass of the original star but now it is confined to a much smaller radius. This leads to an escape velocity greater than the speed of light. In other words, even light cannot escape from a black hole.
Gravitational force between the Earth and the black hole
Now let’s go back to the original question which started this article. What happens if the Sun is replaced by a black hole? Newton’s law of gravitation still holds good and you can find the force using equation 1. Since we are replacing the Sun with a black hole of the same mass, the equation tells us that the force is still the same. The Earth continues in its orbit, so does every other planet.
The difference is that earlier the closest anything could have gotten to the Sun was the surface of the Sun. The black hole is much much smaller at around a 3 km radius. This means you can go even further and get really close to the center. As you get closer, the gravitational force increases, and at some point, you will enter the point of no return — the event horizon!
Summing it up
We started with a very simple question aimed at clearing some misconceptions about black holes and in the process, got to know them even better. I have used Newtonian mechanics to derive the Schwarzschild radius but the right one to use is that of General Relativity. But Newtonian mechanics is easier to understand and form an intuition.
