Escape Speed

<Picture 1; Escape Speed>

 

   In the last post, we talked about the Quantum Mechanics and Probability. Planck, the German physicist, fixed the equation for the blackbody radiation and opened the door of quantum mechanics. In addition, Schrodinger made an thought experiment called Schrodinger's Cat.

 

   Today's topic is the Escape Speed. Escape speed is the minimum speed needed for an object to break free from the gravitational attraction of a massive body. We're gonna talk about the Escape speed and its formula and some examples.

 

1. Inertia vs Gravitational Force

 

<Picture 2; Inertia vs Gravitational Force>

 

   If a spacecraft pass through the earth like picture 2, then there could be 3 cases according to the differences between inertia and gravitational force.

   The first case is that the inertia is much stronger than gravitational force. In this case, the speed of the spacecraft is so fast that the space craft can ignore the gravitational force and just pass away.

   The second case is that the inertia is strong as much as the gravitational force. In this case, if there are no interference of other forces, the spacecraft will rotate around the earth.

   The third case is that the gravitational force is much stronger than inertia. In this case, the speed of spacecraft goes very slow compared to the first case. Therefore, the gravitational force is so strong that the spacecraft will be sucked into the earth.

  If the spacecraft is slower than escape velocity, then it will be sucked into the earth. So, we're gonna find the minimum speed needed for an object to break free from the gravitational attraction of a massive body. Let's derive the formula of Escape speed.

 

2. Derivation of the Escape Speed Formula

 

   According to the law of conservation, the sum of the kinetic energy(K) and potential energy(U) should be constant. So the initial sum of the kinetic energy and potential energy is same as the final sum of them.

 

The formula of the gravitational force is as follows.

  

the integral of it is the potential energy

  

So the initial potential energy is

 

According to the classical physics, the initial kinetic energy is as follows.

  

The final potential energy is zero because the distance between spacecraft and massive body will be infinite.

 

The final kinetic energy is also zero because speed of the spacecraft will converge to zero.

  

Therefore, the conservation formula at the first will be as follows.

 

So, the Escape speed is as follows.

 

3. Examples of the Escape Speed.

   <Picture 3; List of Escape Speeds>

   According to the escape speed formula, the earth's escape speed is 11.2km/s. If you travel with a speed less than 11.2km/s, then you're gonna fall into the earth. For another example, the sun's escape speed is 617.5km/s. So, if you travel with a speed less than 617.5km/s, then you're gonna be sucked into the sun. 

  Check out the picture3. If you look the last part of the list, you're gonna find 'the event horizon'. The event horizon is the point of no return of the black holes. The black holes' mass is so huge. So, it has an extremely high escape speed. Therefore, its escape speed is so fast that even the light(nothing is faster than light) can't return. The reason why we call it a black holes is that it reflected nothing so we can't see anything but black. In the next post, we're gonna talk about the Black Hole and General Relativity. Thank you for reading it.




Bibiology

https://en.wikipedia.org/wiki/Escape_velocity