There are a good amount of confusion and myths in regards to escape speed. So, in this article, we will cover this fundamental topic. Some of this was covered on Instagram post. We will go a bit deeper here.
First Basics: Imagine gunfire. The bullet comes out with speed V. Now after it leaves the gun, it is under the influence of gravity, assuming negligible air drag, for this simple case. In this scenario, the speed needed for the bullet to “just” escape gravity is the escape speed.
It is the ONE TIME speed imparted to the body. Escape speed is for an “unpowered” object.
If the object can power itself (rocket/missile), then escape speed is irrelevant. If you have an “accelerating object”, like a rocket, with enough power to keep on moving at a constant velocity of even 0.1 m/s, it is enough to achieve the same end result.
What about Energy?? The point is the energy needed would be the same if masses were the same. The total mechanical energy of an object is the sum of kinetic energy and gravitational potential energy.
Kinetic energy is half of the product of mass and velocity squared. Gravitational potential energy is the product of gravitational force and distance from the center of the earth. Both these terms contain the “mass” of the object. So, with higher mass, higher energy is needed to escape (again unpowered). But the speed needed to be imparted will remain the same.
Some myths associated with this concept are outlined as follows: –
Myth: The term is called Escape “Velocity”.
Fact: It is speed, not velocity. Fire the bullet in any direction other than towards earth. It will do your job.
Myth: Heavier objects require higher Escape speed
Fact: It is independent of the mass of an object. So, be it 1kg, or 1000 kg, you need the same – one-time velocity imparted to achieve this. Higher mass just means more energy required. As Kinetic energy and potential energy will both contain the “mass” of the object terms.
Myth: For a rocket to reach orbit, it must cross 11.2 Km/s.
Fact: Not needed as a rocket is a powered object. It carries its own energy source.
Fun calculation: A projectile at 45 degrees. The range is given by (Velocity-Squared)/g. Equate this to the diameter of the earth and find out the velocity needed. Surprised by the answer??? Reply with your answer. We can discuss.
The complete derivation(s) of escape speed will be dealt with in the video series (coming soon). Meanwhile, if you have any queries, feel free to ask.