The physics of the rocket launch

With the recent revival in popularity of space travel and exploits, either planned or already achieved, space tourism has become a recent buzzword of newer pioneering space enterprises such as Virgin Galactic and SpaceX. The seeds of a nascent space tourism industry had already been planted but appear to have started growing thanks to the efforts of companies such as these. Over the past 15 years, prices for tickets on rocket launches have risen from around $250,000 to $55 million. Additionally, each night spent on the ISS during the trip would cost an additional $35,000 per astronaut. Despite all this, Virgin Galactic has received enough interest to begin launching flights in the very near future.

With all that, the question is presented: what are the physics behind launching into space?

The launch

The most important concepts describing rocket launches are momentum and impulse. When a rocket is launched, a chemical reaction occurs within its boosters that then produces a force that acts in the direction of the rocket’s nose cone. The rocket’s weight acts as a force in the opposite direction of the boosters’ exhaust fumes. 

This is a basic diagram showing the vectors involved in the launch: 

These equations best explain what is happening.

At the point before launch, the force of the launchpad (normal force) is equal to the force of the weight rocket (and their velocities are zero). Thus momentum is zero at the moment before launch. After the fuel is ignited and the exhaust gas pushes downward (force acts in +y direction because of Newton's third law of motion). This introduces a new constant force, creating an impulse and thus an imbalance in the conservation of momentum equation. In conserving momentum, the rocket must then increase in velocity in the opposite direction of the force (-y direction) because the momentum of the exhaust gases is extremely high. Despite fuel being burned and the mass of the rocket reducing with time, this change in mass does not fully account for the force of the exhaust gases after a certain time period of being applied constantly (which explains the brief period between ignition and launch). Thus, the rocket must accelerate until its momentum ‘catches up’ to the total impulse resulting from thrust (this generally only being achieved by the complete depletion of the fuel tanks)

https://www.cnn.com/videos/tech/2020/11/17/space-tourism-miles-obrien-anderson-cooper-acfc-vpx.cnn/video/playlists/anderson-cooper-full-circle/

https://www.bbc.com/news/business-50929064