The Mathematics Behind Why Rockets Can Escape The Gravitational Pull of the Earth

Robert Goddard’s liquid rocket never reached the 3 kilometer mark because of Tsiolkovsky’s Rocket Equation named after Soviet scientist Konstantin Tsiolkovsky (pronounced “con-stan-tyin tsel-kov-skee”). This equation states that as fuel increases for faster and further voyages, so too does the weight, becoming increasingly heavy as more and more fuel is added. Tsiolkovsky took into account the velocity of a rocket alongside its mass of payload, mass of fuel, and the mass of the rocket itself. The longer the engine burns, the more velocity the rocket will have, however longer burning means more fuel which adds weight and makes it more difficult to push upwards. To travel fast enough to deliver a rocket to space, most of the craft must be fuel. Scientists have battled with this question for decades and although mathematical constructs have been developed to explain the relationship between weight and thrust, no one has yet to develop an idea to get around this problem with currently available technologies. The equation developed to explain this limitation of space travel is △V^R = V^E x log^e (M^P + M^F + M^R / M^P + M^R). This effectively states that only a tiny portion of a rocket can be used to deliver payload, with notable cases being the Apollo missions which employed enormous rockets to carry just a few small astronauts and the things they needed into space. Tsiolkovsky theorized this in the beginning of the 20th century as his calculations demonstrated that kerosine wouldn’t be enough to go from the Earth to the moon with a single craft