Why a multistage rocket is needed to get a spacecraft off the Earth and into the space?

The idea of multistage rockets goes back to the early 1900s when a Russian highschool teacher Konstantin Tsiolkovsky (photo, left) first stated the principle of achieving successful space flight. The idea is simple. A tremendous amount of power is required to lift any object through the atmosphere against the pull of gravity and give it sufficient speed to send it into orbit. No single rocket is adequate for the task. What must be done is to use a combination of rockets linked together one on top of another. The bottom one gives the others a ‘piggy back’ and gets them moving fast before their own engines fire. In this way, the top rocket can be made to travel fast enough to enter orbit. Such a rocket combination is called a multistage rocket.
Such rocket can achieve greater speed because it lightens its weight by dropping stages as it uses up propellant. Moreover, each next stage begins its ascent at higher initial velocity, having been boosted up by the jettisoned lower stage. A three-stage rocket can reach about three times the speed of a single-stage rocket. 
Most spacecraft are launched into space on top of a three-stage rocket. The first stage or booster, is the biggest because it has to lift itself, the other rockets, and the spacecraft through the densest part of the atmosphere. The booster fires for only one or two minutes before its fuel supply is exhausted. Then it separates from the rest of the vehicle and falls back on Earth. The second stage ignitgs for a few minutes and thrusts the now lighter vehicle higher and faster. When its fuel is exhausted the second stage is discarded, and the third stage fires to boost the spacecraft into orbit. In less than 15 minutes the spacecraft has been accelerated from rest to a speed of 28,000 kilometres per hour.

Additional reading:
Multistage rocket (Wikipedia)

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