Shuttle Exercise



The thrust that moves the space shuttle from liftoff to orbit comes largely from two solid rocket boosters (SRB) and three engines on the shuttle whose fuel is stored in an external tank (ET). The two SRBs are fixed to the larger ET as shown in the NASA photograph. The space shuttle Endeavour is attached to the external tank. Note: This photograph and the information page originated from the NASA website under the heading For Educators/Find Teaching Materials/Lithographs. It is reproduced here for convenience.

The following information sheet presents several items relative to liftoff and timing toward orbit. It also provides some data that allows deeper insight into the forces for placing the shuttle into orbit. It is worth examining Newton’s laws of motion and observing what they tell us. That is the task ahead of us, using some of the data in the following table.

Endeavour Data

  1. The total weight of the shuttle, payload, SRBs and external tank require a lifting thrust (force) that exceeds the total weight of the STS. The resulting thrust from the rocket engines exceeding the total weight is what accelerates the STS. The total mass of the components is approximately 2,040,091 kg without payload. Since weight is force as is thrust, we must multiply the 2,040,091 kg by 9.8 m/s2 to obtain approximately a value of 20,000 kilonewtons (kN) for the STS weight.
  1. The thrust of the engines (Two SRBs and three shuttle engines) provides 34,380 kN at sea level and 35,670 kN in vacuum.
  1. At liftoff, the acceleration is determined by Newton’s second law of motion, F=ma, where F is the thrust that exceeds the total weight, m is the mass of the STS in kg, and a is the upward acceleration in m/s2.
  1. The thrust for liftoff is (34,380kN-20,000kN) = 14,380KN
  1. Acceleration at liftoff is then: a=F/m =14,380kN/2,040,091kg = 7.4 m/s2. The acceleration of gravity at the surface of the earth is 9.8 m/s2. Thus, the acceleration that the astronauts feel at liftoff is 7.4/9.8 = 0.75 G’s. Not too bad!
  1. But what happens as the fuel is used up and the STS becomes lighter. Just before the SRBs are jetissoned at two minutes into the flight, the rockets are still burning. Also the external tank is still supplying fuel to the three orbiter engines, but it is much lighter also. At the time just prior to drop, the SRBs each have a mass of approximately 140,000 kg and the external tank is about 3/5 of its gross mass of 750,980 kg or 450,000kg.
  1. Just preceding the jettison of the SRBs, the acceleration is: a=F/m or15,670kN/(109,771+280,000+450,000)kg = 18.6 m/s2 or 1.9 G’s acceleration.

These values above are only approximate, but they do provide a feel for what is taking place and what the astronauts are going through. The dynamic pressure acting on the STS and the astronauts is actually kept under control by thrust adjustments of the orbiter engines in its flight path toward orbit.