VITON13School

Chapter 6 · 1903 – today

The Space Race

By , Founder of VITON13 SCHOOL

The rocket equation

A rocket stands on the pad, and a line shows its exhaust streaming down. In 1903 the Russian teacher Konstantin Tsiolkovsky published the equation that governs every rocket: the gain in speed equals the exhaust speed times the natural logarithm of the starting mass divided by the final mass, or Δv = vₑ · ln(m₀/m₁). Most of a rocket is fuel, and the more it burns, the less each extra kilogram adds. That is why real rockets drop empty stages. Reaching low orbit needs a speed of about 7.8 kilometres per second, and with drag and gravity losses the rocket must gain about 9.4. The equation is maths, tested by every launch.

1 of 5Tsiolkovsky’s equation: a rocket pushes against its own exhaust
Fig. 6.1. Tsiolkovsky’s equation: a rocket pushes against its own exhaust

In numbers

4 Oct 1957
Sputnik 1, the first satellite, goes into orbit
108 min
the length of Gagarin’s single orbit in 1961
20 Jul 1969
Armstrong and Aldrin land on the Moon

Check yourself

Who flew the first human orbit of Earth, and in what year?
What does the rocket equation tell engineers?
Who stayed in orbit around the Moon while Armstrong and Aldrin landed?

Sources

  1. NASA: Sputnik and the Dawn of the Space Age
  2. NASA: Apollo 11
  3. NASA: International Space Station
  4. Encyclopaedia Britannica: Yuri Gagarin