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Rocket Science 101: The tyranny of the rocket equation

How the giant leap for mankind is not the first step on the Moon but attaining Earth orbit

SpaceX’s Falcon 9. Source: John Kraus Photos

Knowing the players

Delta-v

1. Earth’s surface to Low Earth Orbit (LEO) = 9.3 km/s (at 250 km)2. LEO to Low Lunar Orbit (LLO) = 4 km/s3. LEO to surface of the Moon = 5.9 km/s4. LEO to Mars Transfer Orbit = 4 km/s5. LEO to the surface of Mars = 10.4 km/s
  • It takes more than double the delta-v to reach Low Earth Orbit (LEO) from Earth’s surface than it takes to reach Low Lunar Orbit (LLO) from LEO.
  • All destinations between the LEO and the Moon are but a fraction of that required to just reach LEO from the Earth’s surface.
  • Earth’s surface to LEO is also nearly equal to that required from LEO to surface of Mars.

The giant leap for mankind was thus not stepping on the Moon, but attaining Earth orbit!

Exhaust velocity

1. Solid propellant = 3 km/s
(E.g. The Space Shuttle)
2. Kerosene-Oxygen = 3.1 km/s
(E.g. Falcon, Soyuz, Long March 6, Saturn V)
3. Hypergols (propellants that ignite on contact) = 3.2 km/s
(E.g. PSLV, Proton)
4. Hydrogen-Oxygen = 3.4 km/s
(E.g. Ariane 5, Delta IV)
The Space Shuttle boosters (at the sides) used solid propellant. Source: NASA Flickr
Note: Higher specific impulse or exhaust velocity alone isn't enough to get something out of an object's gravitational well. The amount of thrust generated by the engine should be high too, which is why the low-thrust ion engines (despite having high specific impulse) can't get rockets out of Earth's gravity.

Mass ratio

The Rocket Equation

mass ratio = e ^ (delta-v/exhaust velocity),where 'e' is the mathematical constant equal to ~2.72
Mass ratio shoots rapidly with delta-v. Source: Wikipedia
1. If delta-v <= exhaust velocity, the mass ratio is low and large payloads are thus possible.2. If delta-v > exhaust velocity, the mass ratio exponentially increases and only tiny payloads are allowed. Most of the ship will be propellant mass.

The Tyranny of the Rocket Equation

If the Earth was 50% larger, there would be no space program of the type we have now.

To the Moon

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Jatan Mehta

Space and Moon exploration writer ~ Contributing Editor, The Planetary Society ~ Thinker | Website: https://jatan.space