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| Fig. 1: SpaceX Starship. (Source: Wikimedia Commons). |
SpaceX aspires to bring humans to Mars with their spacecraft Starship, whose first orbital flight is potentially happening within the next year. If successful, Starship would be the largest rocket to ever enter orbit. [1] The goal of this report is to determine the amount of energy required to bring Starship into low earth orbit (LEO).
The energy required to bring Starship from Earth's surface to LEO can be determined by computing the heat content of the fuel exhausted from launch to LEO. The total mass at launch is reported as 5,000 tonnes with 4,600 tonnes being made up of fuel. [2] Starship fuel is a mixture of liquid methane and liquid oxygen. [3] The reaction for this mixture can be seen below.
For every 16 grams of liquid methane, 64 grams of oxygen is required for the reaction. Therefore only one fifth of the propellant mass is composed of liquid methane. Liquid methane has a combustion energy of 8.91 × 105 J mol-1 which is equivalent to 5.57 × 107 J kg-1. Thus, the total energy required to launch the Starship into LEO can now be computed.
| E | = | 1 5 |
× 4.6 × 106 kg × 5.57 × 107 J kg-1 | = | 5.12 × 1013 J |
The global energy consumption for 2021 was reported as 595.15 exajoules. [4] With a reported 2021 global population of 7.9 billion, the average amount of energy consumed by a single person over one year is 7.53 × 1010 joules. [5] The energy required to bring Starship to low earth orbit is equal to the amount of energy 680 people use over an entire year. The estimation did not consider the energy required to manufacture Starship, boosters, and rocket fuel, which would only increase the amount of energy required to accomplish this historic feat.
© Jacob Beardslee. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] "SpaceX's Monstrous, Dirt-Cheap Starship May Transform Space Travel", The Economist, 19 Feb 22.
[2] J. Wilken, M. Sippel, and M. Berger, "Critical Analysis of SpaceX's Next Generation Space Transportation System: Starship and Super Heavy", HiSST: 2nd International Conference on High-Speed Vehicle Science Technology, 11 Sep 22.
[3] "Exhaust Plume Calculations for SpaceX Raptor Booster Engine," Sierra Engineering and Software, 18 Jun 19.
[4] "BP Statistical Review of World Energy", British Petroleum, June 2022.
[5] "Global Population Growth and Sustainable Development," United Nations Department of Economic and Social Affairs, 2021.
