Rocket-powered Intercontinental Flight CO₂ Emissions

Introduction

Fig. 1: SpaceX Starship SN-15. The vehicle's first successful test flight on 5 May 2021 resulted in the vehicle touching back down on the launch pad in one piece. (Source: Wikimedia Commons)

Billionaires in space - headlines exalting, lamenting, or just pondering the future of space travel have flooded the news since the successful Virgin Galactic and Blue Origin launches carried private citizens to the edge of space in the summer of 2021. [1,2]

Despite criticism of environmental concerns if adopted on a mass scale, Richard Branson, the chair of Virgin Galactic, and Amazon founder Jeff Bezos, cite their desire to preserve the Earth as their reasons for investing in human spaceflight. [3,4] While it is still too soon to determine the scale of the impact these private enterprises will have due to the lack of available data and their infrequent launches, Elon Musk has consigned humanity to the severe enough destruction of its habitat that he has stated his desire to colonize Mars as humanity's back-up plan for long-term survival as his motivation to invest in the development of space flight technology. [5]

SpaceX has produced impressive and relatively cost-effective solutions in response to the challenges posed by space flight, such as the reusable Falcon rockets quintessential to its brand and the Dragon capsules developed through the NASA Commercial Crew Program. [6] In parallel with US efforts to send humans to the Moon and Mars, the Starship/Super Heavy Launch Vehicle Program is essential to the company's main mission of getting humans to Mars, and with Musk's estimated $2M USD launch cost, could benefit government space endeavors as NASA looks to private companies to lower its launch associated costs. [7]

Although an expensive endeavor at the outset, it is in SpaceX's interest to continue development of this platform with a low launch cost in order to win future NASA contracts. Until then, SpaceX requires a profitable business model for this project before it can pursue its far-off endeavors on Mars. SpaceX officials have since proposed commercial travel capable of reaching intercontinental distances in half an hour or less. [8]

While the space industry currently does not contribute a significant amount to global or US greenhouse gas emissions due to infrequent launches when compared to air travel, some critics worry that making the most powerful rocket since the Saturn V commercially available as an alternative to traditional air travel could have significantly increase carbon dioxide (CO₂) emissions at a time when governments globally are pledging to reduce emissions in an attempt to stave off human-caused climate change. [4,8,9] Just how much would the Starship and Super Heavy program contribute to CO₂ emissions and how do those levels comparable to other industries such as commercial aviation?

SpaceX Starship and Super Heavy Launch Vehicle

Environmental concerns surrounding the endeavor have been raised due to its massive scale in comparison with other SpaceX projects. The Starship and Super Heavy rocket will dwarf their predecessors, standing at a combined height of 120 meters with a 9-meter diameter. [5] The Raptor engines that lift the Starship and Super Heavy will utilize a propellant consisting of liquid oxygen (LOX) and liquid methane (LCH₄) in a 3.6:1 mass ratio. [10] To gain an understanding of the effects of such an enterprise if commercialized for intercontinental travel, we will estimate the annual CO₂ emissions if Starship and Super Heavy launched once daily and compare them to the emissions of the US aviation sector.

Given the dimensions of the Starship and Super Heavy vehicles, the propellant mass, which will be used to determine CO₂ emissions, can be estimated using the densities of LOX, ρ_LOX = 1,141 kg m^-3, and LCH₄, ρ_LCH4 = 422.6 kg m^-3. [11] Assuming a roughly cylindrical shape, the volume of the Starship and Super Heavy combined is v = 2π(4.5m)²= 7,634 m³. The composite fuel density, utilizing the fractional form of the propellant mass ratio, is ρ_composite = 0.722ρ _LOX + 0.278ρ_LCH4 = 945.82 kg m^-3. Assuming the propellant takes up 70% of the vehicles' volume, the propellant mass would be:

The combustion of the LCH₄/LOX propellant can be represented by the chemical reaction:

where the atomic weight of CH₄ is 12 + (4 × 1) = 16 and the atomic weight of 2 O₂ is 2(2 × 16) = 64. Using the propellant mass ratio, the amount of CO₂ emitted per launch can be found by:

If SpaceX were to launch one intercontinental flight per day, the company's annual CO₂ emissions for this project would amount to

Conclusion

In 2019, US CO₂ emissions totaled 5,029×10⁶ MT CO₂, with commercial aviation accounting for 1.342×10⁶ MT CO₂, or 2.64% of US CO₂ emissions. [12] Annually, the Starship and Super Heavy vehicles would require 43,070 launches, or 118 per day, to match current US commercial aviation emissions. Since SpaceX has released neither the cost of production of this project, nor the potential cost of a ticket on one of its intercontinental flights, one can guess that its launches are unlikely to significantly contribute to CO₂ emissions for quite some time because of the inaccessibility caused by high prices and the current lack of easily accessible launch infrastructure. Although critics may rightfully question the necessity of the wealthy spending exorbitant amounts of money on space tourism (Virgin Galactic, for example, has sold 600 tickets for approximately $250,000 USD each) perhaps, "one giant leap for pollution" is, as of yet, an unearned title for the nascent industry. [13,14]

© AnnaMaria Dear. 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.

References

[1] K. Chang, "Branson Completes Virgin Galactic Flight, Aiming to Open Up Space Tourism," New York Times, 11 Jul 21.

[2] D. Streitfield and E. Woo, "The Amazonification of Space Begins in Earnest," New York Times, 21 Jul 21.

[3] J. Jolly and G. Topham, "Richard Branson's Quest: To Boldly Go Where No Billionaire Has Gone Gefore," The Guardian, 10 Jul 21.

[4] S. Kessler, "Jeff Bezos Vows to Fight Climate Change, But Space Tourism Could Do More Harm, Critics Say," New York Times, 21 Jul 21.

[5] K. Chang, "SpaceX Unveils Silvery Vision to Mars: 'It's Basically an I.C.B.M. That Lands'," New York Times, 29 Sep 19.

[6] K. Chang, "SpaceX and NASA to Test Launch Crew Dragon, a New Ride to Orbit," New York Times, 29 Sep 19.

[7] M. Bender, "SpaceX's Starship Could Rocket-Boost Research in Space," Scientific American, 16 Sep 21.

[8] K. Chang, "Elon Musk Sets Out SpaceX Starship's Ambitious Launch Timeline," New York Times, 28 Sep 19.

[9] B. Plumer, B. Migliozzi and N. Popovich, "How Much Are Countries Pledging to Reduce Emissions?," New York Times, 1 Nov 21.

[10] "Exhaust Plume Calculations for SpaceX Raptor Booster Engine," Sierra Engineering and Software, June 2019.

[11] J. Rumble, ed, CRC Handbook of Chemistry and Physics, 102nd Ed. (CRC Press, 2021).

[12] "Inventory of U.S. Greenhouse Gas Emissions and Sinks: 1990-2019," U.S. Environmental Protection Agency, EPA 430-R-21-005, April 2021.

[13] K. Chang, "A Ride to Space on Virgin Galactic? That'll Be $450,000, Please," New York Times, 5 Aug 21.

[14] K. Gammon, "How the Billionaire Space Race Could Be One Giant Leap for Pollution," The Guardian, 19 Jul 21.