Equatorial Rocket Launch Advantage

Quote of the Day

A faith that makes losing a sin will make cheating a sacrament.

Michael Gerson


Introduction

Figure 1: Map of Guyana Space Centre. (Source)

Figure 1: Map of Guiana Space Centre. (Source)

Putting a satellite into orbit requires that you impart a velocity of ~17,000 mph to the satellite. Because the Earth is rotating, its surface velocity gives you a head start on achieving orbital velocity when you launch toward the east – the direction of the Earth's rotation. The closer you move your launch site to the equator, the more velocity you get from the Earth's rotation.

In this post, I will compute the surface velocity for the European launch site in Guiana and at the Cape Canaveral launch complex (example launch pad) in Florida. Figure 1 shows a map of the the Guiana launch site, which is closer to the equator than Cape Canaveral. My objective in this post is to determine the advantage that the Guiana launch site has over Florida's Canaveral launch site.

I became interested in the important of launch site location after reading this article. My results agree with theirs.

Background

Earth Ground Velocity

Equation 1 shows the formula that I used to compute the Earth's velocity at the two launch sites

Eq. 1 \displaystyle {{v}_{{Ground}}}={{\omega }_{{Earth}}}\cdot {{r}_{{Earth}}}\left( {{{\theta }_{{Latitude}}}} \right)

where

  • ωEarth is angular velocity of the Earth [rad/sec]. The angular velocity is computed using the formula {{\omega }_{{Earth}}}=\frac{{2\cdot \pi }}{{{{T}_{{Sideral}}}}}, with TSidereal being the length of the Earth's sidereal day.
  • rEarth is radius of the Earth at the latitude θLatitude [m]

Earth Radius

Equation 2 shows how to compute using Mathcad 15 the Earth's radius as a function of latitude based on the WGS84 reference model. The exact formula I used is from this paper.

Eq. 2

Launch Site Latitudes

The latitude of the launch sites is what determines its velocity boost. I list their latitudes here:

I should mention that the Cape Canaveral launch site consists of numerous launch pads. Figure 2 shows a map.

Figure 2: Map of Cape Canaveral Air Force Station. (Source)

Figure 2: Map of Cape Canaveral Air Force Station. (Source)

Analysis

I want to compute the difference in the Earth's rotational velocity at the the two launch sites. Figure 3 shows how to perform that calculation.

Figure 3: Earth Rotational Velocity at Equation, Guinea, and Canaveral.

Figure 3: Earth Rotational Velocity at Equation, Guinea, and Canaveral.

My analysis shows that the Guiana launch site has a velocity advantage of 126 mph, which is relatively small compared to the 17,000 mph needed to achieve orbit.

Conclusion

I was able to confirm the velocity advantage for the Guiana launch site over that of Cape Canaveral. The ideal launch site would be as near as possible to the equator with nothing but ocean to the east to ensure that failed rockets would drop into the ocean. Polar launches have different requirements – like clear ocean to the north. The US uses Vandenberg Air Force Base for those launches.

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