Why Kenya is the best site for the location of a spaceport.
Kenya is an equatorial country, making it suitable for establishing a launch site. The equator rotates more quickly than other non-equatorial regions of the globe due to the Earth’s shape as an oblate spheroid. Rockets can use this extra velocity boost during equatorial space launches, which results in less fuel usage and hence lower launch costs.
A Space X rocket launch
For this reason, the former Soviet Union and the United States constructed their principal spaceports in Florida and Kazakhstan, respectively, as close to the equator as they could. Furthermore, satellites are typically launched in an easterly direction to benefit from the Earth’s easterly rotation and to launch over vast bodies of water. This lessens the possibility of damage if a rocket explodes or if a guidance system malfunction occurs during launch.
There are only a few spots on Earth where an east-facing shoreline is bisected by the equator. Kenya’s coastline in the Indian Ocean, located slightly south of the equator, is consequently great real estate for spaceports. The early days of the space race saw the recognition of this potential. The Italian space program built a facility on a former oil platform off the coast of Malindi in the 1960s, which was infrequently utilized throughout the following two decades to launch small satellites.
Factors to consider when locating a spaceport.
The openness, flatness, and isolation of a region are taken into account when choosing a launch site. This characteristic was considered when choosing a location for the Luigi Broglio Space Center since the ocean is an open space unaffected by natural features like mountains and flora as well as man-made structures like buildings.
For both security and non-interference, a remote site is sufficient. A space station’s costly, sensitive and advanced technology makes it vulnerable to theft and sabotage. Limited accessibility is made possible by distance, whereas monitoring and surveillance are made possible by openness. The expense of transportation is included here. Although remoteness may be a crucial consideration, a launch location shouldn’t be too far away so that getting supplies and staff there and back won’t cost too much. Already, space exploration is an expensive endeavour. Hence, every chance to cut expenses should be carefully considered.
Viable potential spaceport locations in Kenya.
Viable spaceport locations should have low-trafficked airspace, clear skies and still winds to facilitate the success of a launch. The location of a spaceport should also take into account cultural, economic, and even political affairs when determining the best possible location. Viable spaceport locations include the counties of Marsabit, Tana River, Isiolo, Laikipia, Kilifi, Narok and Turkana. The heat map shows areas with the highest potential.
Potential locations of a spaceport in Kenya
When a spacecraft is launched into orbit, it should end up spinning around the Earth quickly enough not to be pulled back in by the Earth’s gravity. For a spacecraft to reach orbit, it must achieve a high enough velocity such that the centrifugal force it experiences is greater than or equal to gravity. Since the earth is a sphere, It must essentially be falling continuously but travelling so fast that it reaches the horizon before it reaches the earth’s surface/atmosphere and its trajectory is curved by the earth’s gravity to form a continuous orbit with an eccentricity. This is made possible by the enormous thrust provided by the massive rockets required to launch a spacecraft, which is sufficient to reach escape velocity. Yet, the Earth’s rotation itself can also assist in giving it a push. At the equator, the Earth’s surface is already moving at a speed of 1674 kilometres per hour. A ship that is launched from the equator ascends into space while continuing to orbit the Earth at the same speed as previously. Inertia is to blame for this. This speed will assist the spaceship in maintaining a sufficient speed to remain in orbit.
Why the equator? Unbelievable as it may seem, the Earth’s surface is moving more quickly there. If you observe two spots on one line from pole to pole, one spot on the equator and the other half to the pole, each will make a complete revolution in 24 hours and return to where it was. But since the Earth’s shape is round, and the widest point is at the equator the spot on the equator would have to go more miles in that twenty-four-hour period. This indicates that the land is moving faster at the equator than any other place on the surface of the Earth. We multiply this speed (1674 kilometres per hour) by the cosine of the latitude to obtain the velocity boost at different locations. We see that the highest cosine is cos 0 degrees which yields 1 and this progressively decreases as you approach the poles (i.e., cos 50 degrees = 0.6427876) which means a lower velocity boost as you move further from the equator
How do we calculate the velocity boost for a space vehicle with a given mass budget?
To place an object into orbit, the launch vehicle must increase its velocity until it is equal to the velocity required to maintain that orbit while overcoming various losses, such as losses from gravity and drag during flight, and reaching the orbital altitude. The rocket equation, first derived by Konstantin Tsiolkovsky, relates this change in velocity to engine performance and vehicle mass with:
where:
ΔV is the change in velocity produced.
go is the acceleration due to gravity on Earth at sea level.
Isp is the average specific impulse of the vehicle’s engine(s). Isp varies based on the specific oxidizer and fuel combination as well as the overall efficiency of the rocket engine.
minitial is the mass of the entire launch vehicle system at the beginning of the flight and is defined as
𝑚𝑖𝑛𝑖𝑡𝑖𝑎𝑙 = 𝑚𝑝𝑎𝑦𝑙𝑜𝑎𝑑 + 𝑚𝑝𝑟𝑜𝑝𝑒𝑙𝑙𝑎𝑛𝑡 + 𝑚𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒𝑠 𝑎𝑛𝑑 𝑒𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡
mfinal is the mass of the launch vehicle system at the end of a powered flight. The final mass is defined as
𝑚𝑓𝑖𝑛𝑎𝑙 = 𝑚𝑝𝑎𝑦𝑙𝑜𝑎𝑑 + 𝑚𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒𝑠 𝑎𝑛𝑑 𝑒𝑞𝑢𝑖𝑝𝑚𝑒𝑛t
The ratio of initial to final mass is also referred to as the vehicle’s mass ratio.
The table shows the total ΔV required to reach LEO, Geosynchronous Transfer Orbit (GTO), Geosynchronous Earth Orbit (GEO), and Low Lunar Orbit from the Earth’s surface.
The Delta‐V is used to evaluate the requirement of the mission, which, in turn, allows for calculating the fuel necessary to carry out that mission. This Delta‐V needed for a mission can be obtained as:
Where the Δ𝑉orbit refers to the speed that the rocket must reach to orbit the planet in a given orbit, and it is equal to the orbital velocity at the insertion point. Furthermore, the losses or gains related to the rotation of the Earth Δ𝑉r can be expressed as:
Where 𝑉r, h0,f0 is the linear velocity of the Earth at that latitude and altitude, and 𝐴0 is the launch azimuth. In prograde orbits, the rotation component will have a negative value, implying some help from the Earth to launch. Therefore, these two components can be calculated precisely. The rest of the components, the aerodynamic loss Δ𝑉d, propulsive losses Δ𝑉p, and associated losses to gravity Δ𝑉g, cannot be calculated until the final trajectory is known. Δ𝑉margin is a safety margin to consider effects not analysed or errors in the data.
Let us assume a rocket model with an initial mass of 180,750kg, Final mass of 15,750kg and propellant with an Isp of 400s
M-initial = M propellant + M payload + M structure =180,750kg
M-final =M payload + M structure = 15,750kg
Isp = 400s
go =9.81 m/s2
ΔV1=400*9.81In (180750/ 15750) =9.572km/s
∑ ΔV = 9.572+0.465km/s equatorial boost velocity = 10.037km/s
0.465 x 3600 seconds = 1674 km/h
Since we can see that we obtain a velocity boost of 1674 km/h just by positioning a spaceport in Kenya at the Equator contributes to the total velocity gained by the launch vehicle.
Simulation of an Equatorial Low Earth Orbit Satellite launched from Kenya (GMAT)
The land at the equator is moving 1674 km per hour, and land halfway to the pole is only moving 1180 km per hour, so launching from the equator makes the spacecraft move at 494 km/hour faster once it is launched. The earth spins at about 465 meters per second at the equator, with that times the cosine of your latitude anywhere else. A rocket needs to get to 7800m/s to reach orbit. For example, with an Isp of 3400m/s, it’s about 15% extra fuel for polar vs equatorial orbit since rockets need an exponential amount of fuel but due to the upper stages being empty mas that can have a significant impact on payload if the rocket is not designed for anything else than equatorial low orbits.
Ground Track plots of a Satellite orbit along the Equator with a slight inclination (GMAT)
If you launch from a launch site not on the equator the best you can do is go east and launch into an orbit with an inclination equal to your latitude, taking a boost of 465m/s times the cosine of your latitude. However, if you launch into an orbit of inclination higher than your latitude you will only be able to use a boost equal to… roughly 465m/s times the cosine of your inclination. At about 28° the best we could get in any easily reachable orbit from there would be 465´cos (28) = 410m/s. For the International Space Station, we can practically get about 465*cos (51) =292m/s so that is roughly approximated about 118m/s difference which should make something like a 5% payload difference.
However, understanding that any extra payload requires not just extra propellant to carry the extra cargo, but also extra propellant to carry the propellant added resulting in a gradual exponential increase in the mass of the propellant (M propellant).
