By Lanz Lagman
The Philippines will soon have its own space agency.
While one of its more urgent objectives would be to design and make satellites that help us in various ways – such as improving the Internet speed, enhancing territorial defense, and monitoring different environmental activities – one of its long-term objectives would be the construction of several rocket launching sites for our own rockets or have other countries launch theirs at our sites.
This would prove economical for us due to our strategic location. Our country is located near the equator, and launching rockets near or at it is cost-efficient. But why is this the case?
First of all, sending rockets to space is no easy task; this is why the term ‘rocket science’ is used to describe anything that’s hard to understand.
Aside from the specifics of the mission required, scientists have to consider a lot of factors in the design of the rocket: such as the materials used in its construction, how much fuel it carries, how efficiently the fuel is burned, and how efficient the engines are. These are just some of them.
But what could be potentially more difficult than designing rockets? It would be making rocket launches cheaper.
We may consider making more cost-efficient fuel or modifications for engines and fuel tanks, but these would surely take more time. Coming up with improvements for these two could not be done overnight. Why not launch rockets near or from the equator? And how does that work?
We have to look at two scenarios: the velocity of the rocket before the launch, and the final velocity as the rocket gets sent to its designated orbit.
By finding the change in velocity due to this maneuver or delta V, we could see how much rocket fuel is needed depending on where the rocket is located, with respect to the equator.
Rocket at Rest: Initial Velocity
It might seem that the rocket has zero initial velocity, since it sits idly with its fuel on its launch pad. However, since that launch pad is also sitting on a spinning Earth, the rocket is already moving about the Earth’s axis. The way we could describe how it moves depends on its latitude and its distance from the Earth’s equator and axis.
As we can see from this illustration, Φ is the latitude and RE is the Earth’s radius while ρ is the general distance from the axis of rotation. It’s easily seen that ρ is at its maximum at RE. Depending on what altitude the rocket sits, its velocity (tangential velocity) would be:
In this equation, ω is the angular velocity or how much it takes for a spinning object to complete a full spin. Our planet is a big ball of rock with some water on it, and since it takes around 24 hours to complete a full spin, ω would have a very small value, as we will see later. Together with ρ, the tangential velocity vt expands to:
Now that we know how the rocket moves with respect to its latitude while resting on its launch pad, let’s look at how it moves as it reaches its designated altitude where it will proceed to orbit.
|SpaceX’s Falcon 9 launches.
Image credit: SpaceX
Additionally, the minimum inclination of the orbit is equal to the latitude of the launch site. This means that launching from a latitude nearer the equator means the rocket needs to turn less in order to change how inclined its orbit is with respect to the equator, therefore less fuel would be used.
Take note that for the sake of simplicity, we didn’t consider several factors, such as atmospheric drag and overall propulsive efficiency.
|Image credit: Reddit|
Now, regarding the other significant advantage of launching from the equator: the minimum inclination of an orbit is equal to the latitude of the launch site. If a rocket is launched from north of the equator, it has to go southward until it reaches the same distance south of the equator as it started north of it. Only then will it arc back north.
This inclination can be reduced in-flight with a plane-change maneuver or in simpler words, turning the rocket. However, it’s terribly expensive in fuel expenditure. If we want an equatorial orbit (zero inclination), we could either launch from the equator or burn a lot of extra fuel for a plane change maneuver.
If we want a higher inclination, that’s easy; we just point the rocket away from the equator into the desired orbital plane. This makes launching as near as possible to the equator favorable.
Together with the type 4 climate prevalent in the Southern Philippines (with rain being evenly distributed and the weather being stable overall), we do have potential launch sites.
1. SpaceX Falcon 9 v1.1 Data Sheet. (2016, January 17). From http://www.spacelaunchreport.com/falcon9v1-1.html
2. Falcon 9 Launch Vehicle Payload User’s Guide (2015, October 21). From http://www.spacex.com/sites/spacex/files/falcon_9_users_guide_rev_2.0.pdf
3. List of Rocket Launch Sites, from http://en.wikipedia.org/wiki/List_of_rocket_launch_sites