Imperial Star Destroyers and Space Elevators: A "Star Wars" Aerospace Engineering Analysis🌍🚀
In "Ahsoka", Star Wars used a real Aerospace concept to load cargo onto an Imperial Star Destroyer. What would it take to make this technology a reality?
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Bottom Line Up front:
For an Imperial Star Destroyer like the Grand Admiral Thrawn’s Chimaera to enter Geostationary orbit over Peridea as seen on Ahsoka and use the Night Sister’s tower as a space elevator, the planet would need to be as dense as Saturn.
The calculated density of of Peridea is:
For comparison to something in our universe, Saturn’s density is
You may skip to the conclusion if you don’t want to see the calculations, otherwise please continue reading if you want to see how I derived this result.
You can also see the Google Sheet comparing the Density of Earth, Peridea, and Earth’s Moon
Table of Contents:
Introduction: How This Essay Came to Be:
Nerding Out:
Background Context: Space Elevators and Geostationary Orbit:
What is a Space Elevator?
What is a Space Elevator used for?
What is Geostationary Orbit?
Star Wars vs. Reality: The Differences
Aerospace Engineering Scope
Calculations
Bottom Line Up Front
Finding the Gravitational Pull of Peridea
1. Find the Geostationary Orbit Distance of Peridea.
Constants and assumptions we will start with
Utilizing the Orbital Velocity Calculation for Earth:
Google Sheets to compare Peridea to Earth:
Comparing Peridea to Our Solar System:
Conclusion
References
Introduction: How This Essay Came to Be
In the Star Wars series Ahsoka, there is a breathtaking scene in which the main villain of the series, Grand Admiral Thrawn:
brings his Imperial I-Class Star Destroyer, the Chimaera, into a hover over the planet Peridea, docking with the home of a race of witches called the Night Sisters:
The entire sequence is a breathtaking scene in the episode and gives you a sense of scale in the Star Wars Universe. You can see approximately 6 people standing on the tower as the ship approaches the tower to dock, and the visual weight of the ship is brought to full bear on the viewer:
Nerding out:
As I watched this scene in awe, three thoughts occurred to me.
If the Chimaera is hovering at that height above the planet, isn’t it essentially in Geostationary Orbit, and moving as fast as the planet is spinning?
Wouldn’t it make the Night Sister’s Tower a SPACE ELEVATOR!
The excitement of my realization flooded through me.
Star Wars was demonstrating how a Space Elevator would work!
What I knew about Geostationary orbit and Space Elevators would make what the Chimaera was doing impossible on Earth (as you’ll see), but another possibility occurred:
Could I actually calculate the planet Peridea’s size/density such that it would be possible for the Chimaera to enter Geostationary orbit at such a low height above the planet?
And that, is how this essay was born.
Background Context: Space Elevators and Geostationary Orbit:
I had always wanted to describe and learn more about the space elevator concept. The draft was somewhere on my computer, but I could never find a way to make the concept more compelling for me to write about until this moment in Ahsoka, where the concept was essentially demonstrated in a much cooler way than I could have EVER imagined.
What is a Space Elevator:
Ok, so let’s define a Space Elevator:
The most basic definition of a space elevator as defined by NASA is:
“[A] physical connection from the surface of the Earth to a geostationary orbit (GEO) above the Earth ~35,786 km in altitude.”
The concept would be quite similar in principle to that of a bridge that would connect two locations across a body of water.
However: In this case, the two locations would be between Earth-to-Space:
The most feasible method of creating a space elevator on Earth would be to build in two directions and meet in the middle:
From Earth into Space
From a Geostationary Structure in space down to the location on Earth:
From NASA:
A tether structure hanging down from GEO connected to a tall tower constructed up from the Earth appears to be the most efficient and technically feasible method for space elevator construction
A detailed image of the NASA Concept Design of a Space Elevator can be seen below:
What is a Space Elevator Used For:
The primary function of a space elevator would be to reduce the fuel consumption typically associated with rocket launches. The energy needed to reach Low-Earth Orbit (LEO) is considerably lower than that required for Geostationary Orbit (GEO). The primary use and reason for them would be to quickly transport materials and people between the surface of a planet and space.
What is Geostationary Orbit?
A geostationary orbit is defined as a circular orbit that is positioned at a certain altitude above a planet's equator. This altitude allows the satellite's orbital velocity to match the rotational velocity of the planet. To an observer on the planet, this synchronization makes the satellite appear stationary at a single point in the sky.
Star Wars vs. Reality: The Differences
Now that we've examined the scene in Ahsoka in detail and compared it to the high-level overview of its real-life counterpart, let's begin the analysis and identify where the scenes start to diverge.
Let’s compare the image of a Space Elevator for Earth with the image of the Chimaera in Geostationary orbit over Peridea:
The Space Elevator concept:
The Chimaera:
Can you discern any differences between the two?
The most noticeable distinction is the height of Earth's space elevator compared to that of Peridea.
This height discrepancy arises because Star Wars does not adhere to the physical laws that Aerospace Engineers must consider. Specifically, there is no concern over the tower's height or the necessary size of planet Peridea for the Chimaera to dock so near to the surface.
Now, let's factor in Aerospace Engineering calculations:
Aerospace Engineering Scope:
To bookend the scope of my calculations, I will be trying to determine the following:
What conditions have to be right such that Grand Admiral Thrawn’s Imperial Destroyer, the Chimaera, can enter Geostationary orbit at approximately 500 feet above Peridea.
We’ll first find the geostationary speed of Thrawn’s Imperial Star Destroyer at a particular altitude above the height of Peridea
And determine what is unique about Peridea that Thrawn can perform a Geostationary orbit at that height.
We’ll go through this step by step.
Calculations:
Finding the Gravitational Pull of Peridea:
I found out the Gravitational Pull of Peridea by deriving it from the following steps:
Find the Geostationary Orbit Distance of Peridea
And use Google Sheets to determine what is unique about Peridea that Thrawn can perform a Geostationary orbit at that height.
1. Find the Geostationary Orbit Distance of Peridea.
To find the geostationary orbit distance of Peridea, we will utilize the Orbital Velocity Calculation for Earth and then with an excel sheet, start substituting numbers to approximate the Orbital Distance of Peridea.
Constants and assumptions we will start with:
Me = Mass of Earth:
G = gravitational Constant, will stay the same between our world and the star wars universe:
r = orbital radius, which constitutes Radius of the Earth (6,378km), plus Geostationary Orbit Distance of Earth (35,786 km):
Utilizing the Orbital Velocity Calculation for Earth:
To find the speed of a Satellite, we utilize Newton’s Law of Gravity and Second Law of Motion along with centripetal acceleration. The gravitational forces and acceleration by the satellite must equal each other:
where:
ms = Mass of satellite
ag = Gravitational acceleration
ac = Centrifugal acceleration
The Centripetal acceleration provided by the Earth’s Gravity is calculated by:
Magnitudes of acceleration derived from orbital motion:
Where w = Angular velocity in radians per second
r = Orbital radius in meters as measured from the planet’s center of mass:
We have ag and ac defined, so let’s bring back the original equation:
If we set them equal, we then get:
Note that the ms, for the mass of the satellite appears on both sides of the equation, indicating that the mass of the satellite is independent of geostationary orbit.
cleaning up the equation to aim for velocity of Geostationary orbit, we obtain:
Solving for the v in the velocity, and filling in the information for Me, G, and r, we can get orbital velocity of a satellite at geostationary orbit:
v = approximately 3 km/s, so the geostationary speed for a satellite to orbit planet Earth such that it appears stationary in the sky is 3 km/s
2. Google Sheets to compare Peridea to Earth:
You can see the finished Google Sheet Here.
To compare Peridea to Earth, I put the numbers I calculated for Earth into Google Sheet sheet and duplicated it to say Peridea:
The goals I was looking for with this sheet were tw-fold:
Matching the Planet Radius and Orbital speed parameters between Earth and Peridea.
At the same time, have Orbit Distance for Peridea Geostationary Orbit be at 300m matched that of the Chimaera’s altitude above the Night Sisters tower (I am estimating about 300m/~1000ft).
I first started the tests with the assumption that Peridea had the same properties as Earth, e.g, such as mass, gravity, and 24 hour day. I then changed the Orbital Distance to approximately 300m so as to match the distance of Chimaera’s orbit over Peridea:
Not surprisingly, the Chimaera would be traveling at Low Earth Orbit speeds of 7,900m/s at a 300m altitude above the ground, and would not be in geostationary orbit, but rather would circle Peridea every 90 minutes like what the ISS and Starlink satellites do.
Moving on, I then tried other combinations such as Planet Radius:
Try as I could however, I could not find a combination of that seemed to work to get all the properties between Earth and Peridea to match.
Until I tried working with Mass:
Only when Manipulating the mass of the Peridea could I find a planet that matched the size of Earth with a 24 hour day rotation where an Imperial Star Destroyer could enter geostationary orbit at 300m/~1000ft and load cargo on a Space Elevator.
3. Comparing Peridea to Our Solar System
Out of curiosity I decided to look up the calculation of density of the Earth, and found that the density (Rho) of a planet can be related to its mass ((M)) and radius ((R)) using the formula for the volume ((V)) of a sphere:
Since the volume of a sphere is given by:
We then combine these equations to relate density to a planet’s radius:
Simplifying, we get:
We can identify the average density of the planet with this equation.
Finding the average density of Earth to be approximately 5.51 gm/cm3,
I added that calculation to the Excel sheet for Earth:
And to Peridea:
and found that the density of Peridea is RIDICULOUSLY LOW.
Such that I added the moon on the same chart:
and found that a Planet like Peridea if it had similar properties as Earth such as size and a 24 hour day, would have a gravitational pull LESS than that of the moon:
I decided to look around and try to identify what familiar items in space have a similar density to Peridea, and found that Saturn came closest:
Conclusion:
In this issue of The Engineer's Perspective, inspired by an episode of the Star Wars series 'Ahsoka,' I was compelled to calculate the properties of the planet Peridea. This curiosity arose after observing an The Imperial Star Destroyer Chimaera assume a geostationary orbit over the planet and engage with a space elevator for cargo transfer.
Employing fundamental physics principles and utilizing Google Sheets, I deduced that if Peridea were equivalent in size to Earth and had a similar rotational period of 24 hours, its gravitational force would have to be less than that of the Moon. This reduced gravity is necessary to allow a spacecraft to maintain a geostationary orbit at the altitude observed by the Chimaera above the Night Sisters' tower.
After further research and analysis, I found a familiar astral body with a similar density to Peridea: Saturn.
This research showed that the physics in Star Wars and specifically, the planet Peridea’s properties were wildly more accurate than I had thought.
It was my imagination’s limits that were lacking.
Conducting this analysis for The Engineer's Perspective essay was by far the most fun I’ve had while writing The Engineer’s Perspective. I anticipate exploring other scenarios where aerospace engineering intersects with pop culture and science fiction in forthcoming editions.
References:
Find speed of a satellite placed at geostationary orbit (livephysics.com)
Orbital Velocity and Altitude - How Satellites Work | HowStuffWorks
Density of All Elements in g/cm3 (Complete Chart Inside) (periodictableguide.com)
Density of Earth: What is the Earth Made Of? - Earth How
How Ahsoka's Grand Admiral Thrawn Ended Up In Another Galaxy (giantfreakinrobot.com)
Darren Tan - Chimaera & Profundity (artstation.com)
Chimaera by Ka-Pow96 on DeviantArt