One of the challenges of any space mission is getting into orbit. While writing the entry "Mining the Moons of Mars" an idea emerged that has some interesting academic potential. One of the "non-traditional" suggestions for placing objects in orbit is to construct a space tower, although most sci-fi series prefer using a space elevator, by creating a tall enough structure a civilization can avoid much of the energy expenditure required of more traditional rocket launches. For the planet Earth building such a structure would require tremendous advances in science and engineering, a space tower on a Martian moon is a far more straightforward affair.
r is the unknown variable being solved
G is the Gravitational Constant =6.67428e-11 m^3/kg*s^2M represents Mass of Phobos=1.072e16 kg
From all that it was calculated that Phobosynchroneous orbit should be achieved 21.135 km from the
center of Phobos, or roughly a little over 10 km from the average surface altitude. As a point of reference
the tallest man made tower on Earth is the Burj Khalifa at 829.8 meters, a little less than 1/12 the height
of this sci-fi structure. Now here's the fun bit, the force of gravity on Phobos is 1166 times weaker than
on the Earth's surface, drastically reducing the challenge of building this tower. What is even cooler, but
much harder to solve for (read I'm still looking in to how to do the math), is that the tower components
would weigh less at higher parts of the tower. I will try to follow up with some basic tower design
approaches.
Editorial Note (April 24) After getting some notes from my friend Andrew Tremblay, I have made some
mild revisions.
Follow Up 10/1/2015 A cool suggestion from NASA to look into landing on Phobos before a fully
fledged Mars mission, while the ramp makes little sense, building a small scale space elevator, or ideally
a series of elevators around Phobos would allow future mission planners extremely high flexibility on
future missions.
Imagine for a moment that for some small rocky bodies in our solar system the song "Stairway to Heaven" isn't just some song that everyone who picks up a guitar has the urge to play. Under the right circumstances a small body with enough rotation could be altered to allow for the construction of a series of stairs or a ramp that would allow denizens of a planet to walk up into orbit around there world.
Phobos has the most data on its Wikipedia entry and as such will be the source of the general calculations.
(For reference I am using the equation found here and relevant data from the Phobos Wikipedia entry)
r is the unknown variable being solved
G is the Gravitational Constant =6.67428e-11 m^3/kg*s^2M represents Mass of Phobos=1.072e16 kg
ω is the angular velocity of Phobos along its equator and will need to be solved for.
To do this the length of a Phobian day must be estimated. (As Phobos isn't a proper sphere some liberties have been taken.)
Mean Radius of Phobos=11.1 km =Rmean
To do this the length of a Phobian day must be estimated. (As Phobos isn't a proper sphere some liberties have been taken.)
Mean Radius of Phobos=11.1 km =Rmean
Equatorial Rotational Velocity=11km/hr=V
Length of Day=Rmean*π*2/V
Length of Day=Rmean*π*2/V
Phobian "Day" 6.34 hrs
From the length of the Phobian day we can then calculate the angular velocity
ω=[2*π*radians]/[6.34hrs*3600(s/hr)]= 2.75*e-4 radians/second
Now for the epic plug and chug
r=[{(6.67428e-11 m^3/kg*s^2)*(1.072e16 kg)}/{(2.75e-4rad/s)^2}]^(1/3)
unit reduction (radians are unit-less and are being dropped)
r=[{7.15482816e5 m^3}/{7.5625e-8}]^(1/3)
MOAR REDUCTIONS!!
r=[9.4609298e12 m^3]^(1/3)=[9.4609298e12]^(1/3) meters
r=21,135 meters or 21.135 km from the center of Phobos
From the length of the Phobian day we can then calculate the angular velocity
ω=[2*π*radians]/[6.34hrs*3600(s/hr)]= 2.75*e-4 radians/second
Now for the epic plug and chug
r=[{(6.67428e-11 m^3/kg*s^2)*(1.072e16 kg)}/{(2.75e-4rad/s)^2}]^(1/3)
unit reduction (radians are unit-less and are being dropped)
r=[{7.15482816e5 m^3}/{7.5625e-8}]^(1/3)
MOAR REDUCTIONS!!
r=[9.4609298e12 m^3]^(1/3)=[9.4609298e12]^(1/3) meters
r=21,135 meters or 21.135 km from the center of Phobos
From all that it was calculated that Phobosynchroneous orbit should be achieved 21.135 km from the
center of Phobos, or roughly a little over 10 km from the average surface altitude. As a point of reference
the tallest man made tower on Earth is the Burj Khalifa at 829.8 meters, a little less than 1/12 the height
of this sci-fi structure. Now here's the fun bit, the force of gravity on Phobos is 1166 times weaker than
on the Earth's surface, drastically reducing the challenge of building this tower. What is even cooler, but
much harder to solve for (read I'm still looking in to how to do the math), is that the tower components
would weigh less at higher parts of the tower. I will try to follow up with some basic tower design
approaches.
The potential practical applications for building a space elevator on a small moon deal mostly with
fuel delivery and development of space craft construction. As mentioned in previous entries and on the
linked Wikipedia articles, there is a distinct possibility for finding large deposits of water on Phobos,
providing the fuel delivery argument. As to space craft, that is further off, consider the ability to have a
construction platform that is within a few miles of its source materials, impossibly close by interplanetary
standards, but is still capable of building in a micro-gravity environment. That is the potential of a tower
on Phobos. The coolest part, would be the ability to climb a 6 mile tall building and step off into the
expanse of space.
linked Wikipedia articles, there is a distinct possibility for finding large deposits of water on Phobos,
providing the fuel delivery argument. As to space craft, that is further off, consider the ability to have a
construction platform that is within a few miles of its source materials, impossibly close by interplanetary
standards, but is still capable of building in a micro-gravity environment. That is the potential of a tower
on Phobos. The coolest part, would be the ability to climb a 6 mile tall building and step off into the
expanse of space.
Editorial Note (April 24) After getting some notes from my friend Andrew Tremblay, I have made some
mild revisions.
Follow Up 10/1/2015 A cool suggestion from NASA to look into landing on Phobos before a fully
fledged Mars mission, while the ramp makes little sense, building a small scale space elevator, or ideally
a series of elevators around Phobos would allow future mission planners extremely high flexibility on
future missions.
No comments:
Post a Comment