In this experiment, as a form of sheltering-at-home fantasy, we adopt a science=fiction scenario. It’s the year 2520 and you are an astronaut working for a private entity simply called The Company. The CEO of The Company is the 8th clone of Elon Musk. Elon 9 has provided you with a small interstellar spacecraft about a million times faster than anything we can conceive of today. It is your job to check out the potential habitability of a few relatively near potentially habitable planets to see if human colonies can be established there to mine materials for the latest version of the Tesla automobile. But there is a problem. Shortly before your launch, a solar-system-wide pandemic ground human economy to a standstill. So Elon 9 had to cut corners. The only device he could afford for you to measure gravity acceleration on the subject planets is a pendulum with a length of 100 cm. After landing, you will determine the gravitational acceleration at the surface of planet p, gp, with the equation: gp = 3944 /T2 ≈ 4000 /T2 cm/s2. for human settlement. From a standard existing reference, S. H. Dole and I. Asimov, Planets for Man, Random House, NY (1964), the largest gravitational acceleration we could live with is about 1,500 cm/s2. The smallest is probably close to that of Mars, about 400 cm/s2. The planets you will be checking out orbit 5 comparatively near stars: Proxima Centauri at a distance of 4.25 light years, Alpha Centauri A at about 4.3 light years, Alpha Centauri B at 4.3 light years, Epsilon Eridani at about 11 light years and Tau Ceti at about 12 light years. One light year is about 1013 km or 63,000 Astronomical Units. Proxima Centauri is a Red Dwarf star that orbits the double-star Alpha Centauri system. We know today that Proxima Centauri is orbited by a planet in its habitable zone that is only a bit more massive than the Earth. The two central Centauri stars (A and B) are a lot like the Sun and are separated by a sufficient distance to each have one or more habitable worlds, Epsilon Eridani has at least one planet with a mass comparable to Jupiter and Tau Ceti has a planet about 4x as massive as the Earth. It is assumed in this exercise that each of these stars has a potentially habitable planet and you must check this out. Be careful after landing to avoid large extraterrestrial predators and unfriendly natives (who probably don’t really want a Tesla). Use the table below to list planet surface gravity accelerations based upon pendulum period T. Good luck! Table for Pendulum Calculations Planet’s Host Star Pendulum Period T (sec.) Gravity Acceleration at Planet Surface gp ≈ 4000 /T2cm/s2. _______________ _____________________ ______________________________ Proxima Centauri 2.3 seconds cm/s2 Alpha Centauri A 1.8 Alpha Centauri B 2.5 Epsilon Eridani 1.5 Tau Ceti 2.0 Question 1: Which planet has a surface gravitational acceleration closest to that of Earth? Question 2: Which planet has a surface gravitational acceleration closest to that of Mars? Question 3: Which planet or planets would you reject for human habitation?
In this experiment, as a form of sheltering-at-home fantasy, we adopt a science=fiction scenario. It’s the year 2520 and you are an astronaut working for a private entity simply called The Company. The CEO of The Company is the 8th clone of Elon Musk. Elon 9 has provided you with a small interstellar spacecraft about a million times faster than anything we can conceive of today.
It is your job to check out the potential habitability of a few relatively near potentially habitable planets to see if human colonies can be established there to mine materials for the latest version of the Tesla automobile.
But there is a problem. Shortly before your launch, a solar-system-wide pandemic ground human economy to a standstill. So Elon 9 had to cut corners. The only device he could afford for you to measure gravity acceleration on the subject planets is a pendulum with a length of 100 cm. After landing, you will determine the gravitational acceleration at the surface of planet p, gp, with the equation:
gp = 3944 /T2 ≈ 4000 /T2 cm/s2.
for human settlement. From a standard existing reference, S. H. Dole and I. Asimov, Planets for Man, Random House, NY (1964), the largest gravitational acceleration we could live with is about 1,500 cm/s2. The smallest is probably close to that of Mars, about 400 cm/s2.
The planets you will be checking out orbit 5 comparatively near stars: Proxima Centauri at a distance of 4.25 light years, Alpha Centauri A at about 4.3 light years, Alpha Centauri B at 4.3 light years, Epsilon Eridani at about 11 light years and Tau Ceti at about 12 light years. One light year is about 1013 km or 63,000 Astronomical Units.
Proxima Centauri is a Red Dwarf star that orbits the double-star Alpha Centauri system. We know today that Proxima Centauri is orbited by a planet in its habitable zone that is only a bit more massive than the Earth. The two central Centauri stars (A and B) are a lot like the Sun and are separated by a sufficient distance to each have one or more habitable worlds, Epsilon Eridani has at least one planet with a mass comparable to Jupiter and Tau Ceti has a planet about 4x as massive as the Earth.
It is assumed in this exercise that each of these stars has a potentially habitable planet and you must check this out. Be careful after landing to avoid large extraterrestrial predators and unfriendly natives (who probably don’t really want a Tesla). Use the table below to list planet surface gravity accelerations based upon pendulum period T. Good luck!
Table for Pendulum Calculations
Planet’s Host Star Pendulum Period T (sec.) Gravity Acceleration at Planet Surface
gp ≈ 4000 /T2cm/s2.
_______________ _____________________ ______________________________
Proxima Centauri 2.3 seconds cm/s2
Alpha Centauri A 1.8
Alpha Centauri B 2.5
Epsilon Eridani 1.5
Tau Ceti 2.0
Question 1: Which planet has a surface gravitational acceleration closest to that of Earth?
Question 2: Which planet has a surface gravitational acceleration closest to that of Mars?
Question 3: Which planet or planets would you reject for human habitation?
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