A Bored Teenager On Phobos
The year is 2250 CE and your parents have taken a 2 year contract to work on Phobos. Your Mom is a mining engineer and your Dad is a solar system traffic controller.
The Earth is currently being occluded by the Sun so there are no good downloads of the latest movies and you also can't download the latest bug fix update to PUBG version 1233.
You go to Phobos High (go Space Hawks!), school is out for the day and you are bored out of your skull. So you and your buddy head to the surface, put on your spacesuits and try to throw rocks into orbit.
So the question is: can this be done?
Orbital Period
The equation for a small body orbiting a much larger massive object has conveniently been worked out for us (thank you Physicists) and it is given by the equation:
where:
r is the radius of the orbit,
M is the mass of the object, in this case Phobos and it is equal to 1.07 x 1016 kg.
G is the universal gravitational constant and is equal to 6.67 x 10-11 m3/kg s2.
Phobos is shaped a bit like a potato (27 x 22 x 18 km), so for the radius 'r' we will assume that the teen is at the high end of Phobos which is about 27 km / 2 = 13.5 km out from the centre.
Plugging in all of these numbers and we get an orbital period of T = 11,666 seconds = 3.24 hours.
The circumference of this orbit is C = 2πr = 2 x π x 13.5 km = 84.823 km = 84,823 m.
This means that the velocity of the thrown rock will be 84,823 m / 11,666 seconds = 7.27 m/s (16.3 mph).
This is totally achievable even by your average weakling space-born human (Earth pride man!).
Escape Velocity
After throwing rocks for a while it gets boring. So what is the escape velocity of Phobos? Can we throw a rock right out of orbit or even run hard enough to launch yourself into space?
Again this has been worked out for us and the equation is:
Again plugging in all of the relevant numbers we get the escape velocity of ve = 11.24 m/s (25.1 mph).
The fastest human to date can run at 44.7 km/h (27.8 mph) so it is entirely within the realm of possibility that a teenager could run fast enough to reach escape velocity. Not smart but teens will be teens and there will be a rescue service for just such events.
Closing Words
With such a weak gravity field Phobos will be a fun place to take great big bounding leaps to go from one place to another. The problem though is if you get too enthusiastic you could put yourself into a sub-orbital trajectory that would take hours to get back to the surface.
Let's hope that spacesuits will have enough oxygen for reckless teenagers in the far future.
Thank you for reading my post.
Post Sources
Equations generated using the Codecogs LaTeX equation editor.
[1] Phobos.
[2] Orbital period.
[3] Gravitational constant.
[4] Escape velocity.
[5] What is the fastest speed of a human?