How Far Does the ISS Go In …

The International Space Station is in low Earth orbit traveling almost 8 km/s relative to the the surface of the Earth. Just how fast is that?

ISS Speed

The average height of the ISS is around 413 km^[1]. For a circular orbit around the Earth orbital speed is

from math import sqrt

G = 6.67384e-11   # m3 kg-1 s-2  Gravitational Constant
M = 5.972e24      # kg  Mass of the Earth
R_e = 6371e3      # m   Radius of the Earth
R_iss = 412e3     # m   Height of the ISS

v_iss = sqrt((G*M)/(R_e + R_iss))

print "%0.0f m/s" % v_iss

7665 m/s

At that speed, how far does the ISS go in x seconds? We can make a little convenience function

def iss(s):
    return v_iss * s # speed times time in seconds

print "In one tenth of a second the ISS moves %0.1f meters" % iss(0.1)

In one tenth of a second the ISS moves 766.5 meters

Faster than a speeding bullet

Lets say we have a pretty standard 22 rifle with a 0.48 meter long barel.^[2] Lets use standard .22 LR rounds which have a muzzle velocity of about 343 m/s.^[3] If we assume that the bullet accelerates smoothly in the barrel (it doesn’t, but it’s a good first order approximation) then it should take

seconds to leave the end of the rifle after pulling the trigger.

x = 0.48   # m  muzzle length
v = 343.0  # m/s muzzle velocity

t = (2*x)/v

print "A .22 LR takes about %0.5f seconds to leave the barrel" % t

A .22 LR takes about 0.00280 seconds to leave the barrel

Meanwhile the ISS has been traveling …

print "In that time the ISS moves %0.0f meters" % iss(t)

In that time the ISS moves 21 meters

20 meters

So if the ISS were to pass overhead at the exact same time someone pulled the trigger, the ISS would be about 20 meters downrange before the bullet even leaves the barrel! That’s pretty fast.

References

1. Height of the ISS http://www.heavens-above.com/IssHeight.aspx
2. Ruger 10/22 http://www.ruger.com/products/1022Sporter/models.html
3. .22 LR Standard Velocity http://en.wikipedia.org/wiki/.22_Long_Rifle#Standard_velocity