As the Unexpected Finger moved through space, she collided with interstellar detritus.
Interstellar detritus is 99 percent protons, by mass. The number of protons struck by the Finger equalled the number of protons per cubic meter, multiplied by the number of cubic meters she plowed through.
As the Finger raced toward Earth, she plowed through a volume of space equal to her cross-sectional area, multiplied by her velocity.
The finger's velocity was v = 0.2c = 6 ◊107m/s.
The finger's widest spot was her front face, the pillow, a disk with radius r=8m. So her cross-sectional area was A = πr2 = π ◊ (8m)2 = 200m2.
So as the Finger raced toward Earth, she plowed through a volume of space equal to S = Av = 200m2 ◊ 6◊107m/s = 1.2◊1010m3/s.
In our neighborhood, the local interstellar cloud, the density of interstellar detritus is 0.3 protons per cubic centimeter, or 3◊105 protons per cubic meter.
So the number of protons impacting the Finger was n = (Volume of Space) ◊ (Density of Protons) = S ◊ D = 1.2◊1010m3/s ◊ 3◊105/m3 = 3.6◊1015/s.
In other words, the Finger plowed through four million billion protons per second. Sounds bad.
Some of those protons bounced off, or converted to various forms of energy and flew away. But when protons move faster than about ten KeV (and these did) then they usually penetrate and implant, adding their mass to the Finger. How much weight did she gain?
We will consider the worst-case scenario, where all protons implanted. (This will save us trouble later, when we compute drag.)
Protons weigh Mp = 1.7◊10‑27kg, so the mass of impacting protons was Mp ◊ n = (1.7◊10‑27kg) ◊ (3.6◊1015 /s) = 6.1◊10‑12 kg/s.
In other words, the Finger was struck by six nanograms of protons per second.
The fingerís journey lasted 80 years or t = 2.5◊109s, so she was struck by a total proton mass of (6.1◊10‑12 kg/s) ◊ (2.5◊109s) = 15◊10‑3 kg.
Fifteen grams. Four million billion protons per second for eighty years adds up to half an ounce. No wonder people think protons are small.
Half an ounce is not much.Then again, the protons hit pretty hard.