Expert: Philip A. Stahl - 12/8/2008

Question
Hello Philip, thanks for taking my question.

I understand that cosmic rays (let's say from the sun) are mainly protons and small atomic nuclei - not really electromagnetic radiation. These particles travel at close to speed of light, 80% - 99% of light speed, is this correct? My question: If a space ship were able to achieve a velocity of say 25% of the speed of light, and if it were travelling toward the cosmic ray particles (toward the sun), would the particles appear to be moving faster than light? That is, the relative speed of particles and space ship would be 0.80 x C + 0.25 x C = 1.05 x C.
This is definitely not a homework question; I am a retired engineer and now learning new things.
Thanks
Bill


Answer
Hello,

Glad to hear this isn't a HW question, since it fits the profile of many problems I used to give in the last semester of General physics!

Anyway, the error made in your solution is that it doesn't conform to the relativistic addition of velocities (which details, btw, can be found in any standard Gen. Physics college text).

Let the space ship velocity = 0.25c

and the approaching cosmic ray velocity = 0.8 c

then the relative velocity according to the addition formula (again, found in those physics texts) is:

u=  [0.8 c +  0.25c] /  [1 +   0.8c x  0.25c/ c^2]

whence, u =  0.875c  

Not "1.05c"

Hope this helps, but do try to get one of those standard texts and study the details of WHY this is so.

Bottom line to bear in mind for future reference: if the two relative velocities < c, then u  <  c.