Expert: Josh - 11/10/2006

Question
Hello and thanks for your time!

Well, here is my question. I was wondering, (this isn't any school thing or whatever, just curious), think of a plant waay out in the middle of nowhere in space, okay? Now, pretend there is a single pole standing straight up from it, height doesn't matter. Now, imagine there is a rod extending from the pole out into space X miles. At the end of the rod is a space shuttle (orwhatever). What i was trying to figure out is this, if 1/2 a mile out from the pole you measured teh speed at which teh rod was travelling (in a circular motion as if to orbit the planet). The speed yuou measure is 100 mi/hr. If you want teh speed of teh space shuttle to be the speed of light, 186,282.4 mi/s, how long would teh rod have to be? Hope you can help, adn thank you!

Answer
Hi Steve,

That's an interesting thought. Imagine "o" as the pivot of rotation and let "S" represents the space shuttle.

==============o==============S

The basic principle concerning circular motion can be described by F = m*(v^2)/r. Here, F represents the centrifugal force, "m" represents the mass, "v" is the tangential velocity of the space shuttle, and "r" is the radial distance from the pivot.

If measurement reveals that v(r)=100 miles/hour, at a radius of r=0.5 miles (strictly speaking, everything should be expressed in SI units, velocity is measured in meter per second), keeping mass "m" constant, the force at initial distance r(i) must equate to the force at final distance r(f) (within reason). This is necessary for the shuttle to exhibit uniform circular motion and stay in orbit.

So, m*v(i)^2/r(i) = m*v(f)^2/r(f).
Assuming that it is possible for the space shuttle to travel at the speed of light, setting v(f)=186282.4 [mi/s], substituting v(i)=1000 [mi/s] and r(i)=0.5 [mi/s] into this equation, you can solve for r(f) -- the length of the rod.
r(f)=v(f)^2/[v(i)^2/r(i)]
   =r(i)*[v(f)^2/v(i)^2]

I'll let you compute this yourself.

Just one comment. Our current knowledge of physics would suggest that the depicted scenario is completely hypothetical. It is not possible for "particles" to sustain motion at the speed of light -- to do that it has to be an electromagnetic wave travelling through vacuum, without "inertia".

Then again, science could be flawed. At the very least, our knowledge is probably incomplete. Astrophysicists still cannot account for the motion of celestrial bodies based on classical mass/gravity calculations. That's why they have introduced the concept of "dark matter" to make the computer simulation model work. It puts back into the equation, something which ought to be there, in theory, but has never been observed in practice. This is just an artificial construct to get around difficulties and reconcile with "reality".

Cheers:)