Artificial Planet: Finding Year Length in Earth Days

[sps37]

Homework Statement

A science-fiction tale describes an artificial "planet" in the form of a band completely encircling a sun, as shown in the figure . The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth.

What will be the period of revolution, this planet's year, in Earth days?

Homework Equations

g=GMm/r^2
a= v^2/r

The Attempt at a Solution

I tried setting g=9.8ms^2 but I still keep getting stuck. I know that I'm solving for T, but my problem is that I'm left with unwanted variables, such as M, which are not even given in the question. Please any help would be greatly appreciated.

 

[vishal007win]

checked the calculation...
M is always coming into picture..

 

[sps37]

and what does that mean?

 

[sps37]

OK, I know that I have to determine the speed that the band revolves, in order to produce gravitational acceleration of 9.8m/s^2, but I have no clue how speed and gravitational acceleration are related. Please anyone?

 

[pgardn]

OK, I know that I have to determine the speed that the band revolves, in order to produce gravitational acceleration of 9.8m/s^2, but I have no clue how speed and gravitational acceleration are related. Please anyone?

Does v^2/r seem familiar?

 

[sps37]

hahaha thanks for that hint...it actually helped me solve it believe it or not.

BTW vishal, I solved it without using M at all.

 

[DaveC426913]

Or just read the http://www.amazon.com/dp/0345333926/?tag=pfamazon01-20...