What is the period of revolution for an artificial planet

[balletgirl]

Homework Statement

A science fiction tale describes an artificail "planet" in the form of a band completely encircling a sun, the inhabitants living on the inside surface (where it is always noon). Imagine the sun is like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperature), and that the ring rotates quickly enough to produce an apparent gravity of one g as on Earth. What will be the period of revolution, this planet's year, in Earth days?

Msun = 1.98x10^30
Rsun= 6.96x10^8

Homework Equations

g= GM/r^2 a= v^2/r
g= GM/(r+h)^2

The Attempt at a Solution

I'm not sure how to start. Would the distance/height be 1 ly (9.5x10^15m), and doesn't one Earth g = 9.8m/s?

 

[shallgren]

If the ring spins fast enough to produce Earth's gravity (9.8 m/s^2) how fast must it be rotating?

 

[DaveC426913]

Homework Statement

A science fiction tale describes an artificail "planet" in the form of a band completely encircling a sun, the inhabitants living on the inside surface (where it is always noon). Imagine the sun is like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperature), and that the ring rotates quickly enough to produce an apparent gravity of one g as on Earth. What will be the period of revolution, this planet's year, in Earth days?

Msun = 1.98x10^30
Rsun= 6.96x10^8

Homework Equations

g= GM/r^2 a= v^2/r
g= GM/(r+h)^2

The Attempt at a Solution

I'm not sure how to start. Would the distance/height be 1 ly (9.5x10^15m), and doesn't one Earth g = 9.8m/s?

To answer your first question:
"...the distance to the band is the same as the Earth-Sun distance..."

To answer your second:
One Earth g is 9.8m/s^2. How fast would it have to revolve to emulate that?