Ringworld

Given an object like the halo described in the popular X-Box games or ringworld described in Larry Nirven's books, I was just curious how that object would relate to our solar system.

Let's say we put the object halfway between the Earth and Mars orbit (188,767,262 km radius). As I understand it, the spinning action and centrifugal force create the gravitational accelleration to hold the atmosphere, objects, and the Master Chief on the surface of the ring. Let's try to make the gravity similar to Earth's 9.8 meters per second squared.

Centripital Acceleration = Velocity^2 / Radius

So, Velocity = sqrt [(Acceleration) (Radius)]

Velocity = [2 (pi) (Radius)] / (Time of Revolution)

So, Time of 1 Revolution = [2 (pi) (Radius)] / (Velocity)

Therefore, Time of 1 Revolution = [2 (pi) (Radius)] / sqrt [(Acceleration) (Radius)]...

= [(2)(3.14)(188,767,262,000 m)] / sqrt[(9.8 m/s^2)(188,767,262,000 m)]...

= 1.186059687e12 m / 1,360,117.336 m/s...

= 872,027.4756 seconds for one revolution which is about one revolution every 10 days, 2 hours, 13 minutes, and 47 seconds.

Whew, that's fast. With a circumference of 1,186,059,687 km the rotational velocity is about 1,360 km/sec or about Mach 4,000 at sea level. Currently, the fastest manmade object is Helios 2 at 4,022 km/sec and manned object is Apollo 10 at 665 km/sec. So, what would take the Earth 365 days to do, this ring would do in just over 10 days.