Total centripetal acceleration ringworld

[Maiia]

Homework Statement

A) In Larry Niven’s science fiction novel Ringworld, a ring of material or radius 1.54 × 1011 m rotates about a star with a rotational speed of 1.4 × 106 m/s. The inhabitants of this ring world experience a normal contact force ~n. Acting alone, this normal force would produce an inward acceleration of 9.44 m/s2. Additionally, the star at the center of the ring exerts a gravitational force(also pointing inwards) on the ring and its inhabitants. What is the total centripetal acceleration of the inhabitants? The universal gravitational constant is 6.67259 × 10^ −11 N · m2/kg2 . Answer in units of m/s2.
B) The difference btw the total acceleration and the acceleration provided by the normal force is due to the gravitational attraction of the central star. Find the approximate mass of the star. Answer in units of kg.

I wasn't quite sure how to approach this...
I tried first setting the acc of Fn to 4pir^2/T2 to find the period, which I got to be 802,516.9827s and then substituting that into R^3orbit/T^2= GMplanet/4pir^2 to find the mass of the planet...which is more for the 2nd part I guess..

 

[LowlyPion]

Wouldn't you first calculate the centripetal acceleration for the rotational speed at that radius? Then the difference between that and the actual actual given normal force would be the gravitational acceleration toward the sun?

Knowing that force and radius then ...

Picture of Ringworld
http://www.fantasticfiction.co.uk/images/n0/n2565.jpg