Gravitational Force (Earth and Sun)

[jgens]

Homework Statement

To better comprehend the gravitational force between the Earth and the Sun, pretend gravity is turned off and the pull replaced by the tension in a steel cable joining them. How thick would such a cable need to be? You can estimate the diameter by knowing the tensile strength of steel cable is about 5.1 * 10^8 N/m^2.

Homework Equations

Any equations concerning gravitation/cirular motion.

The Attempt at a Solution

This is my attempt at a solution, the answer key says it's wrong.

F = m(4)(pi^2)(r)/t^2

d^2 = m(4)(pi^2)(r)/(t^2)(tensile strength)

thickness = m(4)(pi^2)/(t^2)(tensile strength)

thinkness = 465.45 m or 0.465 km

Where have I gone wrong in my calculations? Can someone please steer me in the right direction. Thanks.

 

[Shooting Star]

F = m(4)(pi^2)(r)/t^2

OK.

d^2 = m(4)(pi^2)(r)/(t^2)(tensile strength)

Didn't understand.

Try to think simply.

Max tensional force/cross-sectional area of cable = tensile strength =>
Centripetal force/area = tensile strength.