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.

 

[Moetasim]

Your calculations are on the right track, but there are a few things to consider. First, the tensile strength of the steel cable is given in units of force per area (N/m^2), so it cannot be used directly in the calculation of thickness. Instead, you would need to use the cross-sectional area of the cable (which can be calculated from its diameter) to determine the force it can withstand.

Secondly, the equation you have used is for centripetal force in circular motion, which is not directly applicable to this scenario. Instead, you would need to use Newton's law of universal gravitation, which states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

So, the equation you would need to use is F = G(m1m2)/r^2, where G is the universal gravitational constant (6.67 * 10^-11 Nm^2/kg^2), m1 and m2 are the masses of the Earth and Sun respectively, and r is the distance between them.

Once you have calculated the force, you can use the cross-sectional area of the cable (based on its diameter) and the given tensile strength to determine the required thickness.

Hope this helps!