Commented+Space+Elevator+Calculation+Program

__**Supplementary Text:**__ A Space Elevator, sometimes called a beanstalk, is a tethered satellite in stationary orbit, it has a lifter which is used to transport people, supplies, and rovers between the planet's surface and the orbiting satellite. in order to prevent the satellite from falling from orbit, a counterweight must be attached in order to introduce a tension in the cable which will prevent the elevator from falling into the planet even when a lifter is introduced to the system. the tension of the cable and the net force on the system with a 5 tonne mass just above the ground is calculated using the Java program below.

__Code (using Java SE 6.0):__

import java.awt.*; import java.io.*; import java.lang.Math;

public class TensionCalc { double tension;// tension of rope (N) double ySt;// yield strength of rope (N/m^2) double xcw; // distance from centre of mass of counterweight to areostationary orbit (m) double csa;// Cross Sectional area of rope (m^2) double density;// density of rope (kg/m^3) double xRopeM = 17025000.0/2.0; //distance to centre of mass of rope from areostationary orbit (m) double rMars = 3397000.0;//radius of mars (m) double mMars = 6.4191*Math.pow(10.0, 23.0);//mass of mars (kg) double gravconst=6.67*Math.pow(10.0, (0-11.0));//Gravitational Constant double tMars=(88775);//rotational period of mars (day in seconds) double omega=(2*3.141592653589793238)/tMars; //angular velocity of surface of mars (rad/s) double mRope;//mass of rope (kg)

// the mass of the Counterweight can be found by using the formula //|xRope*mRope|=|xCounterWeight*mCounterWeight|

TensionCalc{}//empty constructor

public boolean canHold( double x/*distance from CoM of counterweight to areostationary orbit */, double cs/*Cross sectional area of rope*/, double d/*density of rope*/, double ys/*yield strength of rope*/) // tests if given values for rope can hold the space elevator with a 5 tonne lifter { xcw=x; csa=cs; density=d; ySt=ys; // assigns values to global variables

mRope=csa*density*xRopeM+5000; // finds mass of rope and lifter combined

tension=(gravconst*mMars*(mRope+(mRope*xRopeM)/xcw))/((Math.pow((rMars+(xRopeM*2)), 2.0)))+ ((Math.pow(omega, 2.0)*(rMars+xRopeM+xcw)*((mRope*xRopeM)/xcw)+mRope)); /*calculation for tension, tension=(|Fg of elevator|)+ (|centripetal force of elevator|)*/ double netF=-(gravconst*mMars*(mRope+(mRope*xRopeM)/xcw))/((Math.pow((rMars+(xRopeM*2)), 2.0)))+ ((Math.pow(omega, 2.0)*(rMars+xRopeM+xcw)*((mRope*xRopeM)/xcw)+mRope)); /*calculation for tension, netF=(Fg of elevator)+ (centripetal force of elevator) where negative is towards ground*/ System.out.println(netF); //output net force System.out.println(mRope+((mRope*xRopeM)/xcw)); // output total mass of space elevator

System.out.println(tension);// output total tension

System.out.println(tension/csa); //output total pressure on rope at geostationary orbit

boolean viable=false; if((tension/csa)<ySt) viable=true; //evaluate if rope's yield strength can withstand pressure

return viable;//return whether or not it is viable }

public static void main(String [] args) //main argument (runs the program) {

double heightOfCounterweight=10000.0/*km*/*1000.0; double crossSectionalArea=0.00002475/*m^2*/; double densityOfRope=1330.0/*kg/m^3*/; double yieldStrengthOfRope=20.0/*GPa*/*(Math.pow(10.0, 9.0));

TensionCalc a = new TensionCalc; System.out.println(a.canHold(heightOfCounterweight, crossSectionalArea, densityOfRope, yieldStrengthOfRope));//output if viable }

} __Givens:__ Height of Areostationary orbit=17025000 m Calculated Radius of Mars = 3397000 m Mass of Mars = 6.4191 * 10^23 kg rotational period of mars=88775 s height of centre of mass of counterweight above mars=2500 km total cross-sectional area of carbon nanotubes used=0.2475 cm^2 density of carbon nanotubes=1330 kg/m^3 yield strength (assuming no weaving of strands) = 20.0 GPa

__Outputs:__ Net Force = 257652.00100096143 N Total Mass = 527995.42 kg Total Tension = 366060.562206411 N Pressure= -14.7903 GPa viable?=true