Answer
$1.98\times10^{20}\ N$
Work Step by Step
To find the tension in the cable, we simply must find the gravitational force pulling on the cable:
$F=\frac{GM_1M_2}{R^2}$
We know that the moon orbits the earth, so we consult the appendix for data regarding the mass of the moon and the earth to obtain:
$F=\frac{(6.67\times10^{-11})(.0735\times10^{24})\times(5.97\times10^{24})}{(3.84\times10^8)^2}=1.98\times10^{20}\ N$
