Question

Suppose the moon were held in its orbit not by gravity but by a massless cable attached to the center of the earth.Part AWhat would be the tension in the cable? Use the table of astronomical data inside the back cover of the textbook.Express your answer to three significant figures and include the appropriate units.

Answer 1

`1.98\cdot 10^(20)N`

Step-by-step explanation:

The tension in the cable would be exactly equal to the force of gravity between Moon and Earth, which is given by:

`F=G (mM)/(r^2)`

where

`G=6.67\cdot 10^(-11) m^3 kg^(-1)s^(-2)` is the gravitational constant

`m=7.35\cdot 10^(22) kg` is the mass of the Moon

`M=5.97\cdot 10^(24) kg` is the mass of the Earth

`r=3.84\cdot 10^8 m` is the distance between Moon and Earth

Substituting numbers into the equation, we find

`F=(6.67\cdot 10^(-11)) ((7.35\cdot 10^(22))(5.97\cdot 10^(24)))/((3.84\cdot 10^8)^2)=1.98\cdot 10^(20)N`