Question

How many Earth radii above the Earth (not from its center) must you be located to experience an acceleration of gravity of 1.38 m/s/s. Express in terms of Earth-radii; that is, express the answer as the number of times greater than 6.38 x 106 m. Ratio of altitude/REarth

Answer 1

Answer:

It is necessary to be at 2.66 Earth radii to experience an acceleration of  $1.38m/s^{2}$.  

Explanation:          

The height above the earth surface necessary to experience an acceleration of $1.38 m/s^{2}$ can be found by means of the Universal law of gravity:

$F = G\frac{M \cdot m}{r^{2}}$  (1)

Then, replacing Newton's second law in equation 3 it is gotten:

$m\cdot a = G\frac{M \cdot m}{r^{2}}$  (2)

Then, r can be isolated from equation 2    

$a = G\frac{M \cdot m}{m.r^{2}}$

$a = \frac{GM}{r^{2}}$

$r^{2}  = \frac{GM}{a}$

$r  = \sqrt{\frac{GM}{a}}$  (3)

Where G is the gravitational constant, M is the mass of the Earth and a is the acceleration.                

$r  = \sqrt{\frac{(6.67x10^{-11}N.m^{2}/kg^{2})(5.972x10^{24}kg)}{1.38m/s^{2}}}$

$r = 16.989x10^{6}m$    

$Earth_{radii} = \frac{height}{Rearth}$            

$Earth_{radii} = \frac{height}{Rearth}$

$Earth_{radii} = \frac{ 16.989x10^{6}m}{6.38x10^{6} m}$

$Earth_{radii} = 2.66$

Hence, it is necessary to be at 2.66 Earth radii to experience an acceleration of  $1.38m/s^{2}$.