Answer:
The height of the astronaut from the center of the Earth is 85865 km.
Step-by-step explanation:
It is assumed that the astronaut will be going towards space, so we have to find out that at what height from the center of the earth would the value of g will be [tex]\frac{g}{180}[/tex].
The weight of astronaut on the surface of Earth 180 pounds.
g=9.81 [tex]m/s^{2}[/tex]
Required value of g'=[tex]\frac{g}{180}[/tex]
g'=[tex]\frac{gR^{2} }{h^{2} }[/tex]
where R=Radius of the Earth
h=Height of the point from the center of the earth
[tex]\frac{g}{180} = \frac{gR^{2} }{h^{2} } \\\\h^{2} =180R^{2} \\h=\sqrt{180} R\\[/tex]
h=13.42
The value of R is approximately 6400 km.
So, h=85865 km.
