Question

Urgent please help me

Answer 1

1433 km

Explanation:

Let g' = the gravitational field strength at an altitude h

$g' = G\dfrac{M_E}{(R_E + h)^2}$

We also know that g at the earth's surface is

$g = G\dfrac{M_E}{R_E^2}$

Since g' = (2/3)g, we can write

$G\dfrac{M_E}{(R_E + h)^2} = \dfrac{2}{3}\left(G\dfrac{M_E}{R_E^2} \right)$

Simplifying the above expression by cancelling out common factors, we get

$(R_E + h)^2 = \dfrac{3}{2} R_E^2$

Taking the square root of both sides, this becomes

$R_E + h = \left(\!\sqrt{\dfrac{3}{2}}\right) R_E$

Solving for h, we get

$h = \left(\!\sqrt{\dfrac{3}{2}} - 1\right) R_E= 0.225(6.371×10^2\:\text{km})$

$\:\:\:\:\:= 1433\:\text{km}$