Question

Urgent please help me

Answer 1

1433 km

Step-by-step explanation:

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

`g' = G(M_E)/((R_E + h)^2)`

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

`g = G(M_E)/(R_E^2)`

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

`G(M_E)/((R_E + h)^2) = (2)/(3)\left(G(M_E)/(R_E^2) \right)`

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

`(R_E + h)^2 = (3)/(2) R_E^2`

Taking the square root of both sides, this becomes

`R_E + h = \left(\!\sqrt{(3)/(2)}\right) R_E`

Solving for h, we get

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

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