For simplicity, assume an isothermal atmosphere with a temperature of $0$ degrees Centigrade and a constant gravitational acceleration of $9\mathrm{.}81$ m$/$s$2$ in this problem. Assuming that Earth's atmosphere obeys the ideal gas law: 

a$)$ use the barometric formula to calculate the atmospheric pressure and density at the top of the mesosphere $(85$ km$).$ 

b$)$ determine at what height in Earth's atmosphere the pressure would be half of the value you determined in a$).$ 

c$)$ determine at what height in Earth's atmosphere the pressure would be twice the value you determined in a$)$ and compare your answers in b$)$ and c$).$