A possible means of space flight is to place a perfectly reflecting aluminized sheet into orbit around the Earth and then use the light from the Sun to push this "solar sail." Suppose a sail of area A = 6.40 ✕ 105 m2 and mass m = 4,900 kg is placed in orbit facing the Sun. Ignore all gravitational effects and assume a solar intensity of 1,370 W/m2. A) If the solar sail were initially in Earth orbit at an altitude of 360 km, show that a sail of this mass density could not escape Earth's gravitational pull regardless of size. (Calculate the magnitude of the gravitational field in m/s2.) B) What would the mass density (in kg/m2) of the solar sail have to be for the solar sail to attain the same initial acceleration of 1193 µm/s2.

A possible means of space flight is to place a perfectly reflecting aluminized sheet into orbit around the Earth and then use the light from the Sun to push this "solar sail." Suppose a sail of area A = 6.40 ✕ 105 m2 and mass m = 4,900 kg is placed in orbit facing the Sun. Ignore all gravitational effects and assume a solar intensity of 1,370 W/m2. A) If the solar sail were initially in Earth orbit at an altitude of 360 km, show that a sail of this mass density could not escape Earth's gravitational pull regardless of size. (Calculate the magnitude of the gravitational field in m/s2.) B) What would the mass density (in kg/m2) of the solar sail have to be for the solar sail to attain the same initial acceleration of 1193 µm/s2.