Question

The region around the Earth is filling up with space junk such as old satellites. One idea for cleaning up space involves using sails that create drag (see figure below) Perhaps one day satellites will be equipped with sails that are deployed at the end of their missions. The NASA mission NanoSail-D was launched in 2010 to test this idea. This problem compares the drag on a solar sail due to the Earth's upper atmosphere with the force exerted on the sail by the Sun's radiation and with the gravitational force exerted on the satellite by the Earth. NanoSai-D orbited at an altitude of 6.50 × 105 m, and its solar sail had an area of 10 m2. Assume the satellite's total mass was about 4 kg and it was in a circular orbit. Also assume the Earth's atmosphere at that altitude has a density of about 5 × 10-14 kg/m3 and a drag coefficient C1, and the Earth's gravitational force provided the centripetal acceleration. Finally, assume the sail perfectly reflected the sunlight. Estimate the magnitude of the three forces exerted on the satellite. (The distance between the Sun and the Earth is 1 AU-1.5 × 1011 m.) Fdrag = radiation = 9e-5 gravity Need Help? | Read it

Answer 1

V_orbital = sqrt( G*M/R) = sqrt(6.67X10^-11 * (6X10^24)/(6400*1000+6.5*10^5)) = 7534 m/s

Radius of earth = 6400 km, Mass of earth = 6X10^24 kg

Drag = 0.5*density*V^2* A * CD = 0.5*(5*10^-14)*7534^2 * 10*1 = 1.42*10^-5 N

Fgravity = GMm/R^2 = 6.67X10^-11X 6X10^24 * 4 / 7050000^2 = 32.2 N