Question

3. 10 points An interstellar dust grain has a diameter of lum, and a density of p = 3g/cmº. Consider a spherical, completely light-absorbing grain at the Earth's orbit, (1 A.U., or 1.5 x 108km), subject to the radiation pressure from the Sun. The Sun's total radiation intensity is I = 1400W/m2 at 1 A.U. a) Calculate the force on the grain due to radiation pressure. (5 pts) b) Calculate the force due to the Sun's gravity. (4 pts) c) In which direction will a grain move, if it is initially at rest at 1 A.U.? (1 pts)

Answer 1

2 7x10-12 m Drameter of interstellar dust = I lim= 10-6 @ Radiation Power Intensity & Area Area = ty? Tx60-6? Intersity I 3 1400 W/m2. : Power =P = 1400x 7x10-12 Walt -10 = 43.96 x 10 Watt Now, Radiation force = F : Power speed of light = F = 43.96X10 - 10 N. 3x108 - F - 14.65 X10 -18 N. mass of dust vrs - 400x2 - 4,4x60** Ex103kg/m3. -15 40 x 10 kg mass of sun= M = 2x10 2x io song . Gravitational Force Fq GMm d² Here, do 1.5x 10''m . :. FG = -11 66.67X10 X 40 X10 -15 30 x 2X10 2.25x10 22 Fu = 74.46 X 10-18 N

Since, gravitational trace due to sen is 5 times greater than radiation pressure foce. So, the particle will be attracted towards sur l stasks travelling towards it CS Scanned with CamScanner