In the question we have a solar sail that can be modeled as a disk with diameter
ID: 2125243 • Letter: I
Question
In the question we have a solar sail that can be modeled as a disk with diameter 9m and thickness of 7.5*10^-6m. The intensity of solar energy at that location was about 1400 W/m^2.
a. What force did the sun's light exert on this sail, assuming that it struck perpendicular to the sail and that the sail was perfectly reflecting?
c. Does the acceleration seem feasable for space flight? if not how could one improve the sail?
So far I have used Prad=2I/c and F=Prad*A but Im not getting the right answer and Im not sure how else to do it, If someone could help me out with equations that I might use and how to set up the problem I would greatly appreciate it!
In the question we have a solar sail that can be modeled as a disk with diameter 9m and thickness of 7.5*10^-6m. The intensity of solar energy at that location was about 1400 W/m^2. What force did the sun's light exert on this sail, assuming that it struck perpendicular to the sail and that the sail was perfectly reflecting? If the sail was made of magnesium, of density 1.74 g/cm^3 , what acceleration would the sun's radiation give to the sail? Does the acceleration seem feasable for space flight? if not how could one improve the sail? So far I have used Prad=2I/c and F=Prad*A but Im not getting the right answer and Im not sure how else to do it, If someone could help me out with equations that I might use and how to set up the problem I would greatly appreciate it!Explanation / Answer
radiation pressure = 2I / c = 2 x 1400 / 3 x 10^8 = 9.33 x 10^-6 N/m^2
force on the sails = P x A
area of the sails = pi x d^2/4 = 3.14 x 81/4 = 63.585 m^2
force = 9.33 x 10^-6 N/m^2 x 63.585
force = 5.932 x 10^-4 N
volume of the sails = ara of cross section x thickness = 63.585 x 7.5*10^-6m = 4.77 x 10^-4 m^3
mass of the sail = volume x density = 4.77 x 10^-4 m^3 x 1.74 x 1000 = 0.83 kg
aceleration = force /mass
acceleration = 5.932 x 10^-4 N / .83 kg = 7.15 x 10^-4 m/s^2
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