Question

 

Solar Sail

A solar sail allows a spacecraft to use radiation pressure for propulsion, similar to the way wind propels a sailboat. The sails of such spacecraft are made out of enormous reflecting panels. The area of the panels is maximized to catch the largest number of incident photons, thus maximizing the momentum transfer from the incident radiation.

For such spacecraft to work, the force from the radiation pressure exerted by the photons must be greater than the gravitational attraction to the star emitting the photons. The critical parameter is the area density (mass per unit area) of the sail.

Part A

Consider a perfectly reflecting mirror oriented so that solar radiation of intensity is incident upon, and perpendicular to, the reflective surface of the mirror. If the mirror has a surface area, what is the magnitude of the average force due to the radiation pressure of the sunlight on the mirror?

Express your answer in terms of the intensity, the mirror's surface area, and the speed of light.

ANSWER:

=

(2IA)/c Correct

To solve the second part of this problem you will need to know the following:

• the mass of the sun, M sun= 2.0 x 10³⁰ kg,
• the intensity of sunlight as a function of the distance from the sun,

I_sun(R) = 3.2 x10²⁵1/R² (W/m²)

and

• the gravitational constant G=6.67 x10^-11m³/(kg*s²)

Part B

Suppose that the mirror described in Part A is initiallyatrest a distance away from the sun. What is the critical valueofarea density for the mirror at which the radiation pressureexactlycancels out the gravitational attraction from the sun?

Express your answer numerically, to twosignificantfigures, in units of kilograms per metersquared.

ANSWER:

mass/area =

Answer not displayed

I'm having trouble figuring out how to slovepart B.Thanks!