Desperately need help on this problem i have triedeverything!
A solar sail allows a spacecraft to use radiation pressure forpropulsion, similar to the way wind propels a sailboat. The sailsof such spacecraft are made out of enormous reflecting panels. Thearea of the panels is maximized to catch the largest number ofincident photons, thus maximizing the momentum transfer from theincident radiation.
For such spacecraft to work, the force from the radiation pressureexerted by the photons must be greater than the gravitationalattraction to the star emitting the photons. The critical parameteris the area density (mass per unit area) of the sail.
Consider a perfectly reflecting mirror oriented so that solarradiation of intensity I is incident upon, and perpendicular to,the reflective surface of the mirror. If the mirror has surfacearea A, what is F_rad, the magnitude of the average force due tothe radiation pressure of the sunlight on the mirror?
Express your answer in terms of the intensity I, the mirror'ssurface area A, and the speed of light c.
my answersreview part
To solve the second part of this problem you will need to know thefollowing:
* the mass of the sun, M_{\rm sun} = 2.0\times10^{30}\;{\rmkg},
* the intensity of sunlight as a function of the distance R fromthe sun,
I (sun)(R) = 3.2\times10^{25}\,\frac{1}{R^2}\;({\rm W/m^2}),
and
* the gravitational constant G = 6.67 \times 10^{-11}\; {\rmm^3}/({\rm kg}\cdot {\rm s^2})\;.
Part B
Suppose that the mirror described in Part A is initially at rest adistance R away from the sun. What is the critical value of areadensity for the mirror at which the radiation pressure exactlycancels out the gravitational attraction from the sun?
I found part A, but cannot find part B
Desperately need help on this problem i have triedeverything!
A solar sail allows a spacecraft to use radiation pressure forpropulsion, similar to the way wind propels a sailboat. The sailsof such spacecraft are made out of enormous reflecting panels. Thearea of the panels is maximized to catch the largest number ofincident photons, thus maximizing the momentum transfer from theincident radiation.
For such spacecraft to work, the force from the radiation pressureexerted by the photons must be greater than the gravitationalattraction to the star emitting the photons. The critical parameteris the area density (mass per unit area) of the sail.
Consider a perfectly reflecting mirror oriented so that solarradiation of intensity I is incident upon, and perpendicular to,the reflective surface of the mirror. If the mirror has surfacearea A, what is F_rad, the magnitude of the average force due tothe radiation pressure of the sunlight on the mirror?
Express your answer in terms of the intensity I, the mirror'ssurface area A, and the speed of light c.
my answersreview part
To solve the second part of this problem you will need to know thefollowing:
* the mass of the sun, M_{\rm sun} = 2.0\times10^{30}\;{\rmkg},
* the intensity of sunlight as a function of the distance R fromthe sun,
I (sun)(R) = 3.2\times10^{25}\,\frac{1}{R^2}\;({\rm W/m^2}),
and
* the gravitational constant G = 6.67 \times 10^{-11}\; {\rmm^3}/({\rm kg}\cdot {\rm s^2})\;.
Part B
Suppose that the mirror described in Part A is initially at rest adistance R away from the sun. What is the critical value of areadensity for the mirror at which the radiation pressure exactlycancels out the gravitational attraction from the sun?
I found part A, but cannot find part B
