4.31 If the Earth radiates as a blackbody at an equivalent blackbody temperature TE = 255 K, calculate the radiative equilibrium temperature of the satellite when it is in the Earth's shadow. [Hint: Let dE be the amount of radiation flux imparted to the satellite by the flux density dE received within the infinitesimal element of solid angle dw.] Then, dE = mr-Ido where r is the radius of the satellite and I is the intensity of the radiation emitted by the Earth, i.e., the flux density of blackbody radiation, as given by (4.12), divided by 7. Integrate the above expression over the arc of solid angle subtended by the Earth, as computed in the previous exercise, noting that the radiation is isotropic, to obtain the total energy absorbed by the satellite per unit time Q = 2.21r?oT£ Finally, show that the temperature of the satellite is given by Earth satellite 2,21\1/4 T, = TE
4.31 If the Earth radiates as a blackbody at an equivalent blackbody temperature TE = 255 K, calculate the radiative equilibrium temperature of the satellite when it is in the Earth's shadow. [Hint: Let dE be the amount of radiation flux imparted to the satellite by the flux density dE received within the infinitesimal element of solid angle dw.] Then, dE = mr-Ido where r is the radius of the satellite and I is the intensity of the radiation emitted by the Earth, i.e., the flux density of blackbody radiation, as given by (4.12), divided by 7. Integrate the above expression over the arc of solid angle subtended by the Earth, as computed in the previous exercise, noting that the radiation is isotropic, to obtain the total energy absorbed by the satellite per unit time Q = 2.21r?oT£ Finally, show that the temperature of the satellite is given by Earth satellite 2,21\1/4 T, = TE
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![4.31 If the Earth radiates as a blackbody at an
equivalent blackbody temperature TE = 255 K,
calculate the radiative equilibrium temperature
of the satellite when it is in the Earth's shadow.
[Hint: Let dE be the amount of radiation flux
imparted to the satellite by the flux density dE
received within the infinitesimal element of
solid angle dw.] Then,
dE = mr-Ido
where r is the radius of the satellite and I is the
intensity of the radiation emitted by the Earth,
i.e., the flux density of blackbody radiation, as
given by (4.12), divided by 7. Integrate the
above expression over the arc of solid angle
subtended by the Earth, as computed in the
previous exercise, noting that the radiation is
isotropic, to obtain the total energy absorbed
by the satellite per unit time
Q = 2.21r?oT£
Finally, show that the temperature of the
satellite is given by
Earth
satellite](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5a57109-d372-4bdd-a5dc-b56d238136ac%2Fac253e1d-21ab-44a5-ada9-5de2a866f8e5%2F5pdw7lg.png&w=3840&q=75)
Transcribed Image Text:4.31 If the Earth radiates as a blackbody at an
equivalent blackbody temperature TE = 255 K,
calculate the radiative equilibrium temperature
of the satellite when it is in the Earth's shadow.
[Hint: Let dE be the amount of radiation flux
imparted to the satellite by the flux density dE
received within the infinitesimal element of
solid angle dw.] Then,
dE = mr-Ido
where r is the radius of the satellite and I is the
intensity of the radiation emitted by the Earth,
i.e., the flux density of blackbody radiation, as
given by (4.12), divided by 7. Integrate the
above expression over the arc of solid angle
subtended by the Earth, as computed in the
previous exercise, noting that the radiation is
isotropic, to obtain the total energy absorbed
by the satellite per unit time
Q = 2.21r?oT£
Finally, show that the temperature of the
satellite is given by
Earth
satellite
Transcribed Image Text:2,21\1/4
T, = TE
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