Given that the intensity of solar radiation incident on the upperatmosphere of t

Question

Given that the intensity of solar radiation incident on the upperatmosphere of the Earth is 1340 W/m2. (a) Determine the intensity of solar radiationincident on Mercury.
___________W/m2
(b) Determine the total power incident on Mercury.
___________W
(c) Determine the total radiation force that acts on the planet ifit absorbs nearly all of the light acting on the planet.
___________N
(d) What is the ratio of this force to the gravitational attractionbetween Mercury and the Sun? Give youranswer to three significant figures.
___________
(a) Determine the intensity of solar radiationincident on Mercury.
___________W/m2
(b) Determine the total power incident on Mercury.
___________W
(c) Determine the total radiation force that acts on the planet ifit absorbs nearly all of the light acting on the planet.
___________N
(d) What is the ratio of this force to the gravitational attractionbetween Mercury and the Sun? Give youranswer to three significant figures.
___________

Explanation / Answer

(a) intensity is related to the distance the planet is fromthe sun, so you need to know distance for Earth & mercury. In atable...          Earth is   1.496 x1011     mercury is 0.579 x1011    meters . Earth is    1.496 / 0.579  =   2.584 times further, . Since intensity is related to distance squared, intensity atmercury is 2.5842 = 6.676 timesgreater or .      1340 * 6.676 =    8946W/m2 . (b) power incident = cross section area *intensity = * 24300002 * 8945 = .             = 1.660 x1017   Watts . (c)   radiation force = power / c = 1.660 x 1017 / 3.00 x 108 =    5.532 x 108 Newtons . (d)   the grav force = G M m /r2 = 6.67 x 10-11 * 1.99 x1030 * 3.18 x 1023 / (0.579 x 1011)2 = .           =   1.26 x1022   Newtons . so the ratiois          5.532 x108 / 1.26 x 1022   =     4.39 x10-14 . (b) power incident = cross section area *intensity = * 24300002 * 8945 = .             = 1.660 x1017   Watts . (c)   radiation force = power / c = 1.660 x 1017 / 3.00 x 108 =    5.532 x 108 Newtons . (d)   the grav force = G M m /r2 = 6.67 x 10-11 * 1.99 x1030 * 3.18 x 1023 / (0.579 x 1011)2 = .           =   1.26 x1022   Newtons . so the ratiois          5.532 x108 / 1.26 x 1022   =     4.39 x10-14

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