Assignment #6

Assignment #6 (1) Thermal Radiation A telescope is observing another solar system, watching planets orbiting the star Ork. The planet Mork has an average surface temperature of about 350K. The planet Orson has an average surface temperature of about 50K. (2 pts.) (a) What is the wavelength of maximum thermal emission from each of these two planets? (Hint: use Wien's law) According to the Wien’s Law, wavelength of maximum emission= λ max = b T , where b is constant of proportionality, T is absolute temperature. Since b  2898μm  K, the wavelength of maximum thermal emission from Mork, λ max = 2898 μm K 350 K = 8.28 μm = 8280 nm , the wavelength of maximum thermal emission from Orson, λ max = 2898 μm K 50 K = 57.96 μm = 57960 nm (2 pts.) (b) In what region(s) of the electromagnetic spectrum are these emissions? The emission from Mork is infrared radiation; the emission from Orson is microwave radiation. (2 pts.) (c) Which planet emits more energy per square meter of surface area per second? By a factor of how much? (Hint: use the Stefan-Boltzmann law) According to the Stefan-Boltzmann Law, j ¿ = σ T 4 , 350/50=7, thus 7 4 =2401. Mork emits 2401 times the amount of energy. (3 pts.) (d) Mork has a radius that is about 4 times Orson's radius. Mathematically compare the total amount of energy emitted by each planet per second over the whole planet. Mork emits how many times more energy per second? (Remember: the surface area of a sphere is 4 pi R 2 ) According to the Stefan-Boltzmann law, E total = σT 4 ∗ area , since area=4piR 2 , E  R 2 T 4 .

So E mork : E Orson = 4 2 ∗( 350 50 ) 4 =38416 which means the Mork emits 38416 times more energy per second through total surface area than that of Orson. (2 pts.) (e) Planet Mindy orbits Ork at an average distance of 3.76 AU while, on average, Planet Fred 15.04 AU. from Ork. Mathematically compare the intensity (flux) of the light that reaches the surface of the two planets. How many times stronger is the light on Mindy in comparison to the light on Fred? Assume L is the intensity at the surface of the Ork. So the intensity at distance d from the Ork is I = L 4 pid 2 , So I Mindy = L 4 pi d M 2 , I Fred = L 4 pi d F 2 , I Mindy I Fred = d F 2 d M 2 =(15.04/3.76) 2 =16 So the light on Mindy is 16v times stronger than the light on Fred. (2) Spectra (3 pts.) (2 a) The plot above shows an example of a blackbody spectrum, the spectrum given off by a opaque object. What is the wavelength in meters where this spectrum is brightest? 3.5*10 -8 meters. (3 pts.) (2 b) Use Wein's Law to estimate the temperature of the object emitting the spectrum above. According to the Wein’s Law, wavelength of maximum emission= λ = b T = 2898000 T , So, T=2898000/ λ , T(3.5*10 -8 meter)=2898000(nm*K)/(3.5*10 -8 *10 9 nm)=82800K (3 pts.) (2 c) The blackbody spectrum above would be produced by an object at a different temperature. What is the wavelength where it is brightest? 5*10 -7 meters (3 pts.) (2 d) Estimate the temperature of the object emitting the spectrum above. 2898000(nm*K)/(5*10 -7 *10 9 nm)=5796K

(1 pt.) (d) Claudius Ptolemy Claudius Ptolemy’s contributions to Astronomy is that his work allow the astronomers to make accurate predictions of planetary positions and solar and lunar eclipses. Meanwhile he taught his students how to predict the location of heavenly body at anytime from anywhere on Earth with his mathematical model of planet movements. (1 pt.) (e) Nicolaus Copernicus Nicolaus Copernicus’s contribution to Astronomy is that he proposed that the sun is the stationary in the center of the solar system and planets revolve around the sun. (1 pt.) (f) Tycho Brahe Tycho Brahe’s contribution is that his observations of planetary motion is accurate and prove the circular orbits could not work, which serve as a base for transition from geocentric model to heliocentric model even he is advocated the geocentric model. (1 pt.) (g) Johannes Kepler Johannes Kepler discovered that the Earth and planets revolve around the sun in elliptical orbits. (1 pt.) (h) Galileo Galilei Galileo Galilei’s major contribution to the Astronomy is that his inventions, from compasses and balances to improve both the telescopes and microscope, which pave the road for posterity to explore the universe. (1 pt.) (i) Isaac Newton Isaac Newton’s major contributions to the Astronomy are his three laws of motion that established the law of universal gravitation. (1 pt.) (j) William Herschel William Herschel’s main contributions to the Astronomy is that he discovered the planet Uranus, hypothesized that nebulae are composed of stars and further developed a theory of stellar evolution.