Saturn emits radiation at a rate of 1.98 x 1017 w and absorbs sunlight at a rate of 1.11 x 1017 a) Assuming that the radiation excess comes exclusively from Saturn's gravitational potential energy, at what rate dR/dt is Saturn shrinking? b) How long would it take for Saturn's radius to decrease by 1%? W.
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- a. Calculate the surface temperature of Pluto and Charon at perihelion, assuming both bodies are rapid rotators and in equilibrium with the solar radiation field. b. Calculate the escape velocity from Pluto and Charon, and compare these numbers with the velocity of N2, CH4, and H2O molecules. c. Given your answers in (a) and (b), explain qualitatively the differences in surface ice coverage for Pluto and Charon.What is the value of the IR transmission factor (f) for a Venus-like planet, if the measured average surface temperature is 706 K? Assume the following values for the planet: E, = 2.60x10³ W m² and a = 0.71. Would the average temperature increase or decrease if f decreased?What is the escape velocity is km/s from Jupiters exosphere, which begins about 993 km above the surface ? Assume the Gravitational constant is G= 6.67 x10-11m3 kg-1s-2, and that's Jupiter has a mass of 1.8999999999999998e+27kg and a radius of 68.0 x103km
- If Titan could be moved out to the orbit of Neptune would its atmosphere freeze into solid nitrogen? The formula to estimate the blackbody radiation temperature in Kelvin is: where α is the albedo at 0.3, L the luminosity is 1.5 Watts/meter2, σ , the Stefan Boltzmann constant is 5.67 X10-8 W/m2/K. What would be the temperature and would the atmosphere freeze out if the freezing point of N2 gas 63 K? answer choices 63 K, maybe 75 K, no 46 K, yes 103 K, noWhat is the escape velocity in km/s from Venus' exosphere, which begins about 168 km above the surface? Assume the gravitational constant is G = 6.67 × 10-11 m3 kg-1 s-2, and that Venus has a mass of 4.9e+24 kg and a radius of 5800.0 km.K What is the wavelength (in nm) of the most intense radiation emitted from the surface of Mercury at high noon? (Hint: Use Wien's law, Amax = 2.90 x 10° m: K %3D T (in K) nm In which band of the electromagnetic spectrum is that wavelength? (Hint: Examine the following figure.) Visible light Short wavelengths Long wavelengths 4 x 107 5x 107 6x 107 7x 10meters (400 nm) (500 nm) (600 nm) /(700 nm) Wavelength (meters) 10 12 10 10 10 104 102 1 102 104 Gamma- ray Ultra- violet Micro- Radio X-ray Infrared wave UHF VHF FM AM a Opaque Visual window Radio window Transparent Short Wavelength Long b O gamma-ray O X-ray O ultraviolet O visual O infrared O microwave O radio оооо о оо Opacity of Earth's atmosphere
- The fraction of the energy flux received which is reflected into space is the albedo of Venus, av, which is about 0.76. The fraction of the energy flux which is absorbed is then (1-av) = 1. - 0.76 = 0.24. So the amount of energy actually absorbed by Venus in each second is Lv = (1-av)Ev. Lv = (1-av)Ev = ___________________ ergs/s And next calculate the effective temperature of Venus: Tv4 = (Lv/(4pdv2))/s = Lv/(4spdv2) = __________________ K4 and taking the square root of Tv4 twice in succession we get the effective Temperature Tv: Tv = [Lv/(4spdv2)]0.25 = _________________ K Calculate Venus' emittance assuming that the Venus' actual temperature, Tvr, is 472o C = 745 K: ev = Lv/(4pdv2s Tvr4) = __________________ .Since 1995, hundreds of extrasolar planets have been discovered. There is the exciting possibility that there is life on one or more of these planets. To support life similar to that on the Earth, the planet must have liquid water. For an Earth-like planet orbiting a star like the Sun, this requirement means that the planet must be within a habitable zone of 0.9 AU to 1.4 AU from the star. The semimajor axis of an extrasolar planet is inferred from its period. What range in periods corresponds to the habitable zone for an Earth-like Planet orbiting a Sun-like star?Earths daylight surface disk absorbs about 1045 W per m2 from the Sun. Using 6400 km for the Earths radius, how much of this radiative power is emitted by each square meter of the spherical Earth ?
- Question 2: Planet Mars Planetary Attribute Albedo Radius Gravitational acceleration Mean distance from sun Surface pressure Symbol a R (km) g (m/s²) D (km) Po (kPa) Earth 0.29 6378 9.8 150 x 106 101 Mars 0.25 3395 3.7 228 x 106 0.6 (a) Calculate an appropriate value for shortwave solar radiation (SM) incident at the top of the Martian atmosphere (answer in W/m²). The corresponding value for Earth, SE = 1360 W/m². (b) Estimate the average surface temperature on Mars (answer in degrees Kelvin) using a suitable radiative energy balance. The greenhouse effect can be neglected for Mars. (c) Estimate the mass of the Martian atmosphere (answer in kg).a.Calculate the mass loss rate of the Sun M˙ due to the solar wind flow. Assume averageproperties of the solar wind of number density 6 protons cm−3, and a flow speed of 450 kms−1. Express your answer in units of both kg per year, and solar masses per year. b.Suppose the solar wind flow is perfectly radial. Calculate the expected rate of change ofsolar rotation frequency dω/dt at the present time, based on conservation of angular momentum. Give your answer in units of rad s−1 y−1(i.e., radians per second per year) and alsoin terms of fractional change per year, i.e., 1/ωdω/dt .Use a current solar rotation period of P = 25.38 days to calculate the current angularfrequency of rotation ω. The moment of inertia of a uniform sphere is 2/5 MR2. You canassume that the radius of the Sun is approximately constant, and the change in its momentof inertia due to the solar wind is only due to the mass loss. c.By observing the rotation period of stars similar to the Sun, it is inferred that their…Jupiters exosphere has a temperature of about 870.0K what is the thermal speed of hydrogen (in km/s) in Jupiter's exosphere? The mass of a hydrogen atom is 1.67 x 10-27 kg and Boltzmann constant is k= 1.38 x10 -23 Joule/Kelvin