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Transcript
il 3) ~ 1. Consider launching a spacecraft on a least-energy orbit to Mercury. That orbit is an elliptical orbit with the Sun at the focus, and with Earth and Mercury at aphelion and perihelion, respectively. Consider the orbits of Earth and Mercury circular. (a) What is the semi-major axis of the spacecraft's orbit? (A plot would help) (b) What is the eccentricity of this orbit? (c) How long will it take the spacecraft to arrive at Mercury? (d) The Earth orbits around the Sun at about 30 km/s. What is the launch speed (and its direction with respect to Earth's orbital motion) fa!' this probe to follow the least-energy orbit? (Hint: First, find the aphelion speed for the least-energy orbit, and then correct for the Earth's motion). 2. An eclipsing binary has an orbital period of 2d22hrs, the duration hI'S and totality lasts 4 hI'S. of each eclipse is 18 (a) Find the stellar radii in terms of circular orbital radius (a) (b) If spectroscopic data indicate a relative orbital speed of 200 km/s, actual stellar radii (in km and solar radii) 3. what are the (a) How much more energy per centimeter squared is emitted by a star at 20,000 K than one at 5000 K? (b) What is the predominant color of each star in part a? Use the \\fien displacement law and express your answer in wavelengths. 4. You average body temperature is 37° Centigrade. (a) What is this in absolute units (Kelvin)? What is the peak wavelength emitted by a person with this temperature? (b) In what region of the spectrum is this wavelength? Is this consistent with the fact that humans do not appear to glow (optically) in the dark? (c) Estimate the surface area of your body (in m2). You are welcome to make any reasonable assumptions and approximations, but be sure to state what they are! (d) Assuming your body radiates like a blackbody (OK within a factor of 2-3), estjmate the total power L radiated by your body in Watts. How does this compare to the power requirement for a typical light bulb? 5. Consider two stars. Inagnitude 4. The first has apparent magnitude 3, while the second has apparent, (b) Assume the stars are so close together that we cannot distinguish them from one another. Therefore, when we try to measure their brightness we are really measuring their combined brightness. What is the combined apparent rnagnitude of the two stars? (c) Now assume the stars had apparent magnitude 7 and 8 and repeat the first part of this problem (i.e. Now, how much brighter/dimmer is the first star than the second?)