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- Using high resolution adaptive optical techniques, observations of a nearby (9.5 pc) cool star of mass 0.2 solar masses indicate the presence of a small rocky exoplanet in a circular orbit with a radius of 0.01 arcseconds. Using Kepler's Laws, estimate the period of the exoplanet's orbit in days. select units ARadius Problem 4) Is the center of gravity of our solar system (including plantes) exactly in the same location as the Oort Cloud 20,000 to 100,000 AU center of gravity of the sun on its own? reason your answer nt movement, but no neel has a radius of 6 che net torque on theProblem 4. Physical Features of the Giant Planets: Volume and Density of Jupiter (Palen, et. al. 1st Ed. Chapter 8 Problem 57 ) Jupiter is an oblate (Links to an external site.) planet with an average radius of 69,900 km, compared to Earth’s average radius of 6,370 km. How many Earth volumes could fit inside Jupiter? Jupiter is 318 times as massive as the Earth. How does Jupiter’s density compare (Links to an external site.) to that of Earth?
- m AGNITUDE SCALE nadto km or THE Q2: Use the fact that our closest neighboring star (Proxima Centauri) is at a distance of 4.24 1.y. and has a radius of about 98.1 × 10³ km to determine its angular diameter. (b.c 10 Col at its greatest brill! Id:stol s1802 to noiton srit of noitoubortal (i on hapitifunt od insup of hoes olsos A 14/49/phaigo odt pilhade fldgrante lize alter Brightes(sansin-boy) neglich beaten thun-Vaga) endoggi sonowies to note ballso aliso osis)The time it takes for a cloud 106,000 AU in radius to collapse in "free-tall to form a new star is half the time it would take for an object to orbit the star on an extremely elliptical orbit with a semimajor axis of 53,000 AU (half the 106.000 AU radius). Part A Use Kepler's third law to find the collapse time, assuming the star has the same mass as the Sun. Express your answer in years to two significant figures. VE ΑΣΦΑ t= Submit Provide Feedback Request Answer yearsSuppose there were a planet in our Solar System orbiting at a distance of 0.5 AU from theSun, and having ten times the mass and four times the radius of Earth. For reference, theEarth has a mass of 5.97 × 1024 kg and a radius of 6,378 km a) Calculate the density of this hypothetical planet.b) Based on your answer from part a), what do you think this planet would be made of?Explain your reasoning.c) Do this planet’s properties agree with the condensation theory for the formation of ourSolar System? Why or why not?
- Suppose there were a planet in our Solar System orbiting at a distance of 0.5 AU from the Sun, and having ten times the mass and four times the radius of Earth. For reference, the Earth has a mass of 5.97 × 10*24 kg and a radius of 6,378 km. a)Calculatethe density of this hypothetical planet. b)Basedon your answer from part a), what do you think this planet would be made of? Explain your c)Dothis planet’s properties agree with the condensation theory for the formation of our Solar System? Why or why not?Using Appendix G, complete the following table that describes the characteristics of the Galilean moons of Jupiter, starting from Jupiter and moving outward in distance. Table A This system has often been described as a mini solar system. Why might this be so? If Jupiter were to represent the Sun and the Galilean moons represented planets, which moons could be considered more terrestrial in nature and which ones more like gas/ice giants? Why? (Hint: Use the values in your table to help explain your categorization.)White Dwarf Size II. The white dwarf, Sirius B, contains 0.98 solar mass, and its density is about 2 x 106 g/cm?. Find the radius of the white dwarf in km to three significant digits. (Hint: Density = mass/volume, and the volume of a 4 sphere is Tr.) 3 km Compare your answer with the radii of the planets listed in the Table A-10. Which planet is this white dwarf is closely equal to in size? I Table A-10 I Properties of the Planets ORBITAL PROPERTIES Semimajor Axis (a) Orbital Period (P) Average Orbital Velocity (km/s) Orbital Inclination Planet (AU) (106 km) (v) (days) Eccentricity to Ecliptic Mercury 0.387 57.9 0.241 88.0 47.9 0.206 7.0° Venus 0.723 108 0.615 224.7 35.0 0.007 3.4° Earth 1.00 150 1.00 365.3 29.8 0.017 Mars 1.52 228 1.88 687.0 24.1 0.093 1.8° Jupiter 5.20 779 11.9 4332 13.1 0.049 1.30 Saturn 9.58 1433 29.5 10,759 9.7 0.056 2.5° 30,799 60,190 Uranus 19.23 2877 84.3 6.8 0.044 0.8° Neptune * By definition. 30.10 4503 164.8 5.4 0.011 1.8° PHYSICAL PROPERTIES (Earth = e)…
- 1. Planet A has an orbital period of 12 years and radius that is 0.033 times the radius of the star. Calculate the fractional dip of the star brightness in the case that planet A is transiting. Give the answer as a number. Quote the formula you use and explain any assumptions you have to make. 2. Planet B has an orbital period of 1 year and is located closer to its star than planet A. You succeed in detecting planet B with the radial velocity technique as well! From this measurement you calculate a minimum mass of planet B to be 75% that of the Earth. (a) Since you detect the planet with both transit method and radial velocity method, what do you know about the inclination of the planetary system? (b) Given this inclination, estimate the true mass of planet B (in units of Earth mass). You do not need to do a detailed calculation, just explain the argument. 3. You also measure the radius of planet B to be the same as Earth, one Earth radius. (a) How does the density of planet B compare…GMm F, r2 F(r = R) The surface gravity g of a body is. The acceleration due to gravity that an object m would feel on the surface of the body. A. Show that the surface gravity of Earth is ge = 9.8 m/s². B. Determine the surface gravity of the Sun. C. Determine the surface gravity of the Sun when it becomes a red giant star, assuming RG 1 AU. Use this answer to explain the significant mass loss rates observed in these objects.What is the best technique of those below to determine the size of an exoplanet? A. Gravitational microlensing B. Pulsar timing variations C. Eclipsing transits D. Radial velocity