Find the mass of a mystery planet based on the fact that one of its moons has an average orbital radius of r and a period of T. Question 4 r = 843571 km T = 1.0 days M_planet [10^25 kg] = Type your numeric answer and submit 40 You are incorrect Two different planets in circular orbits around the same star have speeds of v1 and v2. Find their radius ratio R_r = r1/r2 and their period ratio R_T = T1/T2. Question 5 v2 = 3.8 v1 Calculate R_r + R_T = Type your numeric answer and submit 47.4 You are incorrect
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Kepler's 3rd Law: This law states that there is a correlation between the distance and orbital period of planets going around our sun (and others stars). This relationship is simple for our solar system because of comparison to Earth. If your period is in years (Earth years) and your distance in AU (1 AU is distance from sun to Earth), then P² = a³ Where "P" is period and "a" is the distance to the planet from the sun. a) If we observe that Mars has a period of 1.88 years, how far from the sun is it in AU? b) This doesn't work as easily for other star systems. The following formula is the complete Kepler's 3rd law, I will simplify it for you one more time after I pose the question. (Big G is the gravitational constant. You won't need the value for this problem) P² = 4π²a³ / GM How long is an orbit of a Mars-like planet around a star that is 3.5 times more massive than our sun (answer in years)? Use the distance you got from part a) as the value for the semi-major axis in this equation (a). To make your life easier, I'm going to let you keep things in years and AU, and realize that this equation now only adds one variable, which is how much more massive this other star is than our sun. I've labeled this as M₋ and that way our new star is 3.5 times more massive than our sun and you can plug 3.5 into the following and ignore the actual mass of the sun, you need no numbers other than what is given: P² = a³ / M₋(in solar units)
Emily A.
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The planet orbiting this star has been detected by both the transit and Doppler techniques, so we can calculate its density and get an idea of what kind of planet it is. 1.) Using the method of Mathematical Insight Finding Sizes of Extrasolar Planets, calculate the radius of the transiting planet. The planetary transits block 2% of the star's light. The star TrES-1 has a radius of about 85% of our Sun's radius. 2.) The mass of the planet is approximately 0.75 times the mass of Jupiter, and Jupiter's mass is about 1.9Ă—10^27 kilograms. Calculate the average density of the planet. Give your answer in grams per cubic centimeter. (Hint: To find the volume of the planet, use the formula for the volume of a sphere: (4/3)Ď€(radius)^3. Be careful with unit conversion.
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