Use Kuiper Belt Object Haumea's eccentricity, e = 0.189, semimajor axis, a = 43.3 AU, and Period, P = 285 yrs, values to a) calculate its perihelion and aphelion distances with Dp = a (1 e) and D₂ = a (1 + e), b) verify if Haumea's a and P satisfy Kepler's third law for all objects orbiting the Sun: p2 = a³. Show your work. Paragraph V Lato (Recom... a) Dp= Da= b) p2 = BI 19px... v U✓ A L ป Q«/> 58° ...
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- You are given the following data from observations of an exoplanet: Using Kepler’s Third Law (r3 = MT2 where M is the mass of the central star) find the orbital radius in astronomical units of this planet. M = 1.5 times the mass of the sun. Remember to convert days to years using 365.25 as the length of a year in days. What is the semimajor axis of this planet in AU? - Knowing the orbital radius in both kn and AU, use the value in km to find the circumference of the orbit, then convert that to meters. (Assume the orbit is a perfect circle). - Knowing the orbital circumference and the period in days, convert the days to seconds (multiply by 86,400) and find the orbital velocity in m/s - With that orbital velocity, the radius of the orbit in meters, find the centripetal acceleration of our exoplanet - Knowing the acceleration that our planet experiences, calculate the force that the host star exerts on the planet - Knowing the force on the planet, the orbital radius, and the mass of the…When the Earth passes directly between the Sun and Mars, the Earth and Mars are closest to each other. If Mars is 1.52 AU from the Sun and there are 1.5 x 108 km in 1 AU, how many times will the width of the U.S. (2,530 miles) fit end-to-end between Mars and Earth? Planets and Sun not drawn to scale. Mars Earth Sun Part 1 of 4 Mars is 1.52 AU from the Sun. How many times further away from the Sun is Mars than the Earth? (The distances in AU are relative to the distance between the Sun and the Earth, so however many AU a planet is away from the Sun is how many times farther it is from Sun than Earth.) 1.52✔ 1.52 times further awayQuestion 1 (Total: 30 points) a. What is a repeat ground-track orbit? b. Explain why repeat ground-track and Sun-synchronous orbits are typically used for Earth observation missions. c. The constraint for a Sun-synchronous and repeat ground-track orbit is given by T = 286, 400, where I is the orbital period in seconds, m the number of days and k the number of revolutions. Explain why this is, in fact, a constraint on the semi-major axis of the orbit.
- 1. The diameter of the Sun is equal to 1.392*10^9 m, and the distance from the Sun to Saturnis equal to 9.5 AU. Suppose you want to build an exact scale model of the solar system,and you are using a volleyball with average diameter of 21 cm to represent the Sun. a) In your scale model, how far away would Saturn be from the Sun? Give your answer inmeters.b) The actual diameter of Saturn is 116,460 km. What would be Saturn’s diameter in yourscale model? Give your answer in centimeters.You land on Mars and observe that one of its moons (Phobos) has an orbital period of 7.66 hours. If the Phobos were farther from Mars than it is now, it’s period would be a) less than 7.66 hrs. b) about 7.66 hrs. c) more than 7.66 hrs. d) difficult to predict without more information.Scale 0.7707346 AU Period= 2.41495 Years Kepler's Laws: Using the orbit shown below and a ruler, measure the scale bar in the top left corner in centimeters. The length of the bar is equal to the distance in AU shown below the bar. Measure the aphelion and perihelion distance of the orbit in
- How many orders of magnitude do you need to grow in spatial scale (size) to form a planet? Let's take the extreme ends of this scale, from a dust particle of radius a = 10-6m to the gas giant Jupiter (you can round up its radius to the nearest ten to keep it simple). What else has this difference in order of magnitude? Maybe pick something that's not a length scale. Be creative!Kepler's 1st law says that our Solar System's planets orbit in ellipses around the Sun where the closest distance to the Sun is called perihelion. Suppose I tell you that there is a planet with a perihelion distance of 2 AU and a semi-major axis of 1.5 AU. Does this make physical sense? Explain why or why not.SnowT is an exoplanet orbiting star 27 Kood. If the planet’s orbital period is 3.75 days and 27 Kood's constant is 2.9X10^-19 s^2/m^3, what is SnowT orbital radius?
- The figure below is a scaled representation of a planet's orbit with a semimajor axis of 1.598 AU. (Use the exact values you enter in previous answer(s) to make later calculation(s).) (a) Find the ratio of the aphelion-to-perihelion distance. TA (b) Find the perihelion and aphelion distances in astronomical units. AU AU (c) Find the distance the Sun is from the center of the orbit. AU1. Moon is at the distance 384400 km from Earth and orbits the Earth every ~28 days. If the radius of the Moon is 1737 km (consider it to be spherical), what is the area of the moon as measured by the observer on Earth? (Hint: Length contraction)On February 20, 1962, John Glenn made the first U.S.-manned flight around the Earth for three orbits on Friendship 7. With Earth at one focus, the orbit of Friendship 7 is given approximately by r =4090.76/(1 - 0.0076 cos θ),where r is measured in miles from Earth’s center. Use the formula and the figure shown to solve:How far from Earth’s center was John Glenn at his closest distance from the planet? Round to the nearest mile. If the radius of Earth is 3960 miles, how far was he from Earth’s surface at this point on the flight?