The following image is from a newly discovered solar system. Star B Sun Based on your knowledge of our solar system, which planet would take the least amount of time to orbit the star?
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- Let's use Kepler's laws for the inner planets. Use the following distances from the sun to calculate the orbital period for each of these planets. Express your answer in terms of Earth years to two significant figures. Answer for the highlighted planet in each question. Note: Use Kepler's law directly. Don't just Google the answers, as they will be a little bit different. When you have calculated them, only submit the value for Earth. Planet Distance from the sun Period of orbit around the sun Earth 150 million km ___ Earth years Mercury 58 million km ___ Earth years Venus 108 million km ___ Earth years Mars 228 million km ___ Earth yearsUsing 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 AThe table below presents the semi-major axis (a) and Actual orbital period for all of the major planets in the solar system. Cube for each planet the semi-major axis in Astronomical Units. Then take the square root of this number to get the Calculated orbital period of each planet. Fill in the final row of data for each planet. Table of Data for Kepler’s Third Law: Table of Data for Kepler’s Third Law: Planet aau = Semi-Major Axis (AU) Actual Planet Calculated Planet Period (Yr) Period (Yr) __________ ______________________ ___________ ________________ Mercury 0.39 0.24 Venus 0.72 0.62 Earth 1.00 1.00 Mars 1.52 1.88 Jupiter…
- 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?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…Suppose 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?
- Part B. 1. The table below shows the gravitational force between Saturn and some ring particles that are at different distance from the planet. All of the particles have a mass of 1 kg. Table 1. Distance and Gravitational Force Data Distance of 1- Gravitational kg Ring Particle from Force between Saturn and 1-kg ring particle (in | 10,000 N) 2. Use the data in the table to make a graph of the relationship between distance and gravitational force. Label your graph "Gravitational Force and distance". Center of Saturn (in | 1,000 km) 100 38 Hint: Put the data for distance on the horizontal axis and the data for gravitational force on the vertical axis. 120 26 130 22 150 17 3. Look at your graphed data, and record in your answering sheet any relationship you notice. 180 12 200 9. 220 8 250 280 O 5Using 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. Key Points to know: - The semimajor axis of the planet in AU is r = 0.0379 AU - The circumference of the orbit is l = 3.562 x 10^10 m - The orbital velocity in m/s is v = 1.874 x 10^5 m/s Questions that need to be answered: - 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 parent star, use the equation for gravitational force to find the mass of our planet (m2). (To get m1 in kg multiply the mass of the star in solar masses by 1.98 x 1030).Pluto’s orbit around the Sun is highly elliptical compared to the planets in our Solar System. It has a perihelion distance of 29.7 AU and an aphelion distance of 49.5 AU. a) What is the semi-major axis of Pluto’s orbit, in AU? b) What is Pluto’s orbital period, in Earth years?
- Exoplanets in eccentric orbits experience large temperature swings during their orbits. Suppose you had to plan for a mission to such a planet. Based on Kepler’s second law, does the planet spend more time closer or farther from the star? Explain.answer each of the following with a brief explanation of the mathematics used to get there. A new mystery planet is detected around our Sun. We measure its position relative to the Sun to be 2 AU at perihelion and 6 AU at aphelion. What is the semimajor axis of this planet's orbit (in AU)? With that information, what is the orbital period of that planet (in years)? If this planet has the same mass as Earth, how does the average force of gravity on the planet by the Sun compare with the average force of gravity on the Earth by the Sun? Please give a numerical ratio of the forces. (Hint: You can take the semimajor axis to represent the average position of the planets)vork Assignment Be sure to answer all parts. A small hole in the wing of a space shuttle requires a 16.0 cm² patch. (a) What is the patch's area in square kilometers (km²)? Enter your answer in scientific notation. x 10 km2 of the patch to the nearest cent? (b) If the patching material costs NASA $4.45/in², what is the