In a distant star system there are many inhabitable planets. One of these planets is named Qomar. Qomar is 3.2 AU's from its star and takes 6.5 Earth years to go around its star once. There is another planet in the same star system called Ferenginar. Ferenginar is 0.9 AUs from the star. What is the length of a Ferengi year (on Ferenginar) in terms of Earth years?
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Q: Explain planetary motion through Kepler's Law
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Using Kepler's 3rd law solve the following problem. Show your work and highlight your answer.
In a distant star system there are many inhabitable planets. One of these planets is named Qomar. Qomar is 3.2 AU's from its star and takes 6.5 Earth years to go around its star once. There is another planet in the same star system called Ferenginar. Ferenginar is 0.9 AUs from the star. What is the length of a Ferengi year (on Ferenginar) in terms of Earth years?
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- The 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…What I can do? A. Directions: Refer to the diagram below and brlefly answer the following questlons by supporting your answer with necessary concepts and Ideas. The planet shown in the drawing above obeys Kepler's Laws 1. At which lettered position is the planet speeding up? Why? 2. Each lettered position represents a particular day during the year. During which day (at which lettered position) will the planet move the shortest distance? Why?Use the diagram and the fact that Planet A has a nearly circular orbit while Planet B has a highly elliptical orbit to answer the following questions. Use examples of Newton’s and Kepler’s laws in your answers. a. Does Planet B travel faster or slower when it is closest to the Sun than at other times? Explain your answer. b. Which planet takes longer to orbit the Sun? Explain your answer. c. Does the gravitational attraction between these planets increase or decrease as their orbits move them closer together? Explain your answer. d. Which planet has the highest average orbital speed? Explain your answer. e. Which planet travels at about the same speed throughout its orbit? Explain your answer.
- 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).Show your solution and answer. Remember that the earth-moon distance is still in kilometers. Orbits and Planetary Motion. Directions: Answer the following problem involving orbits and planetary motion. Refer to information given in the box below. Show your solution and box your final answer Kepler's three laws of planetary motion can be described as follows: • The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses) An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas) The ratio of the squares of the periods (T2) of any two planets is equal to the ratio of the cubes of their average distances from the sun (R). (The Law of Harmonies): 3. Consider a planet with mass Mplanet to orbit in nearly circular motion about the sun of mass Mgun: Prove that T? = using the following equations and GMsun conditions on…
- 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 yearsDrag the moon to various locations in order to determine the quantitative effect of distance upon the gravitational force. Examine the effect of doubling, tripling and quadrupling the distance of separation (as measured from planet'scenter). Consider the planet'ssurface to be a distance of one Earth-radius (1 Rplanet). Use the table at the right to record data for whole-number multiples of Rplanet.Use your data to complete the following sentences.If the separation distancebetween the moonand the planetis ... a. ... increased by a factor of 2, then the Fgravis ______________ by a factor of _______.b. ... increased by a factor of 3, then the Fgravis ______________ by a factor of _______.c. ... increased by a factor of 4, then the Fgravis ______________ by a factor of _______As discussed in class, the moon is receding from the Earth due to tides at a rate of ~4 cm/year. Let’s assume that rate has been constant throughout time (it wasn’t, but we can use it to illustrate some key points). Its current semi-major axis is 384,400 km.a) If the moon formed 4.5 billion years ago and has been receding from the Earth ever since, what was its original semi-major axis? What was its original orbital period?b) What would the apparent size of the Moon have been in the sky as viewed from Earth? That is, in Hmwk 2, you were told the diameter of the Moon spans about 0.5o when viewed from Earth today. What would it have been when the Moon first formed? Reletive Numbers Relevant Numbers1 AU = 150,000,000 km = 1.5x108 kmEccentricity of Earth’s Orbit: 0.0167Radius of Earth: 6371 kmMass of Earth: 5.96x1024 kgRadius of the Moon: 1737 kmMass of Moon: 7.34x1022 kgRadius of Mars: 3390 kmMass of Mars: 6.4x1023 kgRadius of the Sun: R⦿=696,300 kmMass of the Sun: M⦿=2x1030…
- The image below presents a greatly exaggerated view of a planet in orbit around the Sun: Planet m M Sun In accordance with Kepler's first law of planetary motion, the shape of the orbit is an ellipse with the Sun at one focus. a) In your own words, state Kepler's second law of planetary motion, then explain how the law arises from a conservation principle (either energy or momentum). b) Again in your own words, state Kepler's third law of planetary motion, then explain how the law is derived from Newton's laws of motion and his law of universal gravitation.Using MBH = 6.6 × 10 Mo, calculate the below. a. Find radius of the Schwarzschild sphere (Schwarzschild radius Rs). You can calculated from the appropriate formula or just use the fact that for an object of 1 solar mass Rs = 3 km. b. Express Rs in km, in AU, in parsecs. c. Using the distance to M87 and your result above, find angular radius of the SMBH (Schwarzschild radius). Express it in arcseconds (") and micro- arcseconds (pas) d. Take the radius of Pluto's orbit equal to 40 AU and find its angular size (in micro-arcseconds, pas) at the distance of M87.For problems requiring calculations, show the equation you will use to solve, your work, your answer, and correct units. E F=ma 6. A woman has a mass of 30 kg on earth (9am.-9.8m/s*). What is her weight? 7. The same 30 kg woman weighs 245 N on Ceres. What is the acceleration due to gravity on Ceres? 8. A man in the "Strong Man" competition pushes a 1500 kg vehicle with an acceleration of 3 m/s2? How much force did the man exert on the vehicle? 9. Using your answer from the previous question, what force did the vehicle exert on the man?