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Measuring the Orbital Speed of the PlanetsEarth ScienceIntroductionA Boeing 747 can fly 624 miles per hour. That’s pretty fast! Right now, Earth and other objects in the solar system are orbiting the Sun. But how fast are these objects moving? In this assignment, you will calculate the orbital speeds of objects in our solar system.Part A: Planetary PeriodsIn the 1600s, Johannes Kepler discovered three laws that govern the motion of objects around the sun. Kepler’s first law explains that objects travel in an elliptical, or oval-shaped, path around the sun. Kepler’s second law explains that an object travels faster in its orbit when it is closer to the Sun and slower in its orbit when it is farther away. In this activity, you will investigate Kepler’s third law, which describes the relationship between an object’s distance from the sun and the time it takes the object to complete an orbit around the sun.Click >>HERE<< to be taken to the Gizmo for this activity.Zoom out as far as possible.Set the speed to FAST.Click PLAY and observe the orbits of all the planets. Answer Observation question 1.Click RESET () and zoom in as far as possible.Set the speed to SLOW.Click PLAY to set the objects in motion. Click PAUSE when Earth() is aligned with either the grid’s X-axis or Y-axis. Note the starting time in the data table in Observation question 2.Click PLAY to set the objects in motion. Click PAUSE when Earth is in exactly the same position as it was when you recorded the starting time in step 6. Note the ending time in the data table in Observation question 2.Answer Observation questions 3-4.Click the “Additional data” display to find the orbital radius and period of each planet. Complete the first 2 empty columns of the chart in Observation question 5.Answer Observation question 6.Kepler discovered an interesting relationship between the cube of each planet’s orbital radius and the square of its period. Use a calculator to find the cube of each planet’s orbital radius and record these values in the R3 column of the data table in Observation question 5.Record the squares of the periods in the T2 column of the data table in Observation question 5.Answer Observation questions 7-8.Part B: Calculating Orbital SpeedEvery object moves at a different average speed in its orbit around the Sun. In this activity, you will use data collected from Part A to calculate the average orbital speeds of each planet and of Pluto.You should recall that the path an object takes around the Sun is an ellipse, and not a circle. However, to approximate the circumference, or length, of each orbit, you will treat the orbits as circles.Refer back to the data you collected in Part A. Copy the Mean Orbital Radius and Period data to the data table in Observation question 9.Using the mean orbital radius that you recorded for each planet, calculate the circumference of each planet’s orbit. Record it in the data table in Observation question 9.Note that circumference can be calculated using the formula C=2πrCalculate the average orbital speed (AU/year) for each planet and record it in the data table in Observation question 9.Note that this speed can be calculated using the formula Distance/time= Circumference/ periodTo give you a better perspective of how fast these orbital speeds really are, convert the orbital speeds you just calculated from AU/year to miles/hour using the following conversion factor: 1 AU/year =10604 miles/ hour. Record this data in the data table in Observation question 9.Answer Observation question 10.ObservationsWhat is the relationship between the speed of planets and their distance from the Sun?MonthDayYearStarting timeEnding timeUse the starting and ending times recorded above, what is Earth’s orbital period (in Earth years)?The distance units shown on the grid are called astronomical units (AU). Look at Earth’s orbit. How far is Earth from the Sun in AU?PlanetMean orbital radius (AU)Period (Earth years)R3T2MercuryVenusEarthMarsJupiterSaturnUranusNeptuneWhat happens to the period as the orbital radius increases?Look up Kepler’s 3rd Law and relate it back to your calculations of R3 and T2 for each planet. Did you prove the law? Explain why or why not.A new planet was discovered! It has an orbital radius of 45.529 AU. Based on Kepler’s 3rd law, what is the approximate period of its orbit? Show your work and include units with your answer for full credit!ObjectMean Orbital Radius (AU)Circumference of Orbit (AU)Period (Earth Years)Orbital Speed (AU/year)Orbital Speed (miles/hour)MercuryVenusEarthMarsJupiterSaturnUranusNeptuneHow does an increase in orbital radius affect average orbital speed? ................
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