Consider Kepler's equation regarding planetary orbits, given as M = E e sin(E), where M is the mean anomaly, E is the eccentric anomaly, and e measures eccentricity. Find the eccentric anomaly E when 7 and the eccentricity of the orbit e = 0.37. Use Newton's method with initial approximation T the mean anomaly M = Xo = 2 to find x2, rounded to the nearest thousandth. Provide your answer below: x₂ ≈
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- Use your calculator to determine ( √ 6 )3 to three significant figures in two ways. Find √6 to four significant figures; then cube this number and round to three significant figures. Find √6 to to three significant figures; then cube this number and round to three significant figures. Which answer is more accurate? the first or second?Langleyville (43 degrees S, 77.6 degrees w) and Cajun Country (25 degrees s, 77.5 degrees w) have almost the same longitude, which means that they are roughly due north-south of each other. Set up all the work to find the approximate distance in miles between the cities assuming the radius of the earth is 4000 miles.Calculate the following and express the answer in the proper number of significant figures: (5.245x0.03x9.0023)/(4.076x0.029x42.3)=
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- Using your values for 7, calculate the average period Ibar (I) and its standard error. How does the error on the average period /bar (T) compares to the errors on the periods, I? What can you do to reduce the uncertainty on /bar (T)? What can you do to reduce the uncertainty on 7 ? Peried Trial T AT 4 141 $ 10.69 +α-0.5 2 10.60 + or -0.5 2 10.40 +α-0.5 10.43 +α-0.5 S 10.37 + or -0.5 Using your values for T, calculate the average period 7 and its standard error How does the error on the garage period compares to the errors on the periods, 7? What can you do to reduce the uncertainty on 7? What can you do to reduce the uncertainty on T7The radius of circle has been measured as r = (4.19 ± 0.3) cm. Calculate the uncertainty δA (in cm²) of its area (A = πr²). Enter the number only, without unit.The radius of a circle is measured to be (13.6 ± 0.3) m. Calculate each of the following and give the uncertainty in each value. (a) the area of the circle m² ± (b) the circumference of the circle m t m² m