In order to find the True Anomaly at the prediction time t, we will first need to find the Eccentric Anomaly E(t) using Kepler's Equation, then use the value of E(t) to determine the True Anomaly. Since the eccentricity for this particular orbit is nearly 0, the Mean Anomaly and the Eccentric Anomaly should be nearly equal to each other. Please be aware that Kepler's Equation can only be used with angles in terms of radians (not degrees)! M(t) = E(t) - esinE(t) For an easier time, use a Kepler's Equation solver from the Internet or a root-finding code. You should arrive at the following value: E(t) = 1.3778025 radians You can convert the determined Eccentric Anomaly to degrees using the following equation: E(t) (degrees) = [ E(t) (radians) ] [ 180^{o} / p ] E(t) = 78^{o}.94226825 You can now determine the True Anomaly using the equation below. Since the eccentricity for this orbit is nearly 0, the Mean Anomaly, Eccentric Anomaly and the True Anomaly should be similar (but not exactly equal) to each other. cosn(t) = (cosE(t)-e) / (1 - ecosE(t))
n(t)
= 78^{o}.95065818 |
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Step 4: Finding the True Anomaly Was Last Modified On June 25, 2012 |