Consider the Kepler equation of motion M = E − e sin (E) Where : M – mean anomaly E – eccentric anomaly of an elliptic orbit e – eccentricity To find E, we need to solve the nonlinear equation: f(E) = M + e sin(E ) − E = 0 Given e = 0.0167 (Earth’s eccentricity)and M = 1 (in radians) compute E using a. Newton-Raphson Method b. Secant Method All with Ea ≤ 0.00001 To choose appropriate initial approximations or an interval containing the root, plot the function f(E) and then determine graphically where it crosses the E-axis.
Consider the Kepler equation of motion M = E − e sin (E) Where : M – mean anomaly E – eccentric anomaly of an elliptic orbit e – eccentricity To find E, we need to solve the nonlinear equation: f(E) = M + e sin(E ) − E = 0 Given e = 0.0167 (Earth’s eccentricity)and M = 1 (in radians) compute E using a. Newton-Raphson Method b. Secant Method All with Ea ≤ 0.00001 To choose appropriate initial approximations or an interval containing the root, plot the function f(E) and then determine graphically where it crosses the E-axis.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.2: Trigonometric Equations
Problem 99E
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Consider the Kepler equation of motion M = E − e sin (E)
Where :
M – mean anomaly
E – eccentric anomaly of an elliptic orbit
e – eccentricity
To find E, we need to solve the nonlinear equation:
f(E) = M + e sin(E ) − E = 0
Given
e = 0.0167 (Earth’s eccentricity)and M = 1 (in radians) compute E using
a. Newton-Raphson Method
b. Secant Method
All with Ea ≤ 0.00001
To choose appropriate initial approximations or an interval containing the root, plot the function f(E) and then determine graphically where it crosses the E-axis.
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