Example: Finding the Equation of an Elliptical Orbit Given Distances of 20 AU and 50 AU
Consider a planet moving in an elliptical orbit with the sun at one focus. The closest the planet gets to the sun (perihelion) is approximately 20 AU and the furthest (aphelion) is approximately 50 AU. Centering the elliptical orbit at the origin (0, 0) along the x-axis, the total length of the major axis is the sum of the closest and furthest distances: 20 + 50 = 70 AU. This gives a semi-major axis of AU, placing the vertices at and (35, 0) and meaning . Since the closest distance is , the focal distance is AU, placing the sun at the focus (15, 0). The value of is determined using the relation . Substituting the known values yields . Substituting and into the standard equation produces the equation of the orbit: .
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Example: Finding the Equation of an Elliptical Orbit Given Distances of AU and AU
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Example: Finding the Equation of an Elliptical Orbit Given Distances of 20 AU and 50 AU
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Example: Finding the Equation of an Elliptical Orbit Given Distances of 20 AU and 50 AU
Learn After
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