Josh Cryer: 1 revision

2009-01-21T11:02:34Z

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John Creighton at 06:12, 31 July 2005

2005-07-31T06:12:44Z

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Orbital Intersections (Finding the ellipse)

Let the [[basis vectors]] b1 and b2 as defined above form the [[coordinate system]] of the plane so that:

[[Image:B1b1_basis_as_plane_coordinates.gif]] (1.17)

The equation of the ellipse is a two dimensional curve where the sum of the distance to each foci is constant for any two points on the plane. If we consider the two points located with the [[position vector]]s b, m the ellipse of the transfer orbit is given by:

[[Image:Ellips_foci_f_and_s_point_b_sum_d.gif]] (1.18)

[[Image:Ellips_foci_f_and_s_point_m_sum_d.gif]] (1.19)

note the norm of (b-f) is the distance between the position vectors b and f is given by:

[[Image:Norm_b_minus_f.gif]] (1.20)

Equations 1.18 says that f lies in a circle centered at b with radius d-||b-s||. Similarly equation (1.19) says f lies in a circle centered at m with radius d-||m-s||. Thus the second foci can be found by finding the [[intersection between two circles]]. The result is the distance from the center of the big circle along the line between the center of the two the point on the line that is perpendicular to where the circles intersect is given by:

[[Image:Intersect_two_circles_1.gif]] (1.21)

where R is the radius of the big circle r is the radius of the small circle and d is the distance between the center of each circle. The distance the point of intersection is from the line between the two circles is given by:

[[Image:Intersect_two_circles_2.gif]] (1.22)

==Previous Suggested Topic==
[[Orbital plane]]

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Orbital Intersections - Revision history

Josh Cryer: 1 revision

John Creighton at 06:12, 31 July 2005