lecture03 - Computation of ellipse quantities Ellipse...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Computation of ellipse quantities Ellipse quantities may be computed from alge- braic relations we have: b = a q 1 - e 2 is the semiminor axis (put x = 0 into Cartesian conic section equation and solve for y ), p = a (1 - e 2 ) is the semilatus rectum , and is the distance from the attracting focus to the orbit perpendicular to the major axis, r p = a (1 - e ) is the perigee geocentric dis- tance, r a = a (1 + e ) is the apogee geocentric dis- tance. (Check the last two yourself with the conic section formula). L. Healy – ENAE404 – Spring 2007 – Lecture 3 (Feb. 1) 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Semimajor axis in physical quantities Squaring eccentricity vector gives relation of the semimajor axis a to the speed v and the distance r : e 2 = 1 μ 2 r × h ) · r × h ) - 2 μr r · r × h ) + 1 | ˙ r × h | = vh because ˙ r h , and r · r × h ) = ( r × ˙ r ) · h = h 2 so e 2 = v 2 h 2 μ 2 - 2 h 2 μr + 1 1 - e 2 = h 2 μ ± 2 r - v 2 μ ! = p ± 2 r - v 2 μ ! p = 1 - e 2 2 r - v 2 μ a = ± 2 r - v 2 μ ! - 1 . Check the dimensions of the semimajor axis here. L. Healy – ENAE404 – Spring 2007 – Lecture 3 (Feb. 1) 2
Background image of page 2
Summary of orbital motion so far By starting with the law of universal gravita- tion, we get 3 conservation laws, and from those, we can get Kepler’s laws and orbit is in a plane, orbit is a conic section, There’s much else we can find out about the orbit – in fact everything except where the satellite is at a given time; “the orbit in time” problem. The orbital period can be solved but we’ll need Kepler’s equation to find the satel- lite’s position for a particular time anywhere along the orbit. For now let’s explore the implication of these two facts. L. Healy – ENAE404 – Spring 2007 – Lecture 3 (Feb. 1) 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The orbit in two dimensions Ref.: Sellers Sec. 5.1 We have looked at the orbit in its plane and un- derstand that there are three parameters that
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 13

lecture03 - Computation of ellipse quantities Ellipse...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online