11-12-08LectPHY2048

11-12-08LectPHY2048 - Elliptical orbits The circular orbit...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
The circular orbit of satellites we discussed last time is actually the limit of a more general type of orbit that takes the form of an ellipse . Elliptical orbits The ellipse is a curve that has two foci, and , that obeys the rule that for every point on the curve the sum of the distances to the two foci is a constant. F F The body of mass M about which the satellite (mass m << M) orbits is at one of the foci , F , while the other at , , is empty. F
Background image of page 1

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

View Full DocumentRight Arrow Icon
The distance from the center of the ellipse to the furthest point of the orbit is the semi-major axis labeled: a . The distance from the center of the ellipse to the foci is labeled ea where e is a dimensionless number from zero to 1, called the eccentricity , that characterizes how much the orbit deviates from a circle. If e = 0 , ea=0 , the foci coincide, the orbit is a perfect circle and a = r . The eccentricity of earth’s orbit about the sun is small ( e = 0.0167 ) while that of Pluto’s is so much greater ( e = 0.248 ) that at times Pluto's distance to the sun is smaller than Neptune's.
Background image of page 2
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 distance from the sun to the point of closest approach of a planet is called the perihelion , R p , and the furthest distance is called the aphelion R a . (These have nothing to do with the seasons on earth). The angular momentum of the orbiting body must be conserved so, Lr pr m v s i n = ×= φ Since r shrinks on going from the aphelion to the perihelion the orbital speed v must increase for the angular momentum to remain constant. This speed is maximum at the perihelion and minimum at the aphelion .
Background image of page 4
At the perihelion and aphelion φ = 90 o so p pa a LR m v R m v == Lr m v s i n p a Rv = a p a p R vv R = Since
Background image of page 5

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

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 21

11-12-08LectPHY2048 - Elliptical orbits The circular orbit...

This preview shows document pages 1 - 6. Sign up to view the full document.

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