# Elliptic Orbit

- Author:
- Myungsunn Ryu

F: the other focus of the planetary orbit.
S: Sun, or the center of gravitational force.
c: circle of radius = 2x(semimajor axis)
c' : hodograph of the velocity vector. generated by rotating the circle c 90 degrees clockwise(or anticlockwise, according to the assumed direction of orbital motion of the planet.) around S.
D: any point on c
d: perpendicular bisector of segment SD
P: location of the planet, intersection of line d and segment FD
The red ellipse: locus of P as D moves around c.
a: the line parallel to line d
B: intersection of c' and a
SB: line segment parallel to d, the tangent to the ellipse and its length proportional to the orbital speed.
F': center of the hodograph, generated by rotating F 90 degrees clockwise about S.
PP'(the blue arrow): parallel translation of SB with its tail onto P.
Drag D about the circle to see how the point P and the velocity vector moves.
Drag S out of the circle c to get the hyperbolic orbit, and try the tasks for the hyperbolic orbit as well.

- show that the line d is tangent to the locus of P.
- show that the locus of P is an ellipse.
- Show that the product of length SB and of SD is constant.
- Using Kepler's 2nd Law, show that SB is proportional to the orbital speed.
- Show that SB is parallel to the velocity.
- Show that the angles FSP and SF'B are equal.
- Explain physically why the angles FSP and SF'B are equal, using the Kepler's 2nd Law and Newtons Law of Gravitation(i.e. the inverse square law).