Elliptical Orbit

perigee

moon The moon travels about Earth in an elliptical orbit with Earth at one focus. Find the greatest and smallest distances (the apogee and perigee) from Earth to the moon.earth

apogee

768,800 km

767,640 km

2a 768,800

a 384,400

2b 767,640 820,383b

c 3844002 3838202 21,108

384,40021,108 405,508 km

perigee 384,400 21,108363,292 km

Elliptical Orbit

perigee

Sputnik I The first artificial satellite to orbit earth was Sputnik I. Its orbit was elliptical with the center of Earth at one focus. Find the apogee and perigee from Earth’s center to the satellite. Find the least distance and the greatest distance of the satellite to Earth’s surface in this orbit. Earth has a radius of 6378 km.

earth

apogee

13,906 km

13,887 km

2a 13,906

a 6,953

2b 13,887

b 6,943.5

c 69532 6943.52 363.3

6953 363.37316.3 km

perigee 6953 363.36589.7 km

6378 938.3 km

6378 211.7 km

Find the standard form of the equation of the ellipse with center at the origin.

28. Foci: (±2,0); major axis of length 6

36. Center: (2, –1) vertex: (2,1/2); minor axis of length 2

Center (0,6)8a

Vertices: 6,8,6,8

5,0,17,0

11b

6412122 abc

55.757

Foci: ckh , 55.1,0,55.13,0

Major Axis: 222 b

Minor Axis: 162 a

Co-Vertices:

Circles

Standard Form