The earth T moves on an elliptical path f. The Moon X, moves also in an elliptical path m, whose one focus is

the earth. As X moves, the ellipse m rotates also about T. Thus it results a complex absolute movement of the

moon. We can trace the trajectory of X by attaching a pen to it. Part of the trajectory is shown (red).

Construction: (You see the names by clicking on the white space while holding down the SHIFT key)

1) First the ellipse f, through [Curves\Ellipse\Ellips(2 foci+pt)] tool. Foci at L, M, point at N.

2) Set a point P on the ellipse [Ctrl+E] to select the tool, click next to ellipse holding SHIFT-key down.

3) Create a motor, by clicking on the motor button on the upper-right toolbar.

4) Set moving point on f, starting at P: Right click on the motor, select [ Moving] , click at P, then click at the motor. This action creates a point T, initially identified with P. To distinguish from it, you

must move it a little further from P. Press the green button of the motor, then after a while press it again to stop.

5) Create a point R, with fixed relative position w.r. to the moving T. For this select from the context-menu

of the motor the item [Fixed] . Then click at T, then click at R.

6) Create a point S rotating about T, on the circle defined by the moving T(center) and R(pass). For this, select

from motor's context menu the item [Moving] and click at R and the motor.

7) S is initially identified with R, move it a little further by starting/stopping the motor, as in step-4.

8) T and S will be used as foci of the moving ellipse m, whose another point is V. We want an ellipse rotating about T (one focus of m) but preserving its shape. For this we construct a triangle j and addapt it

by similarity to the segment TS: Construct triangle j. Select the tool [Shape-Tools\Polygon tools\Polygon Compasses], click on one side of j and then at T and S. This defines m(TSV).

8) Using the same tool as in step-1, click three times, respectively, next to the points T,S,V. This sets the ellipse m.

9) Start/Stop the motor to see how nice the ellipse moves.

10) Now stop the movement and doing the same as in step-2, put a point W on the ellipse m.

11) Create a moving point point X on m, doing the same as in step-4. Start/stop the motor to see the movement.

12) Attach a pen to the point X. Start the motor. While the system moves, press the F2 key to trace the trajectory of X.

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