Casio fx-CG10 Advanced Operation Manual page 102

Sample Solution—Earth's Revolution
a. Set up an axis system that can describe the Earth's revolution about the Sun
using the center of the major axis of the ellipse as the origin. What are the
coordinates of the Earth at its perihelion and aphelion?
The total distance along the major axis is 2A. We'll find the sum of the
distance from the earth to the Sun at both the perihelion and aphelion. This
will give us the length of the entire major axis and by dividing by 2, we'll have
the value of A.
In the RUN menu, enter the values, using the
this can help us avoid potential mistakes with inputting the correct
number of 0's.
Consequently, A is 1.495 x 10
8
1.495 x 10 km and at the aphelion, it would be at 1.495 x 10
b. What are the coordinates of the Sun?
We will assume we are orienting the ellipse with the sun at the left focus. The
Sun is located 1.47 x 10
the left of the aphelion. Though we need do only one of the calculations, for
confirmation, we do both calculations as shown.
Fostering Advanced Algebraic Thinking with Casio Technology
8
km. At the perihelion, the Earth would be at -
8
km to the right of the perihelion and 1.52 x 10
key as shown below;
8
km.
8
km to