Imagine that we are ancients and we know that the earth is spherical because we have observed its shadow on the moon. In addition, we know that the earth rotates about its own axis because of the fact that we see day and night and the stars moving in circles around Polaris. After walking a distance of 50 km toward the north pole, we notice that the pole star is 1 degree higher in the sky. What is the circumference of our earth?

Today’s model of our solar system is

Find the vector that goes from ([a], [b], [c]) to ([d], [f], [g])   So that the software can check your answer, give the value in the “b” position below:

Retrograde motion of the planets is due to the fact that

The heliocentric model of our solar system was first suggested by

In the pic below, find the value of “b” if a = [a], and c = [c].  Round to 3 decimal places.

Which star is at the highest point in the sky when you located on the earth’s north pole?

Find the  missing part (B) to the equation below of the plane containing ([a], [b], [c]) , (4, -2, 6),  and (2, 3, 5).   A(x – [a])+ B(y – [b]) + C(z – [c]) = D

Find the arclength along the edge of a circle if the radius is [a] cm and the angle subtended is [b] o. Round your answer to 3 decimal places.

Which picture below would match the graph of: