• Earth orbits the sun in the counterclockwise direction as seen from the north.
• Venus orbits the sun in the counterclockwise direction as seen from the north.
• Both orbits are approximately circles.
• Both orbits are approximately in the same plane.
• The radius of the earth's orbit is 1.0 AU. (Astronomical unit. This is the definition of the astronomical unit.)
• The radius of Venus's orbit is 0.7 AU.
• The period of the earth's orbit is 1 year. (This is the definition of one year.)
• The period of Venus's orbit is 0.6 year.

It is useful to plot the path of Venus taking the earth as fixed. To do this, first draw two arrows, the first from Earth to the sun, the second from the sun to Venus:

• The first arrow starts at the earth, has a fixed length of 1.0 AU, and rotates counterclockwise once per year.
• The second arrow starts at the end of the first arrow, has a fixed length of 0.7 AU, and rotates counterclockwise once every 0.6 year.

The result.

Here we see a small circle of radius 0.723 AU that revolves about the earth (at the center). The center of the small circle moves along a big circle of radius 1.00 AU once each year. Venus, represented as a red dot, revolves about the center of the small circle once every 0.615 years. After the point of closest approach, I have changed the red dot to a blue dot for clarity.

Connecting the dots gives the path of Venus relative to the earth.

Here is the path of Venus relative to the earth over 8 Earth years (which is 13 Venus years).

Here is what we get if we plot the position of Venus on the celestial sphere on successive days.

Prediction for what we see.

For a while we see Venus in the evening sky. Then it appears in the morning sky. Here is a picture of what we would see on successive nights one hour after sunset.