# The Distance to Venus

Tonight you will determine the location of Venus in its orbit around the Sun and the distance between the Earth and Venus.

#### Part I: Naked-eye observation

Your first task is to go outside, face the western horizon, and make a sketch. Your sketch should include the following features, all drawn in their proper places:

• the western horizon
• Venus
• your best guess at the location of the sun below the horizon; that is, its altitude (which will be negative) and its azimuth
• arrows showing North and South

Use your sketch to estimate the angular distance between Venus and the Sun. You may use the rough rule that a fist held at arm's length subtends about 10 degrees, or you may devise some other means to measure angular distance. Describe the method you use, and state clearly your estimate of the angular distance in degrees.

#### Part II: Telescopic observations of Venus

Each person in the class must make a sketch of Venus. Groups should discuss their sketches and come to a consensus.

Your next job requires a telescope. You must use the same telescope and same eyepiece to make the observation. Your goal is to draw the shape of Venus: is it a disk, a crescent, or something in between?

Point the telescope at Venus and focus carefully. Draw a picture of Venus, using the circular frame of the picture to denote the edges of the field of view. Try very carefully to depict the shape of the visible portion of the planet.

#### Part III: Analysis

1. The shape of the lit portion of Venus depends on its position relative to the Earth. In the diagram below, draw a picture which shows the appearance of Venus at points A, B, C and D, as seen from the Earth.

2. Based on the appearance of Venus in your picture, indicate in the diagram where Venus must be right now. Explain your reasoning.

3. You measured the angle between the Sun and Venus earlier. That angle appears in your diagram. Label it and give its size, in degrees.

4. The Earth's orbit has a radius of R(Earth) = 150 million km. Venus' orbit has a radius of about R(Venus) = 108 million km. Use these values and your diagram to figure out the distance between the Earth and Venus, right now.

#### Part IV: Evaluation

Use the SkyMap Pro program to check the the actual distance from the Earth to Venus. How close was your value? Can you explain which step in your observations and calculations is responsible for most of any error?