Activity 7
The Size of Space
Background Information
Parallax is the apparent shift in position of an object viewed from two different places. The line between these two viewing sites is called the baseline. Notice that the size of the shift depends on the direction of the baseline. If the baseline lies along the direction from the observer to the object there is no shift at all. (See drawing on p. 338.) If the baseline is perpendicular to that direction, the shift is maximized, as shown.
If the length of the baseline is known, and the angles between the baseline and the direction to the object are measured, the distance to the object can be found. One way to find this distance is to make a scale drawing, as the students do in this activity. Another way is to use trigonometry.
tan(A1) = x/D1
tan(A2) = x/D2
The angles and baseline are measured, the tangents are calculated and the distance is determined. Astronomers use parallax to measure distances within the solar system. The baseline can be provided by the rotation of the Earth. If the object, such as an asteroid, can be seen near dusk and dawn, then the baseline will be almost as large as the diameter of the Earth.
The asteroid is photographed against the background of stars. The angular shift of the asteroid, due to the rotation of the Earth, can be computed from the photographs. For objects outside the solar system, a longer baseline is needed. Measurements of the distance to nearby stars use the baseline of the Earth’s orbit. Observations are made six months apart. Again, the shift of the star being observed against the background star is measured from photographs taken at either end of the baseline. (See drawing on p. 337.)
The Size of Space
Background Information
Parallax is the apparent shift in position of an object viewed from two different places. The line between these two viewing sites is called the baseline. Notice that the size of the shift depends on the direction of the baseline. If the baseline lies along the direction from the observer to the object there is no shift at all. (See drawing on p. 338.) If the baseline is perpendicular to that direction, the shift is maximized, as shown.
If the length of the baseline is known, and the angles between the baseline and the direction to the object are measured, the distance to the object can be found. One way to find this distance is to make a scale drawing, as the students do in this activity. Another way is to use trigonometry.
tan(A1) = x/D1
tan(A2) = x/D2
The angles and baseline are measured, the tangents are calculated and the distance is determined. Astronomers use parallax to measure distances within the solar system. The baseline can be provided by the rotation of the Earth. If the object, such as an asteroid, can be seen near dusk and dawn, then the baseline will be almost as large as the diameter of the Earth.
The asteroid is photographed against the background of stars. The angular shift of the asteroid, due to the rotation of the Earth, can be computed from the photographs. For objects outside the solar system, a longer baseline is needed. Measurements of the distance to nearby stars use the baseline of the Earth’s orbit. Observations are made six months apart. Again, the shift of the star being observed against the background star is measured from photographs taken at either end of the baseline. (See drawing on p. 337.)