11/15/99Norm Herr (sample file) Finding the distance using Parallax With your arm outstretched, hold...

11/15/99 Norm Herr (sample file)

Finding the distance using Parallax

• With your arm outstretched, hold up a finger so that, when viewed with your right eye, it is in line with something at the end of the other end of the room

• Now, keeping your finger steady, close your right eye and look at the finger with the left eye.

. Notice the apparent change in the position of your finger relative to the object at the end of the room.

11/15/99 Norm Herr (sample file)

. The position of your finger or of the object at the end of the room have not changed but, because you look from a different place, they seem to move relative to each other.

. This effect is called PARALLAX and it can be used to measure the distance to an object.

. It is fairly easy to demonstrate in the classroom how parallax can be used to measure how far away certain stars are.

11/15/99 Norm Herr (sample file)

Finding the distance to nearby stars using Parallax: 1

. Set up the apparatus as shown so that the centre of the meter stick is directly in front of a spot on a distant wall in the lab and the stick is parallel to the wall.

. View the spot through the straw. (Try to use relatively long straws if possible).

. Read the angle between the metre stick and the straw using the protractor, which is under the straw (see inset top left).

• Repeat this procedure at the other end of the metre stick.

• The two angles should be very similar. Add and divide by two to get the average. Subtract this from 90 to get the angle P in degrees.

11/15/99 Norm Herr (sample file)

• From the diagram we can see that, tan(P) = (0.5/distance). Therefore the distance = 0.5/tan(P)

• Fill in the value for P to find your answer. Now measure the distance from the metre stick to the spot.

• The two answers will be very close.• There are some obvious sources of error in this experiment, which

lead to incorrect answers.

11/15/99 Norm Herr (sample file)

Finding the distance to nearby stars using Parallax: 2

• This experiment illustrates the basic idea involved in stellar parallax.

• The first step is to identify a ‘nearby’ star by observing its parallax relative to the ‘fixed’ distant stars.

• It is then possible to find angle P and, knowing the radius of the Earth’s orbit around the Sun, to calculate the distance from the Earth to the nearby star.

11/15/99 Norm Herr (sample file)

• It is important to realise that the angles involved in this method are extremely small and so difficult to measure accurately.

• For example, the parallax angle to the nearest star (other than the Sun, of course), Proxima Centauri, is 0.772 seconds of arc.

• This is roughly the same as the angle subtended by an object of diameter 2 cm (e.g. a 5 cent coin) viewed from a distance of 5.3 km.