Exercises

We have included a Modellus model of a simple binary system. To run it you can download a freeware version of Modellus here (1.4mb file).

Open the Modellus model and press the 'run' button.

This model of a simple binary system is initially set with the yellow sun as 8 solar masses and the red sun as 5 solar masses.

1. Try making the yellow sun more massive (using the slider control on he left). What changes?

2. Now try making the red sun less massive. Can you see the effect more clearly now? If the yellow sun was even more massive, then it would hardly appear to 'wobble' at all. Then the model would look like a planet (e.g. the earth) orbiting a star (e.g. the sun). This is always true - masses always affect each other, but the bigger the difference between them, the less noticeable the effect on the larger mass.

3. Try making the two suns equal in mass. Now they orbit each other about a common centre. This is a bit like two ice-skaters spinning each other around on the ice. Can you think of any other examples of things spinning each other around?

4. Try increasing the separation between the two suns using the top slider control. When the masses are different, you can see the difference between the radii of their orbits even more clearly.

5. If one star is much brighter than the other then from a long distance away you would probably only be able to see the brighter one, but you might be able to see that it 'wobbles'. Try reducing the separation as far as it will go and see what happens. Wobbles like this can tell astronomers a lot about what else might be close to a distant star, even when they can't see it.

Some other questions:

If Castor is about 50 light years away, that means that the light we see from it left the system 50 years ago. A light year is approximately 1016 metres (1 with 16 zeros after it!)

6. How many metres are there in a light day?

7. The sun is about 8 light minutes away from us. How far is that in metres?

8. The average distance from the earth to the sun is called an Astronomical Unit (AU). Castor Ba is only 0.03 AU from Bb. What is this distance in metres? (You'll need the answer to the last question).

9. What is the total distance that one of these stars travels in a single orbit? (This orbit is almost a circle, which makes things easier!)

10. If each orbit takes 2.93 earth days, how fast is this star travelling?




ANSWERS:?
1. The yellow sun moves in a smaller orbit
2. ---
3. An Olympic shot-putter is a good example; the shot travels round in a circle as the shot-putter spins it, but he (or she) spins round in a circle too (a smaller one).
4. ---
5. ---
6. 6.2.7 x 1013 m (27,000,000,000,000m)
7. 1.5 x 1011 m (150,000,000,000m)
8. 4.5 x 109 m (4.5 million km)
9. 1.4 x 1010 m (14,000,000,000m)
10. 56,000 m/s (56 km/s)

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