Download 1. What is parallax? What unit is it measured in? 1a. Parallax is the

1. What is parallax? What unit is it measured in?
1a. Parallax is the change in the direction to a star due to the Earth’s motion around the Sun. Its usually
measured in arcseconds.
2. Draw a labelled diagram showing a star with a 1 arcsecond parallax. What about a star with a 2
arcsecond parallax?
2a. See class.
3. How many arcseconds in a degree? How many arcseconds in 360 degrees?
3a. 60 × 60 arcseconds in a degree. 60 × 60 × 360 arcseconds in 360 degrees.
4. Stars A, B, C, D have parallaxes of 2, 1, 0.5, 0.1 arcseconds. What are their distances? Get the units
of this distance right.
4a. The distances are respectively, 0.5, 1, 2 and 10 parsecs respectively.
5. So if I halve the parallax angle of a star, what happens to its distance?
5a. It doubles.
6. If I move a star to 4 times as far away, what happens to its parallax angle? How about if this star is
moved to 10 times as far away - what happens to its parallax angle?
6a. The parallax angle decreases by a factor of four. If its moved 10 times as far away, the parallax angle
gets smaller by a factor of 10.
7. A star is a distance 1 parsec away. What is its parallax angle?
7a. Its 1 arcsecond.
8. The following questions relate the brightness of an object to its intrinsic brightness or luminosity.
9. Define the luminosity of an object - what units is it measured in? Whats the luminosity of the Sun?
9a. The Luminosity is the total energy radiated by the Sun per second: Units are Watts which are
Joules/second. The SUn hasa luminosity of about 1026 watts.
10. How is brightness different from luminosity?
10a. Brightness involves distance and luminosity. Luminosity is independent of distance.
11. Write down the formula relating brightness, luminosity and distance?
11a. B = L/4πd2 .
12. Does a 100W light bulb still emit 100W if its 1m away and if its 10m away and if its one million m
away?
12a. Yes.
13. Does the luminosity of a star vary with its distance from us?
13a. No.
14. Does a 100W light bulb look the same if its 1m away, 10m away or one million miles away?
14a. No, it looks fainter the further away it is.
15. Does the brightness of a star vary with its distance from us?
15a. Yes - the inverse square law.
15. Star X is 100 parsecs from Earth. Its moved to a distance of 200 parsecs. What happens to its luminosity
and its brightness?
15a. Luminosity stays constant, Brightness goes down by a factor of four.
16. Now do the same question but star X is moved to distances 300, 400, 500 and 600 parsecs from Earth.
What happens to its luminosity and brightness?
16a. Always luminosity is constant, but brioghtness goes down by factorys of 9, 16, 26 and 36 respectively.
17. This is the inverse square law of light and is one of the most fundamental concepts in science. This is why
things get fainter the further away they are. Now Ill try and lead you onto a geometric understanding
of this. You need to know that the surface area of a sphere is 4 × 3.141 × (sphere0 sradius)2 .
18. So whats the surface area of a sphere of radius 1m, 2m, 3m, 4m? What happens when you double, triple
and quadruple the radius of a sphere?
18a. The surface area is, respectively, 4π, 4π × 4, 4π × 9, 4π × 16. The surface area of the sphere is increased
by a factor of 4, 9 and 16 respectively.
19. A star emits 1000 photons per second. Suppose these photons travel at 1m/s. So 1 second later the
same 1000 photons are on a sphere of radius 1m. How about 2 seconds later and 3 seconds later?
19a. 2 seconds later they are on a sphere of radius 2m and 3 seconds later they are on a sphere of radius 3m.
20. As time goes on are these 1000 photons more or less spread out on this imaginary sphere?
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20a. They are more spread out.
21. So if you had a photon collector - a bucket of area 1m2 , on which sphere would it collect the most
photons - on the 1m, 2m or 3m sphere? Hence where would the object look brightest - on the 1m, 2m
or 3m sphere? On which sphere would the object look the faintest - on the 1m, 2m or 3m sphere?
21a. On the 1m sphere - it would look faintest on the 3m sphere.
22. Stars A, B, C, D, E, F have apparent magnitudes 0, -1, 3, 4, 2.5 and 2 respectively. Put them in order
of how bright they appear in the sky starting with the least bright.
22a. D, C, E, F, A, B.
23. Stars A, B, C, D, E have absolute magnitudes -2, 0, 3, 5, 1 respectively. Put them in order of how
bright they appear in the sky starting with the least bright.
23a. Cant do this since we dont know their distances.
24. Star A’s absolute magnitude is 2.8. Its moved 10 times as far away. What happens to its luminosity
and absolute magnitude?
24a. Nothing.
25. A star has a parallax angle of 1 second of arc. Would the parallax angle of this star be be greater, less
or the same if veiwed from a) Venus and b) Jupiter?
25a. From Venus, parallax angle gets smaller. From Jupiter parallax angle gets bigger.
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