| 1. | At a particular opposition of Mars, the planet was simultaneously observed from two points on the equator, one where it was rising, the other where it was setting. If the positions on the celestial sphere differed by 41", what was the distance to Mars?
tan(41")=diameter of earth/answer=40000/pi/answer
answer=64,500,000km=0.43AU
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| 2. | What is the tangential velocity of a star having a proper motion of 0.01" and a parallax of 0.01"?
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| 3. | In 41 years a star is observed to move 1'22" with respect to a galaxy. What is the proper motion of the star?
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| 4. | If the parallax of the above star is 0.070" (usually written 0"070) what is the tangential component of the star's space motion?
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T=4.74x2/0.07=135.4km/s -- pretty speedy!
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| 5. | If the D1 line (lab wavelength 588.9950, ignore the D2 589.5924 component for this problem) appears at 588.9000nm what is the radial component of the space motion?
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Vr=300000(588.9-588.995)/588.995=-48.4km/s
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| 6. | Is the above star approaching or receding? What is the space speed of the star?
Approaching us at 48.4km/s, space speed is
v=sqrt(135.42+48.42)=143.8km/s
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| 7. | Alpha Crucis (a Cru) shines at magnitude V=+0.85 and b Cru shines at V=+1.28, how many times brighter is alpha than beta?
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0.43 magnitudes is a factor of 1.486 (close to 1.43?)
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| 8. | In fact, a Cru is a binary star, one having V=+1.39 and the other +1.90 so their brightness ratio is:
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0.51 magnitudes is a factor of 1.6
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| 9. | Now verify that the combined magnitude of the a Cen binary is about +0.8... Hint: get the brightness relative to zero magnitude, add them, then go back to magnitudes. Watch out, relative to V=0 the brightness is less than one!
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| 10. | If a star has a color index of B-V=+1.5, how many times brighter or fainter is the star in the visible than the blue?
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1.5 magnitudes is about a factor of four.
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| 11. | If a star has a bolometric correction of BC=2, what fraction of the light is visible?
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two magnitudes -- evidently 1/6.25 of the light is in the V band -- 16%.
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