Astro 210 Homework 1 Solutions - Astronomy 210 Spring 2011...

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Astronomy 210 Spring 2011 Homework Set #1: Solutions 1. SOHO and the Angular Speed of the Sun (a) As the Earth orbits the sun the apparent position of the sun against the starry background traces a closed path. Since the sun completes one orbit through the celestial sphere in Δ t = P = 365 . 24 days, and one orbit consists of Δ θ = 360 , the average angular speed is ω = Δ θ Δ t = 360 365 . 24 day = 0 . 98 / day 1 / day (1) (b) Compare images of the same star at diFerent times. Measure the length (on the screen or paper printout) Δ s that the star moves in “image units” of cm (or, egad! inches). We want to ±nd the angular displacement Δ θ this corresponds to. To do this, we note that the image gives the Sun’s disk diameter, which we know corresponds to an angular diameter θ = 0 . 5 . Measure the length D of the Sun’s diameter in “image units.” Now, all lengths in image units are proportional to the corresponding angular sizes. So we must have Δ θ θ = Δ s D (2) Thus we can solve for Δ θ = Δ s D θ (3) ²rom the timestamp on the images, you can also ±nd the elapsed time Δ t between the two images. Thus you can ±nd the star’s angular speed with respect to the Sun, which is the same as the Sun’s angular speed with respect to the celestial sphere: ω = Δ θ Δ t (4) If all has gone well, your should indeed ±nd a speed very close to 1 /day, or about 2 solar diameters a day. 2. (a) We see that the Earth is more than half illuminated, but not entirely, so the phase is gibbous.
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Astro 210 Homework 1 Solutions - Astronomy 210 Spring 2011...

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