A planetary nebula expanded in radius 0.2 arc seconds in 10 years. Doppler measurements show the nebula is expanding at a rate of 25 km/s. How far away is the nebula in parsecs? If the nebula now has a radius of 9 arc minutes, how long ago (in years) did the star explode? Part 1 of 3 We first need to determine what distance (in pc) the nebula expanded in parsecs during the time mentioned. Ad = V pc/s¹s So we first need to convert the rate into pc/s and the time into seconds: 1 pc Vpc/s = Vkm/s 3.09 x 10¹3 km 8.09e-13 pc/s (Tyr)(365 days/yr) (24 hrs/day)(3600 s/hr) 3.1536e8 3.15e+08 s pc/s = 8.09e-13 Ts Ts Ad = V pc Ad pc pc/s's = 2.551e-4 Part 2 of 3 Now we can use the small angle formula to calculate the distance (in pc). 2.06 x 105 D = 262.75 D = Ad- 0 0.000255 pc as 263 pc

A planetary nebula expanded in radius 0.2 arc seconds in 10 years. Doppler measurements show the nebula is expanding at a rate of 25 km/s. How far away is the nebula in parsecs? If the nebula now has a radius of 9 arc minutes, how long ago (in years) did the star explode? Part 1 of 3 We first need to determine what distance (in pc) the nebula expanded in parsecs during the time mentioned. Ad = V pc/s¹s So we first need to convert the rate into pc/s and the time into seconds: 1 pc Vpc/s = Vkm/s 3.09 x 10¹3 km 8.09e-13 pc/s (Tyr)(365 days/yr) (24 hrs/day)(3600 s/hr) 3.1536e8 3.15e+08 s pc/s = 8.09e-13 Ts Ts Ad = V pc Ad pc pc/s's = 2.551e-4 Part 2 of 3 Now we can use the small angle formula to calculate the distance (in pc). 2.06 x 105 D = 262.75 D = Ad- 0 0.000255 pc as 263 pc

Astronomy

1st Edition

ISBN:9781938168284

Author:Andrew Fraknoi; David Morrison; Sidney C. Wolff

Publisher:Andrew Fraknoi; David Morrison; Sidney C. Wolff

Chapter19: Celestial Distances

Section: Chapter Questions

Problem 32E: The best parallaxes obtained with Hipparcos have an accuracy of 0.001 arcsec. If you want to measure...

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Consider the following five kinds of objects: open cluster, giant molecular cloud, globular cluster, group of O and B stars, and planetary nebulae. A. Which occur only in spiral arms? B. Which occur only in the parts of the Galaxy other than the spiral arms? C. Which are thought to be very young? D. Which are thought to be very old? E. Which have the hottest stars?
The best parallaxes obtained with Hipparcos have an accuracy of 0.001 arcsec. If you want to measure the distance to a star with an accuracy of 10%, its parallax must be 10 times larger than the typical error. How far away can you obtain a distance that is accurate to 10% with Hipparcos data? The disk of our Galaxy is 100,000 light-years in diameter. What fraction of the diameter of the Galaxy’s disk is the distance for which we can measure accurate parallaxes?
Look at the four stages shown in Figure 21.8. In which stage(s) can we see the star in visible light? In infrared radiation? Figure 21.8 Formation of a Star. (a) Dense cores form within a molecular cloud. (b) A protostar with a surrounding disk of material forms at the center of a dense core, accumulating additional material from the molecular cloud through gravitational attraction. (c) A stellar wind breaks out but is confined by the disk to flow out along the two poles of the star. (d) Eventually, this wind sweeps away the cloud material and halts the accumulation of additional material, and a newly formed star, surrounded by a disk, becomes observable. These sketches are not drawn to the same scale. The diameter of a typical envelope that is supplying gas to the newly forming star is about 5000 AU. The typical diameter of the disk is about 100 AU or slightly larger than the diameter of the orbit of Pluto.
According to the text, a star must be hotter than about 25,000 K to produce an H II region. Both the hottest white dwarfs and main-sequence O stars have temperatures hotter than 25,000 K. Which type of star can ionize more hydrogen? Why?
The Large Magellanic Cloud has about one-tenth the number of stars found in our own Galaxy. Suppose the mix of high- and low-mass stars is exactly the same in both galaxies. Approximately how often does a supernova occur in the Large Magellanic Cloud?
A planetary nebula expanded in radius 0.3 arc seconds in 30 years. Doppler measurements show the nebula is expanding at a rate of 35 km/s. How far away is the nebula in parsecs? First, determine what distance the nebular expanded in parsecs during the time mentioned. Δd = vpc/sTs So we first need to convert the rate into pc/s and the time into seconds: vpc/s = vkm/s (1 pc / 3.09 x 1013km) vpc/s = ? Ts = (Tyr)(365 days/yr)(24 hrs/day)(3600 s/hr) Ts = ? s Δd= vpc/sTs Therefore, Δd = ? pc
. The radius of the nebula is about 0.401 light-years. The gas is expanding away from the star at a rate of about 37 kilometers/second . Considering that distance = velocity x time, calculate how long ago the gas left the star if its speed has been constant the whole time. Make sure you use consistent units for time, speed, and distance. Answer in years.
In a star of 1 solar mass (M☉), the core hydrogen burning phase, also known as the main sequence phase, lasts for approximately 10 billion years. Suppose there's a star of 15 solar masses (M☉). Stars of higher mass burn through their hydrogen at a faster rate, following an approximate relation that the lifetime of a star on the main sequence (T) is proportional to its mass (M) raised to the power of -2.5 (T ∝ M^-2.5). Calculate approximately how long this 15 solar mass star would remain in the main sequence phase, compared to the 1 solar mass star.
At the average density of a star-forming molecular cloud, about 900 atoms per cm3, determine how large a sphere you would need to encompass mass equal to that of the Sun? Enter the radius of this sphere in light-years. (HINTS: 900 atoms per cm3 corresponds to a density of 1.51×10-18kg/m^3; the mass of the Sun is 2×1030kg) (The volume of a sphere is 4/3 * π * R3) (my previous answer of 6.812 X 1015 was incorrect)
For a main sequence star with luminosity L, how many kilograms of hydrogen is being converted into helium per second? Use the formula that you derive to estimate the mass of hydrogen atoms that are converted into helium in the interior of the sun (LSun = 3.9 x 1026 W). (Note: the mass of a hydrogen atom is 1 mproton and the mass of a helium atom is 3.97 mproton. You need four hydrogen nuclei to form one helium nucleus.)
A star with spectral type A0 has a surface temperature of 9600 K and a radius of 2.2 RSun. How many times more luminous is this star than the Sun? (if it is less luminous enter a number less than one) This star has a mass of 3.3 MSun. Using the simple approximation that we made in class, what is the main sequence lifetime of this star? You may assume that the lifetime of the sun is 1010 yr. Compare this to the lifetime of a A0 star listed in Table 22.1 (computed using a more sophisticated approach). Is the value you calculated in the previous problem longer or shorter than what is reported in the table? (L for longer, S for shorter) (You only get one try at this problem.)
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