Astronomy Take-Home Final Problems
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 1000 solar masses, radius 10 parsec, and temperature of 10 K begin to collapse?
33
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The mass of the cloud is 2 × 10 kg, and the radius is 3.1 × 10 m. We use the formula for
escape speed
v
2GM
= 925 m/s, or 0.93 km/s
R
Half of this is 0.46 km/sec. The average molecular speed of hydrogen at 10 K is given by
 0.157 
√
10
 0.35 km/s.
2
This is less than half of the escape velocity, so the cloud can contract – just barely!
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 0.6-solarmass, 15000-km-diameter white dwarf.
30
The central mass is 0.6 times the mass of Sun, which is 1.19 ×10 kg, and the distance is
15,000,000 m. We use the formula for orbital speed:
v
GM
= 2,300,000 m/s or 2300 km/s
r
Some constants and formulas:
MassSun =2x1030 kg
1 parsec= 3,1x1016 m
G= 6,67x10-11 m3/kgs2
Orbital Speed: v=SQRT((GxM)/r)
Escape Speed: v= SQRT((2xGxM)/R)
Average molecular speed: 0,157xSQRT(Temperature/Molecular mass)
1 AU= 1,5x108 km
1
AST 341
Introduction to Astronomy Final
Name: BUSE GÜL KARABEKMEZ
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 900 solar masses, radius 11 parsec, and temperature of 11 K begin to collapse?
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 0.7-solarmass, 15100-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
2
AST 341
Introduction to Astronomy Final
Name: SEDEF SEMİHA KOL
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 905 solar masses, radius 12 parsec, and temperature of 12 K begin to collapse?
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 0.75-solarmass, 15200-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
3
AST 341
Introduction to Astronomy Final
Name: AİŞE NUR AĞBA
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 910 solar masses, radius 13 parsec, and temperature of 13 K begin to collapse?
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 0.8-solarmass, 15300-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
4
AST 341
Introduction to Astronomy Final
Name: NESLİHAN SEMİZ
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 915 solar masses, radius 14 parsec, and temperature of 14 K begin to collapse?
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 0.85-solarmass, 15400-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
5
AST 341
Introduction to Astronomy Final
Name: AKIN YARAŞIK
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 920 solar masses, radius 15 parsec, and temperature of 15 K begin to collapse?
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 0.9-solarmass, 15500-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
6
AST 341
Introduction to Astronomy Final
Name: NİYAZİ ÜÇBİLEK
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 925 solar masses, radius 16 parsec, and temperature of 16 K begin to collapse?
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 0.95-solarmass, 15600-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
7
AST 341
Introduction to Astronomy Final
Name: SÜREYYA EZGİ KADIOĞLU
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 930 solar masses, radius 17 parsec, and temperature of 17 K begin to collapse?7
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 1-solarmass, 15700-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
8
AST 341
Introduction to Astronomy Final
Name: CEMAL GÜLTEKİN
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 935 solar masses, radius 18 parsec, and temperature of 18 K begin to collapse?
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 1.05-solarmass, 15800-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
9
AST 443
Observational Astronomy Final
Name: GÜLDİLA GİZEM HEYFEGİL
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 940 solar masses, radius 19 parsec, and temperature of 19 K begin to collapse?
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 1.1-solarmass, 15900-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
10
AST 443
Observational Astronomy Final
Name: DERYA ECEVİT
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 945 solar masses, radius 20 parsec, and temperature of 20 K begin to collapse?
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 1.15-solarmass, 16000-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
11
AST 443
Observational Astronomy Final
Name: MERVE OCAK
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 950 solar masses, radius 21 parsec, and temperature of 21 K begin to collapse?
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 1.2-solarmass, 16100-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
12
AST 443
Observational Astronomy Final
Name: AYDAN KÜPELİ
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 955 solar masses, radius 22 parsec, and temperature of 22 K begin to collapse?
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 1.25-solarmass, 16200-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
13
AST 443
Observational Astronomy Final
Name: ÖZGE GÖKÇELİ
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 960 solar masses, radius 23 parsec, and temperature of 23 K begin to collapse?
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 1.3-solarmass, 16300-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
14
AST 443
Observational Astronomy Final
Name: BERK KELEŞ
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 965 solar masses, radius 24 parsec, and temperature of 24 K begin to collapse?
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 1.35-solarmass, 16400-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
15
AST 443
Observational Astronomy Final
Name: GÜROL SAKAOĞLU
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles
must be less than half the cloud’s escape speed. Will (spherical) molecular hydrogen (H2) cloud
of mass 970 solar masses, radius 25 parsec, and temperature of 25 K begin to collapse?
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 1.4-solarmass, 16500-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
16
AST 443
Observational Astronomy Final
Name: MERVE ÇATAK
Sign:……………..
1. In order for an interstellar gas cloud to contract, the average speed of its constituent
particles must be less than half the cloud’s escape speed. Will (spherical) molecular
hydrogen (H2) cloud of mass 975 solar masses, radius 26 parsec, and temperature of 26 K
begin to collapse?
Solution:
Answer:
Escape speed:…………………………………….km/s
Average molecular speed:…………………km/s
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 1.45solar-mass, 16600-km-diameter white dwarf.
Solution:
Answer:
Orbital speed:…………………………………….km/s
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