Homeworks 1: Difference between revisions

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'''By Radius'''
'''By Radius'''
# Neutron = <math>3 quarks \;</math> (or <math>r \approx 1 fm \;</math> = <math>1.11 \times 10^{-15} m \;</math>) <ref>Which is larger, the proton or the neutron? http://www.physlink.com/education/AskExperts/ae570.cfm</ref> <ref>What are the sizes of protons neutrons and electrons? http://wiki.answers.com/Q/What_are_the_sizes_of_protons_neutrons_and_electrons</ref> <ref>On the Radius of the Neutron, Proton, Electron and the Atomic Nucleus http://www.wbabin.net/physics/yue.pdf</ref>
# Neutron = <math>3 quarks \;</math> (or <math>r \approx 1.11 \times 10^{-15} m \;</math>) <ref>Which is larger, the proton or the neutron? http://www.physlink.com/education/AskExperts/ae570.cfm</ref> <ref>What are the sizes of protons neutrons and electrons? http://wiki.answers.com/Q/What_are_the_sizes_of_protons_neutrons_and_electrons</ref> <ref>On the Radius of the Neutron, Proton, Electron and the Atomic Nucleus http://www.wbabin.net/physics/yue.pdf</ref>
# Atom = empirical atomic radius <math>r \approx 62 - 520 pm \;</math> = <math>0.62 - 5.20 \times 10^{-10} m \;</math> <ref>Information about Atomic Radii: http://www.webelements.com/</ref> <ref>J.C. Slater, ''J. Chem. Phys.'' 1964, '''41''', 3199.</ref>
# Atom's empirical atomic radius <math>\approx 0.62 - 5.20 \times 10^{-10} m \;</math> <ref>Information about Atomic Radii: http://www.webelements.com/</ref> <ref>J.C. Slater, ''J. Chem. Phys.'' 1964, '''41''', 3199.</ref>
# Biological Cell = <math>10 \mu m \;</math> = <math>1.00 \times 10^{-5}</math> <ref>The Biological Cell on Wikipedia http://en.wikipedia.org/wiki/Cell_(biology)</ref> <ref>Campbell, Neil A.; Brad Williamson; Robin J. Heyden (2006). [http://www.phschool.com/el_marketing.html Biology: Exploring Life]. Boston, Massachusetts: Pearson Prentice Hall. ISBN 0-13-250882-6</ref>
# Biological Cell <math>\approx 1.00 \times 10^{-5} m</math> <ref>The Biological Cell on Wikipedia http://en.wikipedia.org/wiki/Cell_(biology)</ref> <ref>Campbell, Neil A.; Brad Williamson; Robin J. Heyden (2006). [http://www.phschool.com/el_marketing.html Biology: Exploring Life]. Boston, Massachusetts: Pearson Prentice Hall. ISBN 0-13-250882-6</ref>
# Person = height = 4'11" = <math>1.50 m \;</math> <ref>[[User:KimberlyWynne|Kim Wynne]]'s height</ref>
# Human's height <math>\approx 1.50 m \;</math> <ref>[[User:KimberlyWynne|Kim Wynne]]'s height</ref>
# Neutron Star = <math>12 km \;</math> = <math>1.20 \times 10^4 m \;</math> <ref>http://en.wikipedia.org/wiki/Neutron_star</ref> <ref>Paweł Haensel, A Y Potekhin, D G Yakovlev (2007). [http://books.google.com/books?id=iIrj9nfHnesC&printsec=frontcover#PPA12,M1 Neutron Stars]. Springer. ISBN 0387335439. </ref>
# Neutron Star <math>\approx 1.20 \times 10^4 m \;</math> <ref>http://en.wikipedia.org/wiki/Neutron_star</ref> <ref>Paweł Haensel, A Y Potekhin, D G Yakovlev (2007). [http://books.google.com/books?id=iIrj9nfHnesC&printsec=frontcover#PPA12,M1 Neutron Stars]. Springer. ISBN 0387335439. </ref>
# Earth = radius of the Earth = <math>6378.1 km \;</math> = <math>6.38 \times 10^6 m \;</math> <ref>Google "radius of the Earth"</ref>
# Earth = <math>6.38 \times 10^6 m \;</math> <ref>Google "radius of the Earth"</ref>
# Sun = radius of the Sun = <math>695500 km \;</math> = <math>6.96 \times 10^8 m \;</math> <ref>Google "radius of the Sun"</ref>
# Sun = <math>6.96 \times 10^8 m \;</math> <ref>Google "radius of the Sun"</ref>
# Solar System = radius of the comet Oort Cloud's orbit = <math>7.5 \times 10^{12} km \;</math> = <math>7.50 \times 10^{15} m \;</math> <ref>http://curious.astro.cornell.edu/question.php?number=374</ref>
# Solar System  
# Galaxy = radius of most galaxies = <math>50000 ly \;</math> = <math>4.73 \times 10^{20} m \;</math> <ref>http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/001205a.html</ref>
## Radius of the farthest comet's orbit (Oort Cloud) = <math>7.50 \times 10^{15} m \;</math> <ref>http://curious.astro.cornell.edu/question.php?number=374</ref>
# Local Group of Galaxies = radius of Local Group = <math>5 \times 10^6 ly \;</math> = <math>4.73 \times 10^{22} m \;</math> <ref>http://www.universetoday.com/guide-to-space/galaxies/local-group/</ref>
## Distance from the Sun to Jupiter = <math>7.48 \times 10^{11} m</math> <ref>Lecture #2 - Slide 8</ref>
# Cluster of Galaxies = approximate size of most clusters = <math>5 Mpc \;</math> = <math>1.54 \times 10^{23} m</math> <ref>http://www.damtp.cam.ac.uk/user/gr/public/gal_lss.html</ref>
# Galaxy <math>\approx 5 \times 10^4 ly \;</math> = <math>4.73 \times 10^{20} m \;</math> <ref>http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/001205a.html</ref>
# Local Group of Galaxies <math>\approx 5 \times 10^6 ly \;</math> = <math>4.73 \times 10^{22} m \;</math> <ref>http://www.universetoday.com/guide-to-space/galaxies/local-group/</ref>
# Cluster of Galaxies <math>\approx 5 Mpc \;</math> = <math>1.54 \times 10^{23} m</math> <ref>http://www.damtp.cam.ac.uk/user/gr/public/gal_lss.html</ref>


'''By Volume'''
'''By Volume'''


To be Completed
# Neutron <math>V=(1 fm)^3=10^{-45} m^3 \;</math>
# Atom <math>V=(10^{-9} m)^3=10^{-27} m^3 \;</math>
# Biological cell<math>V=(10^{-6} m)^3=10^{-18} m^3 \;</math>
# Human <math>V=(2m)^3=8 m^3 \;</math>
# Neutron Star <math>V= \tfrac{4}{3} \pi (12 \times 10^3 m)^3=8\times 10^{10} m^3 \;</math>
# Earth <math>V=\tfrac{4}{3} \pi (6 \times 10^6 m)^3=10^{21} m^3 \;</math>
# Solar System <math>V=(4\times10^{12})^3=64 \times 10^{36} m^3 \;</math>
# Galaxy (contains many star systems)
# Local group of galaxies (contains many galaxies)
# Galaxy Cluster (contains many groups of groups of galaxies, larger than local group)


'''By Mass'''
'''By Mass'''


'''1.''' Neutron = 1.67492729×10^-27 kg  
# Neutron = <math>1.67492729\times10^{-27} \;</math> kg  
'''2.''' Atom = 1.67×10^−27 to 4.52×10^−25
# Atom = <math>1.67 \times 10^{−27} \;</math> to <math>4.52\times10^{−25} kg \;</math>
'''3.''' Biological cell = varies (eukaryotic cells are more massive than prokaryotic cells)  
# Biological cell = varies (eukaryotic cells are more massive than prokaryotic cells)  
'''4.''' Human = 76-83kg for males (average) and 54-64kg for females (average)  
# Human = <math>76^{-83} kg \;</math> for males (average) and <math>54-64kg \;</math> for females (average)  
'''5.''' Earth = 5.9736×10^24 kg  
# Earth = <math>5.9736 \times 10^{24} kg \;</math>
'''6.''' Sun = 1.9891×10^30 kg  
# Sun = <math>1.9891 \times 10^{30} kg \;</math>
'''7.''' Solar System = 1.991768x10^30 kg (excluding Asteroid Belt, Kuiper Belt, and comets)  
# Solar System = <math>1.991768 \times 10^{30} kg \;</math> (excluding Asteroid Belt, Kuiper Belt, and comets)  
'''8.''' Neutron star = 2.69x10^30 to 4.177x10^30 kg (1.35 to 2.1 Solar masses)  
# Neutron star = <math>2.69 \times 10^{30} \;</math> to <math>4.177 \times 10^{30} kg \;</math> (<math>1.35 \;</math> to <math>2.1 M_{\odot} \;</math>)  
'''9.''' Galaxy = varies (Milky Way is approximately 5.8x10^11 Solar masses)  
# Galaxy = varies (Milky Way is approximately <math>5.8 \times 10^{11} M_{\odot}\;</math> )  
'''10.''' Local Group = (1.29 ± 0.14)×10^12 Solar masses
# Local Group = <math>(1.29 \pm 0.14) \times 10^{12} M_{\odot} \;</math> 
'''11.''' Galactic cluster = varies; usually approximately 10^13 Solar masses
# Galactic cluster = varies; usually approximately <math>10^{13} M_{\odot}\;</math>


==Problem 2==
==Problem 2==
The nearest star outside the solar system is about 4 light years away.
'''The nearest star outside the solar system is about 4 light years away.'''
# How far away is the star in kilometers?
# '''How far away is the star in kilometers?'''
# Suppose you travel to the nearest star in a rocket ship moving at 100 km per hour (100 km/hr is
#: One light year is approximately <math>9.460730472 \times 10^{15} m</math>.
about 62 mi/hr, a typical automobile speed on a Florida highway). How many years will it take
#: Therefore, this star is approximately <math>3.784 \times 10^{13} km</math>.
you to get to the star?
# '''Suppose you travel to the nearest star in a rocket ship moving at 100 km per hour (100 km/hr is about 62 mi/hr, a typical automobile speed on a Florida highway). How many years will it take you to get to the star?'''
# Suppose you travel to the star at 10 km per second (the speed of a rocket in orbit around the Earth). How many years will it take you to get to the star?
#: Knowing the distance of this star in kilometers, one can find the time it takes to get there with <math>t = \tfrac{d}{v}</math>.
 
#: <math>t = \frac{3.784 \times 10^{13}km}{\tfrac{100km}{hr}} = 3.784 \times 10^{11} hrs</math>.   
1.  One light year is approximately 9.460730472 x 10^15 meters.  Therefore, this star is approximately
#: This equates to about 43,196,347 years!
    3.784 x 10^13 kilometers.
# '''Suppose you travel to the star at 10 km per second (the speed of a rocket in orbit around the Earth). How many years will it take you to get to the star?'''
 
#: Again, use <math>t = \tfrac{d}{v}</math>, but with time in seconds
2.  Knowing the distance of this star in kilometers, one can find the time it takes to get there with t = d/v.
#: <math>t = \frac{3.784 \times 10^{13}km}{10\tfrac{km}{s}} = 3.784 \times 10^{12} s</math>.
    t = (3.784 x 10^13km)/(100km/hr) = 3.784 x 10^11 hours.  This equates to about 43,196,347 years!
#: This equates to about 120,000 years!
 
3.  Again, use t = d/v, but with time in seconds.  t = (3.784 x 10^13km)/(10km/s) = 3.784 x 10^12 seconds.
    This equates to about 120,000 years!


==Problem 3==
==Problem 3==
Use the size of the Astronomical Unit in kilometers and the length of the year in seconds to calculate how fast the Earth moves in its orbit in kilometers/second.
'''Use the size of the Astronomical Unit in kilometers and the length of the year in seconds to calculate how fast the Earth moves in its orbit in kilometers/second.'''
 


The speed of Earth in its orbit around the sun can be determined from the total distance it travels in a certain time period.  For convenience, in one year, the Earth has completed one revolution about the sun (or the circumference of a circle with radius 1AU).
The speed of Earth in its orbit around the sun can be determined from the total distance it travels in a certain time period.  For convenience, in one year, the Earth has completed one revolution about the sun (or the circumference of a circle with radius 1AU).
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==Problem 4==
==Problem 4==
Describe the essential differences between the Ptolemaic, Copernican, and Keplerian descriptions
'''Describe the essential differences between the Ptolemaic, Copernican, and Keplerian descriptions
of planetary motion.
of planetary motion.'''


The Ptolemaic description of planetary motion was that of a geocentric solar system in which all planets and the sun orbit the earth. Ptolemy also described the retrograde motion of the planets and moon using epicycles.
The Ptolemaic description of planetary motion was that of a geocentric solar system in which all planets and the sun orbit the earth. Ptolemy also described the retrograde motion of the planets and moon using epicycles.


Copernicus introduced the heliocentric model of the solar system in which all plnets orbit the sun. Copernicus also explained that the apparent retrograde motion of the planets and moon is actually a result of the earth's motion.
Copernicus introduced the heliocentric model of the solar system in which all planets orbit the sun. Copernicus also explained that the apparent retrograde motion of the planets and moon is actually a result of the earth's motion.


Kepler maintained the heliocentric model of planetary motion and introduced that planets move in elliptical orbits about the sun with his idea of conic sections.
Kepler maintained the heliocentric model of planetary motion and introduced that planets move in elliptical orbits about the sun with his idea of conic sections.

Latest revision as of 10:50, 16 October 2009

Homeworks 1
Homeworks 1
Funny.jpg
About this Assignment
Topics Sizes
Algebra
Conversion
Solar Systems
Elliptical orbits
Chapters 1 - 2
Lectures 2 - 4

Homeworks 1 is the attempted solution to our second task[1] in the course Introduction to Astrophysics. This assignment is due on Wednesday 09/09/09 and was assigned on 09/01/09. Solutions were created by Group 1 (RyanT, KimW, SaraC, ZackM, TiaraD) to be completed by 09/11/09.

This assignment covers Chapter 1 and 2 in the book, Lectures 2 through 4. The topics in this assignment range from sizes, to solar systems, to why the orbits of the planets are elliptical.

Problem 1

List in order of increasing size and give the approximate size of the following objects: An atom, a biological cell, a cluster of galaxies, the Earth, a galaxy, the Local Group of galaxies, a neutron, a neutron star, a person, the Solar System, our sun. Note: you may have to look in other books besides your textbook to get all this information.

There are 3 ways to approach this problem: By radius, by volume, and by mass. 

This problem coincides with Lecture #2.
Sizes.jpg

By Radius

  1. Neutron = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3 quarks \;} (or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r \approx 1.11 \times 10^{-15} m \;} ) [2] [3] [4]
  2. Atom's empirical atomic radius Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \approx 0.62 - 5.20 \times 10^{-10} m \;} [5] [6]
  3. Biological Cell Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \approx 1.00 \times 10^{-5} m} [7] [8]
  4. Human's height Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \approx 1.50 m \;} [9]
  5. Neutron Star Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \approx 1.20 \times 10^4 m \;} [10] [11]
  6. Earth = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6.38 \times 10^6 m \;} [12]
  7. Sun = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6.96 \times 10^8 m \;} [13]
  8. Solar System
    1. Radius of the farthest comet's orbit (Oort Cloud) = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7.50 \times 10^{15} m \;} [14]
    2. Distance from the Sun to Jupiter = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7.48 \times 10^{11} m} [15]
  9. Galaxy Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \approx 5 \times 10^4 ly \;} = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4.73 \times 10^{20} m \;} [16]
  10. Local Group of Galaxies Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \approx 5 \times 10^6 ly \;} = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4.73 \times 10^{22} m \;} [17]
  11. Cluster of Galaxies Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \approx 5 Mpc \;} = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1.54 \times 10^{23} m} [18]

By Volume

  1. Neutron Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V=(1 fm)^3=10^{-45} m^3 \;}
  2. Atom Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V=(10^{-9} m)^3=10^{-27} m^3 \;}
  3. Biological cellFailed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V=(10^{-6} m)^3=10^{-18} m^3 \;}
  4. Human Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V=(2m)^3=8 m^3 \;}
  5. Neutron Star Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V= \tfrac{4}{3} \pi (12 \times 10^3 m)^3=8\times 10^{10} m^3 \;}
  6. Earth Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V=\tfrac{4}{3} \pi (6 \times 10^6 m)^3=10^{21} m^3 \;}
  7. Solar System Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V=(4\times10^{12})^3=64 \times 10^{36} m^3 \;}
  8. Galaxy (contains many star systems)
  9. Local group of galaxies (contains many galaxies)
  10. Galaxy Cluster (contains many groups of groups of galaxies, larger than local group)

By Mass

  1. Neutron = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1.67492729\times10^{-27} \;} kg
  2. Atom = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1.67 \times 10^{−27} \;} to Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4.52\times10^{−25} kg \;}
  3. Biological cell = varies (eukaryotic cells are more massive than prokaryotic cells)
  4. Human = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 76^{-83} kg \;} for males (average) and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 54-64kg \;} for females (average)
  5. Earth = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 5.9736 \times 10^{24} kg \;}
  6. Sun = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1.9891 \times 10^{30} kg \;}
  7. Solar System = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1.991768 \times 10^{30} kg \;} (excluding Asteroid Belt, Kuiper Belt, and comets)
  8. Neutron star = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2.69 \times 10^{30} \;} to Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4.177 \times 10^{30} kg \;} (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1.35 \;} to Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2.1 M_{\odot} \;} )
  9. Galaxy = varies (Milky Way is approximately Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 5.8 \times 10^{11} M_{\odot}\;} )
  10. Local Group = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (1.29 \pm 0.14) \times 10^{12} M_{\odot} \;}
  11. Galactic cluster = varies; usually approximately Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 10^{13} M_{\odot}\;}

Problem 2

The nearest star outside the solar system is about 4 light years away.

  1. How far away is the star in kilometers?
    One light year is approximately Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 9.460730472 \times 10^{15} m} .
    Therefore, this star is approximately Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3.784 \times 10^{13} km} .
  2. Suppose you travel to the nearest star in a rocket ship moving at 100 km per hour (100 km/hr is about 62 mi/hr, a typical automobile speed on a Florida highway). How many years will it take you to get to the star?
    Knowing the distance of this star in kilometers, one can find the time it takes to get there with Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t = \tfrac{d}{v}} .
    Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t = \frac{3.784 \times 10^{13}km}{\tfrac{100km}{hr}} = 3.784 \times 10^{11} hrs} .
    This equates to about 43,196,347 years!
  3. Suppose you travel to the star at 10 km per second (the speed of a rocket in orbit around the Earth). How many years will it take you to get to the star?
    Again, use Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t = \tfrac{d}{v}} , but with time in seconds
    Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t = \frac{3.784 \times 10^{13}km}{10\tfrac{km}{s}} = 3.784 \times 10^{12} s} .
    This equates to about 120,000 years!

Problem 3

Use the size of the Astronomical Unit in kilometers and the length of the year in seconds to calculate how fast the Earth moves in its orbit in kilometers/second.

The speed of Earth in its orbit around the sun can be determined from the total distance it travels in a certain time period. For convenience, in one year, the Earth has completed one revolution about the sun (or the circumference of a circle with radius 1AU).

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} |v| &=\frac{l}{t}\\ &=\frac{2\pi\times1AU}{1yr}\\ &=2\pi\frac{AU}{yr}\times\frac{1.5\times10^8km}{1AU}\times\frac{1yr}{365.25days}\times\frac{1day}{24hr}\times\frac{1hr}{3600s}\\ &=30\frac{km}{s}\\ \end{align} }

Therefore, the speed of Earth in its orbit is approximately 30km/s.

Problem 4

Describe the essential differences between the Ptolemaic, Copernican, and Keplerian descriptions of planetary motion.

The Ptolemaic description of planetary motion was that of a geocentric solar system in which all planets and the sun orbit the earth. Ptolemy also described the retrograde motion of the planets and moon using epicycles.

Copernicus introduced the heliocentric model of the solar system in which all planets orbit the sun. Copernicus also explained that the apparent retrograde motion of the planets and moon is actually a result of the earth's motion.

Kepler maintained the heliocentric model of planetary motion and introduced that planets move in elliptical orbits about the sun with his idea of conic sections.

Problem 5

Use Newton’s laws to show that the orbits of planets are ellipses.

Kepler's First Law is that the orbits of our planets are ellipses (with the sun at one focal point). However it does not explain why the planets move as they do in elliptical loops. Therefore, this question can be restated: Use Newton's laws to derive Kepler's First Law. 

This problem coincides with Chapter 2.3 Kepler's Laws Derived and Lecture #4.
Ellipticalorbit.jpg

where

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a \;} = semimajor axis
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b \;} = semiminor axis
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \textbf{r} \;} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \textbf{{r}'} \;} = distances to focal points
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \textbf{F} \;} and = focal points
= eccentricity
This problem is incomplete.

The Equation for an Ellipse is , and in polar coordinates

for

Conservation of Angular Momentum

Define Reduced Mass

Total Angular Momentum with respect to Reduced Mass

With reduced mass (and because of it), total angular momentum is constant.

Kepler's 1st Law

Notes

  1. ↑ Our first task was to register our PRS, visit the course web-page on Blackboard, look at the textbook, and write an equation for our wiki
  2. ↑ Which is larger, the proton or the neutron? http://www.physlink.com/education/AskExperts/ae570.cfm
  3. ↑ What are the sizes of protons neutrons and electrons? http://wiki.answers.com/Q/What_are_the_sizes_of_protons_neutrons_and_electrons
  4. ↑ On the Radius of the Neutron, Proton, Electron and the Atomic Nucleus http://www.wbabin.net/physics/yue.pdf
  5. ↑ Information about Atomic Radii: http://www.webelements.com/
  6. ↑ J.C. Slater, J. Chem. Phys. 1964, 41, 3199.
  7. ↑ The Biological Cell on Wikipedia http://en.wikipedia.org/wiki/Cell_(biology)
  8. ↑ Campbell, Neil A.; Brad Williamson; Robin J. Heyden (2006). Biology: Exploring Life. Boston, Massachusetts: Pearson Prentice Hall. ISBN 0-13-250882-6
  9. ↑ Kim Wynne's height
  10. ↑ http://en.wikipedia.org/wiki/Neutron_star
  11. ↑ Paweł Haensel, A Y Potekhin, D G Yakovlev (2007). Neutron Stars. Springer. ISBN 0387335439.
  12. ↑ Google "radius of the Earth"
  13. ↑ Google "radius of the Sun"
  14. ↑ http://curious.astro.cornell.edu/question.php?number=374
  15. ↑ Lecture #2 - Slide 8
  16. ↑ http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/001205a.html
  17. ↑ http://www.universetoday.com/guide-to-space/galaxies/local-group/
  18. ↑ http://www.damtp.cam.ac.uk/user/gr/public/gal_lss.html

References

  • B.W. Carroll & D. A. Ostlie (2007). An Introduction to Modern Astrophysics (Chapter 2). Addison Wesley. ISBN 0-8053-0402-9
  • Lecture #2
  • Lecture #3
  • Lecture #4
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