Dr. Robert Roseberry: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=114945
en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSun, 16 May 2021 06:19:11 GMTSun, 16 May 2021 06:19:11 GMTNew applications published by Dr. Robert Roseberryhttps://www.maplesoft.com/images/Application_center_hp.jpgDr. Robert Roseberry: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=114945
Calculating the Zeeman Effect
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The Ap star BD+0°4535 has a powerful magnetic field of 2.1 T. Calculate the wavelengths of the H[alpha]
line caused by Zeeman splitting.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Calculating the Zeeman Effect" style="max-width: 25%;" align="left"/>The Ap star BD+0°4535 has a powerful magnetic field of 2.1 T. Calculate the wavelengths of the H[alpha]
line caused by Zeeman splitting.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154311&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryThe Sun
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For the Sun, calculate the (A) central pressure, (B) central temperature, (C) pressure scale height, (D) adiabatic sound speed for a monatomic gas, and (E) the adiabatic convection by Mixing-length Theory<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="The Sun" style="max-width: 25%;" align="left"/>For the Sun, calculate the (A) central pressure, (B) central temperature, (C) pressure scale height, (D) adiabatic sound speed for a monatomic gas, and (E) the adiabatic convection by Mixing-length Theory<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154310&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryGraphing the Planck Function
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Make a plot of the Planck function for temperatures of 2000 K, 3000 K, 4000 K, 5000 K, 6000K, and 7000 K<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Graphing the Planck Function" style="max-width: 25%;" align="left"/>Make a plot of the Planck function for temperatures of 2000 K, 3000 K, 4000 K, 5000 K, 6000K, and 7000 K<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154309&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberrySirius A
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Sirius A (Alpha Canis Majoris) is close enough to Earth for accurate parallax measurement of its distance. This knowledge enables an accurate determination of its luminosity. Calculate its (A) mass, (B) radius, and (C) effective temperature, assuming (correctly) that it is a Main Sequence star with mass near that of the Sun.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Sirius A" style="max-width: 25%;" align="left"/>Sirius A (Alpha Canis Majoris) is close enough to Earth for accurate parallax measurement of its distance. This knowledge enables an accurate determination of its luminosity. Calculate its (A) mass, (B) radius, and (C) effective temperature, assuming (correctly) that it is a Main Sequence star with mass near that of the Sun.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154308&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryCalculating and Graphing the Bremsstrahlung Emission Over All Frequencies for the Orion Nebula
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Calculate and graph the bremsstrahlung emission over all frequencies for the Orion Nebula.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Calculating and Graphing the Bremsstrahlung Emission Over All Frequencies for the Orion Nebula" style="max-width: 25%;" align="left"/>Calculate and graph the bremsstrahlung emission over all frequencies for the Orion Nebula.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154307&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryRadio-Band and B-Band Luminosity and Brightness of Galaxy NGC 5236
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Compare the radio and B-band intensity with the radio and B-band luminosity of the galaxy NGC 5236.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Radio-Band and B-Band Luminosity and Brightness of Galaxy NGC 5236" style="max-width: 25%;" align="left"/>Compare the radio and B-band intensity with the radio and B-band luminosity of the galaxy NGC 5236.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154306&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryFinding the Mass of Sagittarius A* by Measuring the Orbit of S2
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From data describing the orbit of the star S2 around the black hole at the centre of the Galaxy, Sagittarius A*, calculate the black hole's mass in solar mass units. The period (P) of S2 is 15.559 years; the orbital eccentricity (e) is 0.88; and the parigalacticon distance (d) is 1.835 * 1013 m.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Finding the Mass of Sagittarius A* by Measuring the Orbit of S2" style="max-width: 25%;" align="left"/>From data describing the orbit of the star S2 around the black hole at the centre of the Galaxy, Sagittarius A*, calculate the black hole's mass in solar mass units. The period (P) of S2 is 15.559 years; the orbital eccentricity (e) is 0.88; and the parigalacticon distance (d) is 1.835 * 1013 m.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154337&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryThe Moving-Cluster Method: The Hyades
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The moving-cluster method can be used to find the appoximate distance to relatively nearby star clusters. Use the moving-cluster method with the data given below to estimate the distance to the Hyades open cluster.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="The Moving-Cluster Method: The Hyades" style="max-width: 25%;" align="left"/>The moving-cluster method can be used to find the appoximate distance to relatively nearby star clusters. Use the moving-cluster method with the data given below to estimate the distance to the Hyades open cluster.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154336&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryCalculating the Power Output of a Radio Galaxy
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The Effelsberg radio telescope, with a diameter of 100 m., was used by Lara et al. (2000) to observe the giant radio galaxy 8C 0821+695 at a Hubble distance of z = 0.538 in a radio band centred on 4.85 GHz with a bandwidth of 34.5 MHz. The telescope has a reception sensitivity in this band of 55% (Reich, 1997).<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Calculating the Power Output of a Radio Galaxy" style="max-width: 25%;" align="left"/>The Effelsberg radio telescope, with a diameter of 100 m., was used by Lara et al. (2000) to observe the giant radio galaxy 8C 0821+695 at a Hubble distance of z = 0.538 in a radio band centred on 4.85 GHz with a bandwidth of 34.5 MHz. The telescope has a reception sensitivity in this band of 55% (Reich, 1997).<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154335&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryQuasar j2348-3054
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The quasar j2348-3054 is one of the most distant objects in the visible Universe. Use the given data to calculate its (1) z-distance, (2) recession velocity, (3) distance in megaparsecs and light-years, (4) mass, and (5) absolute magnitude.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Quasar j2348-3054" style="max-width: 25%;" align="left"/>The quasar j2348-3054 is one of the most distant objects in the visible Universe. Use the given data to calculate its (1) z-distance, (2) recession velocity, (3) distance in megaparsecs and light-years, (4) mass, and (5) absolute magnitude.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154334&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryDark Matter: Coma Cluster
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This worksheet makes use of data about the huge Coma cluster (Abell 1656) of more than 1000 galaxies (Rowe 2010) at a distance of approximately 92 Mpc<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Dark Matter: Coma Cluster" style="max-width: 25%;" align="left"/>This worksheet makes use of data about the huge Coma cluster (Abell 1656) of more than 1000 galaxies (Rowe 2010) at a distance of approximately 92 Mpc<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154331&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryCalculating the Amount of Hydrogen on the Sun's surface
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(A) Use two lines of the Paschen series of hydrogen, along with the general curve of growth of the Sun, to calculate the number of hydrogen atoms with electrons in the n = 3 orbital above each square metre of the Sun's surface. The Paschen series results from an electron making an upward transition from the n = 3 orbital of the hydrogen atom. (B) Then use the Bolztmann and Saha equations to calculate the total number of hydrogen atoms above each square metre of the Sun's surface.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Calculating the Amount of Hydrogen on the Sun's surface" style="max-width: 25%;" align="left"/>(A) Use two lines of the Paschen series of hydrogen, along with the general curve of growth of the Sun, to calculate the number of hydrogen atoms with electrons in the n = 3 orbital above each square metre of the Sun's surface. The Paschen series results from an electron making an upward transition from the n = 3 orbital of the hydrogen atom. (B) Then use the Bolztmann and Saha equations to calculate the total number of hydrogen atoms above each square metre of the Sun's surface.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154330&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberrySaha's Equation (helium in a white dwarf)
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The atmosphere of a DB white dwarf is pure helium. Use Saha's equation to calculate the ionization ratios NII/NI and NIII/NII for temperatures of 5,000 K, 15,000 K, and 25,000 K. Express NII/Nt (Nt = total number of ions) in terms of these ratios and plot NII/Nt for temperatures from 5,000 K to 25,000K. Determine the temperature at which half the helium is ionized.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Saha's Equation (helium in a white dwarf)" style="max-width: 25%;" align="left"/>The atmosphere of a DB white dwarf is pure helium. Use Saha's equation to calculate the ionization ratios NII/NI and NIII/NII for temperatures of 5,000 K, 15,000 K, and 25,000 K. Express NII/Nt (Nt = total number of ions) in terms of these ratios and plot NII/Nt for temperatures from 5,000 K to 25,000K. Determine the temperature at which half the helium is ionized.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154329&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryLane-Emden Equation
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Use the Lane-Emden equation to create a basic model for the white dwarf Sirius B. Calculate and provide plots of density and pressure. Note that a polytropic index of 3 applies to all white dwarfs.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Lane-Emden Equation" style="max-width: 25%;" align="left"/>Use the Lane-Emden equation to create a basic model for the white dwarf Sirius B. Calculate and provide plots of density and pressure. Note that a polytropic index of 3 applies to all white dwarfs.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154328&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryJeans Mass
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Derive the Jeans-mass formula. Then Calculate the Jeans mass of a typical molecular cloud with a temperature of 10 degrees K, a molecular hydrogen number density of 1010, and a corresponding density of 2mH nH2.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Jeans Mass" style="max-width: 25%;" align="left"/>Derive the Jeans-mass formula. Then Calculate the Jeans mass of a typical molecular cloud with a temperature of 10 degrees K, a molecular hydrogen number density of 1010, and a corresponding density of 2mH nH2.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154327&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryMain Sequence Lifetime
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(A) Calculate the Main Sequence lifetime of the Sun. (B) Devise a formula in solar units relating the Main Sequence lifetime to stellar mass, and use it to calculate the Main sequence lifetimes of (i) a 17-solar-mass star, and (ii) a 0.34-solar-mass star.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Main Sequence Lifetime" style="max-width: 25%;" align="left"/>(A) Calculate the Main Sequence lifetime of the Sun. (B) Devise a formula in solar units relating the Main Sequence lifetime to stellar mass, and use it to calculate the Main sequence lifetimes of (i) a 17-solar-mass star, and (ii) a 0.34-solar-mass star.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154326&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryFind the Masses of Stars in a Binary System
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Calculate the masses of Sirius A and Sirius B, given the data below.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Find the Masses of Stars in a Binary System" style="max-width: 25%;" align="left"/>Calculate the masses of Sirius A and Sirius B, given the data below.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154338&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryPulsating Star
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Given the relevant data of a pulsating star, calculate the star's rate of change in surface velocity, radius, and pressure.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Pulsating Star" style="max-width: 25%;" align="left"/>Given the relevant data of a pulsating star, calculate the star's rate of change in surface velocity, radius, and pressure.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154340&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryBinary Star or Star with Exoplanet: Fitting a Curve to the Orbital Data
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The star 51 Pegasi shows a regular variation in redshift, indicating that it is orbiting around a common barycentre. This indicates the possibility that it is a single-line spectroscopic binary or that it has a planet of significant mass orbiting it. Fit a curve to the given data as a first step in determining which of these possibilities is the case.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Binary Star or Star with Exoplanet: Fitting a Curve to the Orbital Data" style="max-width: 25%;" align="left"/>The star 51 Pegasi shows a regular variation in redshift, indicating that it is orbiting around a common barycentre. This indicates the possibility that it is a single-line spectroscopic binary or that it has a planet of significant mass orbiting it. Fit a curve to the given data as a first step in determining which of these possibilities is the case.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154339&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryPulsar Magnetic Field
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Estimate the magnetic field strength of the Vela pulsar.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Pulsar Magnetic Field" style="max-width: 25%;" align="left"/>Estimate the magnetic field strength of the Vela pulsar.<BR><BR>For more information on how to do this problem, and for tables of relevant data, see <A HREF="http://www.canismajor.ca">www.canismajor.ca</A>.https://www.maplesoft.com/applications/view.aspx?SID=154341&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert Roseberry