Astrophysics: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=185
en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemWed, 27 Oct 2021 06:30:16 GMTWed, 27 Oct 2021 06:30:16 GMTNew applications in the Astrophysics categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgAstrophysics: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=185
4D Spatially-Extended Photon and Electron Quantum Mechanical Observables For All Wavelengths and Energy Levels
https://www.maplesoft.com/applications/view.aspx?SID=154590&ref=Feed
4D Einstein-Maxwell energy density analysis initiates with the fact the quantum composed in the total field formal frame of the electromagnetic stress tensor Tšš of the Einstein equations, requires the negative outward pressure -Pa of quantum energy, e.g., as calculated by Baez and Tatom in "What's the energy density of the vacuum?", to have some nonstandard basis for the missing 4D quantum volumetric wavelength š parameterization -- beyond the zero-dimensional (0D) Dirac delta functional š¹ imaginary-invisible mathematical point particle QED-Standard Model representations of the quantum mechanical observables. Accordingly, the present nonstandard 4D photon string-like cylindrical coordinate transverse lemniscate expansion of the Poynting energy flux vector over one wavelength renders for all š the photon energy and angular momentum ā observables. Likewise, a 4D electron spherical coordinate expansion parameterized by the Bohr radii renders for all energy levels n the electron rest mass and angular momentum ā/2 observables.<img src="https://www.maplesoft.com/view.aspx?si=154590/4DPhotonElectron_11_4.gif" alt="4D Spatially-Extended Photon and Electron Quantum Mechanical Observables For All Wavelengths and Energy Levels" style="max-width: 25%;" align="left"/>4D Einstein-Maxwell energy density analysis initiates with the fact the quantum composed in the total field formal frame of the electromagnetic stress tensor Tšš of the Einstein equations, requires the negative outward pressure -Pa of quantum energy, e.g., as calculated by Baez and Tatom in "What's the energy density of the vacuum?", to have some nonstandard basis for the missing 4D quantum volumetric wavelength š parameterization -- beyond the zero-dimensional (0D) Dirac delta functional š¹ imaginary-invisible mathematical point particle QED-Standard Model representations of the quantum mechanical observables. Accordingly, the present nonstandard 4D photon string-like cylindrical coordinate transverse lemniscate expansion of the Poynting energy flux vector over one wavelength renders for all š the photon energy and angular momentum ā observables. Likewise, a 4D electron spherical coordinate expansion parameterized by the Bohr radii renders for all energy levels n the electron rest mass and angular momentum ā/2 observables.https://www.maplesoft.com/applications/view.aspx?SID=154590&ref=FeedMon, 18 Nov 2019 05:00:00 ZDavid HarnessDavid HarnessQuantum Electromagnetic Radiation Pressure Spectrum
https://www.maplesoft.com/applications/view.aspx?SID=154576&ref=Feed
Electromagnetic transverse wave energy density radiation pressure spectrum loglogplot of -Pa vs wavelength Ī». Annotations indicate shorter Ī» are compressive of central cosmological constant vacuum energy density pressure Ī and longer Ī» rarefactive of Ī. Present 4D Einstein-Maxwell energy density analysis, of the computationally dualistic total field units of energy density and mass density pascals, introduces a nonstandard basis for the missing photon volumetric Ī» parameterization ā missing in the zero-dimensional (0D) Dirac delta functional imaginary-invisible mathematical point particle QED-Standard Model representations of the photon. Equations (1-4) introduce a basis for quantum gravity renormalization, in terms of 4D spacetime curvature via quantum energy density computational duality with quantum mass density.<img src="https://www.maplesoft.com/view.aspx?si=154576/EMtransverseRadPaSpectrumGIF_10_15.gif" alt="Quantum Electromagnetic Radiation Pressure Spectrum" style="max-width: 25%;" align="left"/>Electromagnetic transverse wave energy density radiation pressure spectrum loglogplot of -Pa vs wavelength Ī». Annotations indicate shorter Ī» are compressive of central cosmological constant vacuum energy density pressure Ī and longer Ī» rarefactive of Ī. Present 4D Einstein-Maxwell energy density analysis, of the computationally dualistic total field units of energy density and mass density pascals, introduces a nonstandard basis for the missing photon volumetric Ī» parameterization ā missing in the zero-dimensional (0D) Dirac delta functional imaginary-invisible mathematical point particle QED-Standard Model representations of the photon. Equations (1-4) introduce a basis for quantum gravity renormalization, in terms of 4D spacetime curvature via quantum energy density computational duality with quantum mass density.https://www.maplesoft.com/applications/view.aspx?SID=154576&ref=FeedFri, 15 Nov 2019 05:00:00 ZDavid HarnessDavid HarnessPredicting the Orbital Period of Exoplanets by Analyzing the Wobble of Stars
https://www.maplesoft.com/applications/view.aspx?SID=154528&ref=Feed
Stars are pulled in a circle or ellipse in reponse to the gravity of orbiting planets. By analyzing the "wobble" (or radial velocity) of a star, astronomers can predict the presence and orbital period of exoplanets.
<BR><BR>
Radial velocity is recorded, often over months or years, with a spectrograph connected to a telescope. This data is used to generate a periodogram, in which a peak is evidence of an exoplanet; the orbital period of the exoplanet is given by the location of the peak.
<BR><BR>
However cloud cover, scheduling conflicts and other issues can often disrupt observations, so data is generally not regularly sampled. This means that standard Fourier techniques cannot be used to generate a periodogram, and other approaches are needed. A common method for the frequency analysis of irregularly sampled data is the Lomb-Scargle technique.
<BR><BR>
Fischer (2003) recorded the radial velocity of the star HD 3561 (also known as 54 Piscium), and generated a periodogram to show evidence of an exoplanet (now known as 54 Piscium b).
<BR><BR>
This application uses Maple 2019's new Lomb-Scargle tools to reproduce the analysis; the periodogram shows a periodicity of 62.2 days, agreeing with value given by Fischer (2003).
<BR><BR>
References:
<UL>
<LI>A Sub-Saturn Mass Planet Orbiting HD 3651, Fischer D.A. et al., The Astrophysical Journal, 590:1081ā1087, 2003 June 20
<LI>Orbital velocity data found at http://astrostatistics.psu.edu/datasets/exoplanet_Doppler.html
</UL><img src="https://www.maplesoft.com/view.aspx?si=154528/thumbnail.jpg" alt="Predicting the Orbital Period of Exoplanets by Analyzing the Wobble of Stars" style="max-width: 25%;" align="left"/>Stars are pulled in a circle or ellipse in reponse to the gravity of orbiting planets. By analyzing the "wobble" (or radial velocity) of a star, astronomers can predict the presence and orbital period of exoplanets.
<BR><BR>
Radial velocity is recorded, often over months or years, with a spectrograph connected to a telescope. This data is used to generate a periodogram, in which a peak is evidence of an exoplanet; the orbital period of the exoplanet is given by the location of the peak.
<BR><BR>
However cloud cover, scheduling conflicts and other issues can often disrupt observations, so data is generally not regularly sampled. This means that standard Fourier techniques cannot be used to generate a periodogram, and other approaches are needed. A common method for the frequency analysis of irregularly sampled data is the Lomb-Scargle technique.
<BR><BR>
Fischer (2003) recorded the radial velocity of the star HD 3561 (also known as 54 Piscium), and generated a periodogram to show evidence of an exoplanet (now known as 54 Piscium b).
<BR><BR>
This application uses Maple 2019's new Lomb-Scargle tools to reproduce the analysis; the periodogram shows a periodicity of 62.2 days, agreeing with value given by Fischer (2003).
<BR><BR>
References:
<UL>
<LI>A Sub-Saturn Mass Planet Orbiting HD 3651, Fischer D.A. et al., The Astrophysical Journal, 590:1081ā1087, 2003 June 20
<LI>Orbital velocity data found at http://astrostatistics.psu.edu/datasets/exoplanet_Doppler.html
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154528&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanCalculating and Graphing the Bremsstrahlung Emission Over All Frequencies for the Orion Nebula
https://www.maplesoft.com/applications/view.aspx?SID=154307&ref=Feed
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 RoseberryJeans Mass
https://www.maplesoft.com/applications/view.aspx?SID=154327&ref=Feed
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 RoseberrySaha's Equation (helium in a white dwarf)
https://www.maplesoft.com/applications/view.aspx?SID=154329&ref=Feed
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 RoseberryCalculating the Amount of Hydrogen on the Sun's surface
https://www.maplesoft.com/applications/view.aspx?SID=154330&ref=Feed
(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 RoseberryFind the Masses of Stars in a Binary System
https://www.maplesoft.com/applications/view.aspx?SID=154338&ref=Feed
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 RoseberryPulsar Magnetic Field
https://www.maplesoft.com/applications/view.aspx?SID=154341&ref=Feed
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 RoseberryThomson Cross Section
https://www.maplesoft.com/applications/view.aspx?SID=154313&ref=Feed
(A) Calculate the Thomson Cross Section and give its value. (B) Which has the greater cross section: electrons or protons? Why? (C) What effect does wavelength have on Thomson scattering? (D) Calculate the optical depth to Thomson scattering in the warm, neutral (HI) medium of the Galactic ISM, normal to the disk. (E) How might Thomson scattering be used to reveal a hidden active galactic nucleus?<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="Thomson Cross Section" style="max-width: 25%;" align="left"/>(A) Calculate the Thomson Cross Section and give its value. (B) Which has the greater cross section: electrons or protons? Why? (C) What effect does wavelength have on Thomson scattering? (D) Calculate the optical depth to Thomson scattering in the warm, neutral (HI) medium of the Galactic ISM, normal to the disk. (E) How might Thomson scattering be used to reveal a hidden active galactic nucleus?<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=154313&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryDoppler Broadening
https://www.maplesoft.com/applications/view.aspx?SID=154314&ref=Feed
Calculate the Doppler broadening of the iron lines at the surface 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="Doppler Broadening" style="max-width: 25%;" align="left"/>Calculate the Doppler broadening of the iron lines at the surface 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=154314&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryGrey and Eddington Approximations
https://www.maplesoft.com/applications/view.aspx?SID=154318&ref=Feed
Determine the values of Iin and Iout as functions of vertical optical depth (Ļ), using the Eddington Approximation for a plane-parallel atmosphere. Then find the optical depth at which the radiation field is isotropic to within 5%.<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="Grey and Eddington Approximations" style="max-width: 25%;" align="left"/>Determine the values of Iin and Iout as functions of vertical optical depth (Ļ), using the Eddington Approximation for a plane-parallel atmosphere. Then find the optical depth at which the radiation field is isotropic to within 5%.<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=154318&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryRadiation From a Plane-Parallel Atmosphere
https://www.maplesoft.com/applications/view.aspx?SID=154319&ref=Feed
Assuming a plane-parallel atmosphere, (1) show that emission lines will appear if
"j[lambda]>>1"
and there is no radiation entering the atmosphere from outside. (2) Further, show that, if radiation enters from below, the relation between specific intensity and source function will determine whether emission or absorption lines are seen.<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="Radiation From a Plane-Parallel Atmosphere" style="max-width: 25%;" align="left"/>Assuming a plane-parallel atmosphere, (1) show that emission lines will appear if
"j[lambda]>>1"
and there is no radiation entering the atmosphere from outside. (2) Further, show that, if radiation enters from below, the relation between specific intensity and source function will determine whether emission or absorption lines are seen.<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=154319&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryDistance to a Cepheid Variable
https://www.maplesoft.com/applications/view.aspx?SID=154321&ref=Feed
Use the given data to calculate the distance to the first Cepheid variable to be discovered, Eta Aquilae.<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="Distance to a Cepheid Variable" style="max-width: 25%;" align="left"/>Use the given data to calculate the distance to the first Cepheid variable to be discovered, Eta Aquilae.<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=154321&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryUsing the Method of Main Sequence Fitting to Estimate the Distance of the Pleiades Open Cluster
https://www.maplesoft.com/applications/view.aspx?SID=154322&ref=Feed
Stars in an open cluster are approximately the same age and at the same distance from the Earth. The method of Main Sequence fitting can, therefore, be used to estimate their distance.<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="Using the Method of Main Sequence Fitting to Estimate the Distance of the Pleiades Open Cluster" style="max-width: 25%;" align="left"/>Stars in an open cluster are approximately the same age and at the same distance from the Earth. The method of Main Sequence fitting can, therefore, be used to estimate their distance.<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=154322&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryCalculating the Distance to a Supernova by the Expanding Photosphere Method
https://www.maplesoft.com/applications/view.aspx?SID=154323&ref=Feed
Use Doppler shifting and the "expanding photosphere method" to calculate the distance to the type II supernova remnant SN 1969L<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 Distance to a Supernova by the Expanding Photosphere Method" style="max-width: 25%;" align="left"/>Use Doppler shifting and the "expanding photosphere method" to calculate the distance to the type II supernova remnant SN 1969L<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=154323&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryDistance by Parallax
https://www.maplesoft.com/applications/view.aspx?SID=154324&ref=Feed
Derive the formula for parallax. Then use the formula to calculate the distance, angular separation, and actual separation in parsecs and astronomical units of Proxima Centauri and Alpha Centauri (A).<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="Distance by Parallax" style="max-width: 25%;" align="left"/>Derive the formula for parallax. Then use the formula to calculate the distance, angular separation, and actual separation in parsecs and astronomical units of Proxima Centauri and Alpha Centauri (A).<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=154324&ref=FeedMon, 25 Sep 2017 04:00:00 ZDr. Robert RoseberryDr. Robert RoseberryLane-Emden Equation
https://www.maplesoft.com/applications/view.aspx?SID=154328&ref=Feed
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 RoseberryDark Matter: Coma Cluster
https://www.maplesoft.com/applications/view.aspx?SID=154331&ref=Feed
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 RoseberryQuasar j2348-3054
https://www.maplesoft.com/applications/view.aspx?SID=154334&ref=Feed
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 Roseberry