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elevator is not an inertial frame However because we are considering kinematics only and not dynamics the problem can actually be considered in either frame The solution given provides the answer in the elevator s frame of reference If the

Original URL path: http://www.astro.queensu.ca/~irwin/phys106/assignments/assignment2_note.html (2016-02-13)

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get you to think about a horizontal leap as being equivalent to the object being at a point which is at the top of a complete trajectory Also the equations given in the notes are derived from the original kinematic equations and are equivalent to them so either can be used EXCEPT NOTE THE FOLLOWING The range and height equations given in the page 11 notes are for the specific

Original URL path: http://www.astro.queensu.ca/~irwin/phys106/assignments/assignment3_note.html (2016-02-13)

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v C B Think of the C s above as cancelling out The addition must be done vectorially So let s look at the raindrop problem The velocity of the rain with respect to the train desired quantity is v r t v r g v g t where v r g is the velocity of the rain with respect to the ground and v g t is the velocity of the ground with respect to the train Now re write this as v r t v r g v t g because what we know is v t g the velocity of the train with respect to the ground We can now draw this vector diagram with the knowledge that v r g is vertical downwards and we are given the angle theta The result is v r g v t g tan theta If you had a more complicated problem you might try to consider the x and y components of motion separately For example suppose you have a problem involving projectile motion but there is relative motion in x only but not in y Since you need to deal with these two motions separately anyway you would simply write down the usual equations for y motion Then for the x motion only make the correction for relative motion Once this correction is applied proceed as usual 5 This problem is actually quite straightforward because it involves only substituting values into the equations of constant angular acceleration i e the equations involving theta omega and alpha given on page 11 of the notes Circular Motion Since we are told that the acceleration along the track is constant this means that a theta alpha r constant Since the motion is along a circle r constant this means that alpha

Original URL path: http://www.astro.queensu.ca/~irwin/phys106/assignments/assignment4_Soln.html (2016-02-13)

Open archived version from archive - Phys 215 Assignment 1

through this telescope using an eyepiece that gave a magnification of 80 X determine how many resolution elements you could discern across the Moon in this case Is this system now detector limited or not Assume that the observer has good eyes 2 a Based on the specifications for HST s WF PC2 see text Section 6 2 and assuming that the 4 adjacent CCDs each 800 X 800 are arranged in a square with no gaps in between determine the angular size of the field of view in planetary mode b If the system of part a were observing Mars at opposition what would be the linear size of Mars image on the CCD c Is this system diffraction limited seeing limited or detector limited Explain d How many resolution elements are there across Mars using this system e How large would a radio telescope operating at a wavelength of 90 cm have to be in order to match the HST s resolution 3 The Ellis Hall telescope is a 0 4 meter f 10 and the CCD is an Apogee AP7b with 512 by 512 square pixels each 24 microns in size and no significant gaps in between

Original URL path: http://www.astro.queensu.ca/~irwin/phy215/y2002/assignment1.html (2016-02-13)

Open archived version from archive - Phys 215 Assignment 1

the peak of its spectrum be Doppler shifted i e find lambda max new Should there be any change in the value of the specific intensity of the Doppler shifted photon c Now compute the value of B lambda T of the unshifted spectrum at the wavelength of the new peak lambda max new c Determine how much of a change in specific intensity in percent there is between the two values above of B lambda T Do you think that the peak of the shifted spectrum could be distinguished from the peak of the unshifted spectrum sufficiently to determine this radial velocity Assume that your measuring instruments can detect changes of about 5 or larger d Refer to example 9 8 on page 296 of the text regarding the width of a typical spectral line in the sun and comment on the possibility of detecting a radial velocity of 50 km s by using such a spectral line instead 3 Suppose by using special techniques a telescope in orbit about earth measures the angular diameter of a star of unknown distance to be theta 0 02 arcseconds The telescope then also makes a single measurement of apparent magnitude in the V band centered at a wavelength of 0 5556 microns finding V 3 2 for this star Note that the apparent V magnitude of the calibrator star Vega is V 0 corresponding to a flux density of 3 44 x 10 5 erg s cm 2 micron in this waveband Using only the assumption that the star emits as a black body consider each of the quantities below and indicate whether the quantity can or cannot be determined If it can be determined then compute it Use cgs units and the wavelength form of the Planck curve a The

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the central ionizing star and by balancing recombinations with photoionizations This development and the expression for the radius of the sphere r s is given on pages 465 467 of the text a Determine the size of the resulting HII region i e find r s if the sun were to enter an HI cloud of the same density as Orion A See example 12 4 in the text for data and the procedure However unlike the example do not assume that all the photons have the same peak wavelength Rather determine the number of ionizing photons coming from the sun by doing an integration over the Planck curve over the wavelength or frequency range of importance Hint consider whether an approximation to the Planck curve can be used to simplify the integration Integrate by parts or look up the integral b Compare your result to that found for Orion A and qualify the statement only the hottest stars can create HII regions 2 Do question 8 12 in the text It is helpful to look at example 8 3 first To answer the last question compute the mean separation between hydrogen nuclei and compare this with the radius of

Original URL path: http://www.astro.queensu.ca/~irwin/phy215/y2002/assignment3.html (2016-02-13)

Open archived version from archive - Phys 215 Assignment 4

linear depth s of the region over which tau increases from 0 to 1 becomes optically thick if the mass absorption coefficient kappa nu 0 264 cm 2 g 1 at optical wavelengths and the density rho 2 5 x 10 7 g cm 3 both constant over this depth Explain why the sun s limb appears sharp to an observer on earth If looking through a ground based telescope would the sun s limb still appear sharp Explain 3 a Consider the case in which a foreground HI cloud is absorbing a background continuum source If the background continuum brightness temperature T B background is subtracted off of the total emission T B HI background show that the result will be T B HI background T B background T k T B background 1 exp tau where T k is the kinetic temperature of the cloud and tau is its optical depth b I have extracted two 5 degree by 5 degree fields from the Canadian Galactic Plane Survey CGPS each shown in false colour The first is an image containing only continuum emission i e at a frequency just off the 21 cm HI spectral line With the exception of the large features near the top which are due to sources in our own Galaxy virtually every point source in this image will be of some distant quasar in the far reaches of the universe The brightness temperature of the source at Galactic Longitude 136 2 degrees Galactic Latitude 0 9 degrees is T B background 471 K The second is an image of the same field showing total emission minus continuum i e T B HI background T B background which shows wispy emission from HI clouds in our own Galaxy over the entire field just for

Original URL path: http://www.astro.queensu.ca/~irwin/phy215/y2002/assignment4.html (2016-02-13)

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maximum etc 2 a Taking the sun s circular velocity and distance from the Galactic Center to be V 0 220 km s and R 0 8 kpc respectively compute the following quantities assuming that the Galactic Center is at rest i The sun s angular velocity Omega 0 radians s ii The proper motion of the Galactic Center mu in arcsec yr due to the sun s motion Given that modern radio telescopes can measure positional changes of about a milliarcsecond i e 1 1000 of an arcsecond how long would one have to wait between consecutive measurements in order to detect this proper motion b With the help of a clear diagram derive an expression in a manner similar to that done in class for the observed radial velocity V r of an object which is outside of the solar circle i e at R R 0 How does V r vary along the line of sight if the circular velocity V is constant e g always increasing always decreasing increasing then decreasing etc Is there a distance ambiguity problem in this regime Explain 3 An HII region is observed at a Galactic longitude of l 45 degrees

Original URL path: http://www.astro.queensu.ca/~irwin/phy215/y2002/assignment5.html (2016-02-13)

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