Telescopes and Galaxies - Assignment Example

PART C: SHORT ANSWER QUESTIONS 1. A telescope with a 20 cm primary mirror has an f# of 5. What would be the focal length of the eyepiece required to give a magnification of 100? Is it possible to change the “power” of the telescope (brightness of light reaching the image plane) without physically altering the mirror? A telescope (here we consider only an optical telescope) is a device, which is used to collect and concentrate light that is coming largely from the part of the electromagnetic spectrum that corresponds to visible light. The light is further used for viewing a magnified image of the object that is observed by the telescope directly, for making photos, or for collecting data using digital image sensors. Telescopes have many different types of models and designs. In telescopes constructed using a prime focus design where are no secondary optics used, and the image can be viewed at the focal point of the telescope’s primary mirror. The telescope’s magnification power is the primary focal length divided by the focal length of the eyepiece. The primary focal length is found by multiplying the diameter of the telescope’s primary mirror by the f number. Thus, the focal length of the eyepiece is equal to the diameter of the primary mirror multiplied by the f number and divided by the telescope’s magnification power: The power of the telescope directly depends upon the diameter (or, so called, aperture) of the objective lens (that is, mirror) of the telescope. Only larger objectives can gather more light. Therefore, there is no way to increase the power of the telescope without changing physical characteristics of its mirror. However, more sensitive digital imaging equipment can be used produce higher-quality images from the same amount of light harnessed by the telescope. 2. Explain how is it possible to determine the age of a globular star cluster by measuring the magnitudes and colours of the stars it contains. Note the key assumptions that must be made about the stars in such a cluster for this technique to work. Sketch example H-R diagram for a hypothetical cluster and use it to help answer the question. When we are determining the age of the globular star cluster the following assumptions should be made (Sagar, 1997): 1) all cluster stars have formed almost simultaneously from the same interstellar gas cloud; 2) the cluster stars have very similar chemical composition, because the original gas cloud was well mixed, so the individual cluster stars should contain the same mix of chemical elements and molecules; 3) all cluster stars are located at the same distance away from us (the spread in distance is considerably smaller than the distance to the star cluster, so we can ignore it). It means that the only noticeable difference between stars in a globular cluster is their mass. Astronomers have observed in many different locations of the universe that when stars form from an interstellar gas cloud, there are very few stars with high mass and many stars with low mass. Therefore, the relative proportion of stars of different masses that form can be considered as a kind of universal law that is valid for all globular clusters in the universe regardless of the size and environment of the region where stars form, and how long ago the stars have been formed. The Hertzsprung–Russell (HR) diagram is a graph of stars, which shows the relationship between the absolute magnitudes (or luminosity) of the stars against their spectral types and effective temperatures (or colour). Since the HR diagram is a well researched issue and astronomers can fairly well predict how a star would behave during its evolution, the computer models can be used to create theoretical colour-magnitude HR diagrams for star populations with a specific age. Then the astronomers plot a line that goes via the points of all stars in the HR diagram. This line, which is called an isochrone, indicates the colour-magnitude relationship of stars with a specific age. Then the astronomers plot the observed colours and magnitudes for the stars in an observed globular star cluster. The age of the cluster is found when the best match between a theoretical isochrone and the stars in the cluster is discovered. An example of the HR diagram for M3 globular cluster with 10 billion year isochrone fitted is presented in Fig. 1. Fig. 1. M3 color-magnitude diagram with 10 Gyr isochrone (Fanelli) 3. Astronomers have determined that the Sun has a total luminosity of 3.84×1026 Watts. a. If the Sun remains on the main sequence for 10 billion years (with constant luminosity), how much mass (in kg) does it convert to energy in total? The fuel of the Sun matches the total amount of energy that is available, and the energy consumption rate is how much energy per second the Sun emits. Luminosity is the energy per second that a star emits. Therefore, the energy emitted by the Sun during a time period is equal to luminosity of the Sun multiplied by time: The relationship between energy and mass is described by the Einstein’s formula: Therefore, the mass converted by the Sun into energy during 10 billion years (with each year having 365.35 days, each day having 24 hours, and each hour having 3600 seconds) assuming its constant luminosity is: b. Compare your answer to the current mass of the Sun and comment. The current mass of the Sun is equal to 1.9891×1030 kg (Williams, 2004). We shall calculate the percentage of the mass that the Sun will loose during 10 billion years: So the amount of mass lost by the Sun because of light emission is pretty small. c. Assuming the only energy source is the repeated fusion of four Hydrogen atoms into one Helium atom, work out the mass of Hydrogen that will be converted into Helium by the Sun during its lifetime. We believe that the energy source of the sun is nuclear fusion of hydrogen to helium: H1 + H1 → H2 + e+ + ν H2 + H1 → He3 + γ He3 + He3 → He4 + 2 H1 where γ is the gamma-ray and ν is the electron neutrino, H1, H2 are the Hydrogen isotopes, and He3, He4 are the Helium isotopes. According to this procedure one helium atom is produced from four hydrogen atoms. Assuming that the Sun during its formation was 100% made of hydrogen, the mass of the Sun was roughly the same as now, and the sun has burned hydrogen at the same constant conversion rate, we can calculate the mass of Hydrogen that will be converted into Helium by the Sun during its lifetime as follows: Currently, the conversion rate of the Sun is about 3.6×1038 Hydrogen atoms converted to Helium atoms every second (Astronomy.com). So, the mass of converted Hydrogen during Sun’s lifetime is: d. How does the total mass of Hydrogen “lost” (by conversion into Helium and through the release of energy) compare to the mass of the Sun? Comment. We compute the percentage of the converted Hydrogen mass to the mass of the Sun: Currently, the mass of Helium atoms converted from Hydrogen makes only 23.8% of the mass of the Sun. The difference is because the current age of Sun is estimated about 5 billion years, that is about one half of the estimated total Sun’s lifetime. References Astronomy.com Forums. How much hydrogen converted to helium in sun? http://cs.astronomy.com/asycs/forums/p/35465/392182.aspx Fanelli, M. Star clusters. http://personal.tcu.edu/~mfanelli/imastro/imastro_star_clusters.html Sagar, R. (1997). The Ages of the Galactic Globular Clusters. J. Astrophys. Astr. 18, 295–301. Williams, D.R. (2004). Sun Fact Sheet. NASA. Retrieved 2009-09-23. Read More