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Recently Asked Astrophysics Questions

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  • Q1: NATS 1880 Project 3 Due: Monday, April 8, 2024 at 11:59 pm Please submit electronically via eClass Student name: Yusra Rostom Student number: 218647735 1 Project Description For nearly 20 years, astronomers have been monitoring the brightness of distant stars in an attempt to determine whether or not any of them host a planetary system. A measure of a star's brightness as a function of time is known as a light curve. Periodic fluctuations within a star's light curve are an indication that planetary transits may be occurring, where a planet is periodically passing between Earth and the distant star causing a temporary decrease in its brightness (although fluctuations can be caused by other astrophysical phenomena as well!). Over 3000 confirmed exoplanets have been detected via this Transit Method, mostly due to the Kepler Space Satellite and the Transit Exoplanet Survey Satellite. In Project 3, you will be provided with a simulated light curve that is comparable to those studied by astronomers today. Through an analysis of this light curve, you will determine whether or not your target star has any planets orbiting around it and what some of their properties are. You will also be asked to infer what other properties the planet(s) may have and evaluate its habitability. Both course materials and independent sources will have to be consulted in order to complete this project. Be sure to cite any sources used in your analysis. 2 Data The target star that was studied by your fictitious telescope has a mass, luminosity, radius, and temperature of 0.30 Mo, 0.008 Lo, 0.31 AU and 3157.18K. To access the observational data, go to link posted on eClass and find the .csv file named after your student number. A small portion of the data is illustrated in Figure 1. If you don't have experience with comma separated values (csv) files, note that they can be opened with Microsoft Excel. However you may use any software program that you wish (e.g. Google Sheets, TOPCAT). Each file contains measurements of the star's light curve, with the first two columns marking the time of a brightness measurement (in years) and the relative brightness. For this project, we will ignore measurement uncertainties that typically come with this type of 1 Relative Brigthness 1.000 0.999 0.998 0.997 0.996 0.00 0.02 0.04 0.06 0.10 0.12 0.14 0.08 Time (Years) Figure 1: Portion of your simulated light curve, which is a plot of relative brightness versus time (in years). 2 data. I highly recommend first trying to reproduce Figure 1 to make sure you are handling the data correctly, however a reproduction of Figure 1 is not necessary for your report. 3 Analysis Your report should begin with an Abstract (maximum 250 words) that summarizes your findings and an Introduction (maximum 500 words) that outlines our motivation for finding exoplanets and how the transit method works. The rest of your report should be followed by sections titled Results, Analysis, and Bibliography, which have no word limits. For your analysis, make a plot of the entire light curve and then create a zoomed-in graph of one transit for each confirmed exoplanet. Note that, just like real observations, there are some times when it was not possible to observe the target star. So be sure to choose a well resolved transit to plot as your zoomed-in image. Also be sure the axis are properly labelled and the axis range is appropriate to view the transit event such that the detailed shape of the transit can be seen. Your submitted report should contain a section with all the necessary figures in the Results section. From these figures, answer the following questions and include them in the Analysis section of your report. a) How many exoplanets are you able to confirm are orbiting your target star? How do you know? [2 marks, approx. 25-100 words] b) How many unconfirmed exoplanets do you have orbiting your target star? How do you know and why are they unconfirmed? [2 marks, approx. 25-100 words] c) For the confirmed exoplanets that you have discovered, what are their orbital periods and size (e.g. radius)? Put the data in a table and explicitly show your calculations below the table for one exoplanet. [4 marks] d) What properties of the confirmed exoplanets can you derive from the information given, other than their orbital periods and radii? Put the data in a table and explicitly show your calculations below the table for one exoplanet. [4 marks] e) What can you say about the habitability of this planet to life-like-us based on the evidence alone? [2 marks, approx. 25-100 words] f) Would your analysis of any exoplanets that you deemed habitable in the previous question change if, through transit spectroscopy, you learn the exoplanet has a 90.00atm atmosphere that is 96.00% carbon dioxide? Explain your reasoning [2 marks, approx. 25-100 words] 3 g) How confident are you in your conclusion about each planet's habitability? What informa- tion would you need to increase your confidence. Be specific! [2 marks, approx. 25-100 words] Finally, end your report with a Bibliography section if you used any additional sources. You should also have in-line citations throughout the report wherever the information was used. + 4 Additional Notes • Due to the uniqueness of each dataset, it is entirely possible that you have been provided a simulated light curve is difficult to analyse. So please note that all light curves are meant to have a minimum of 1 exoplanet (if not more). If you feel like your data contains an error and has no confirmed exoplanets, please contact nats1880@yorku.ca or stop by my virtual office hours. • You are all encouraged to discuss the project amongst yourselves, but the submitted work must be done by you and you alone. Directly collaborating on another student's analysis is an academic offense. • In addition to the posting questions on eClass and providing help after class or during office hours, there will be a dedicated Project 3 help session on March 21 instead of a lecture. 5See Answer
  • Q2: SPH 4UV FCA Final Culminating Activities LAB - complete a report and find the mathematical relationship between 2 variables (possible topics listed on the following page) Check list Writing: ☐ Include headings for report (Objective, Materials, Procedure, Observations, Results, Conclusions) ☐ Procedure has enough detail that I could reproduce the lab and come up with similar values BUT it does not have any of my teacher voice giving instructions to students Writing is formal, third person Tables and graphs are explained and embedded in writing Communication of tables & graphs: ☐ graphs have the following: gridlines, titles, units, error bars, shown to origin (if appropriate) ☐ Tables are well organized have units & headings Concepts ☐ Appropriate line / curve shown on the graph Terminology matches appropriate line / curve (proportional, linear, quadratic, root, inverse OR possibly a polynomial of higher degree) ☐ Equation matches appropriate line / curve BUT is a general case discussed in class (for example do NOT use y=3x+0.0004 if you are saying it's proportional> use y=3x if it's proportional) ☐ If a curve is used, the fit is CONFIRMED by adding a column (or a new table) AND by checking for a proportional graph (and the proper variables are graphed for this) ☐ If you are using data from the textbook, you MUST ALSO provide a log-log graph with the slope calculated to confirm your curve (instructions for this are on the first test) ☐ Sources of error are mentioned ☐ Conclusions give equation and name the relationship POSSIBLE TOPICS: C. Go to the planetary data (posted under content / circular & celestial motion) and find the relationship between the period of revolution of orbit and the mean radius of orbit. Confirm with radius cubed and period squared AND create a log-log graph of period vs orbit and find the slope. OPTION C: Planetary Data Assignments ar System Object Mass (kg) Radius of Object (m) Sun 1.99 X 1030 6.96 X 108 Period of Rotation on Axis (s) 2.14X106 Mean Radius of Orbit (m) Period of Revolution of Orbit (s) Orbital Eccentricity Mercury 3.28 X 1023 2.44 X 106 5.05 x 106 5.79 x 1010 7.60 x 106 0.206 Venus 4.83 x 1024 6.05 x 106 2.1 x 107 1.08 x 1011 1.94 x 107 0.007 Earth 5.98 X 1024 6.38 x 106 8.64 x 104 1.49 X 1011 3.16 x 107 0.017 Mars 6.37 x 1023 3.40 x 106 8.86 X 104 2.28 X 1011 5.94 x 107 0.093 Jupiter 1.90 X 1027 7.15 x 107 3.58 X 104 7.78 × 1011 3.75 X 108 0.048 Saturn 5.67 x 1026 6.03 x 107 3.84 x 104 1.43 X 1012 9.30 X 108 0.056 Uranus 8.80 X 1025 2.56 x 107 6.20 x 10 2.87 x 1012 2.65 x 109 0.046 Neptune 1.03 X 1026 2.48 × 107 5.80 x 106 4.50 X 1012 5.20 x 109 0.010 Pluto 1.3 x 1023 1.15X106 5.51 X 105 5.91 X 1012 7.82 X 109 0.248 Moon 7.35 X 1022 1.74 x 106 2.36 x 106 3.84 X 108 2.36 x 106 0.055See Answer
  • Q3:Instructions Access the simulator & provide the answers to the following questions. Typed work needed HR Diagram Explorer: https://astro.unl.edu/naap/hr/animations/hr.html/n Lab 11: HR Diagram Background Information Work through the background sections on Spectral Classification, Luminosity, and the Hertzsprung-Russell Diagram. Then complete the following tables. Table 1: The table below summarizes the relationship between spectral type, temperature, and color for stars. Surface Temperature K Spectral Type Color M1 M5 4560 K G2 6100 K F5 8590 K 13000 K 09 40000K Table 2: Complete the following table related to stellar luminosities in solar units using the equation L × R²T4. Note that Ro represents the radius of the Sun, To its temperature and Lo its luminosity. Radius (R) Temperature (To) Luminosity (LO) 1 1 1 2 2 1 1 1/3 10 1 1 10 Table 3: Complete the following table relating luminosity and mass in solar units for main sequence stars using the equation L × M³.5 Mass (Mo) Luminosity (Lo) 1 2 5 3160 0.1 HR Diagram Explorer Open the HR Diagram Explorer. Begin by familiarizing yourself with the capabilities of the Hertzsprung-Russell Diagram Explorer through experimentation. An actual HR Diagram is provided in the upper right panel with an active location indicated by a red x. This active location can be dragged around the diagram. The options panel allows you to control the variables plotted on the x-axis: (temperature, B-V, or spectral type) and those plotted on the y-axis (luminosity or absolute magnitude). One can also show the main sequence, luminosity classes, isoradius lines, or the instability strip. The Plotted Stars panel allows you to add various groups of stars to the diagram. The Cursor Properties panel has sliders for the temperature and luminosity of the active location on the HR Diagram. These can control the values of the active location or move in response to the active location begin dragged. The temperature and luminosity (in solar units) are used to solve for the radius of a star at the active location. The Size Comparison panel in the upper left illustrates the star corresponding to the active location on the HR Diagram. Note that the size of the sun remains constant. Exercises Drag the active location around on the HR Diagram. Note the resulting changes in the temperature and luminosity sliders. Now manipulate the temperature and luminosity sliders and note the corresponding change in the active location. Table 4: Check the appropriate region of the HR diagram corresponding to each description below. Description Hot stars are found at the: Cool stars are found at the: Luminous stars are found at the: Dim stars are found at the: Top Right Bottom Left Drag the active location around on the HR Diagram once again. This time focus on the Size Comparison panel. Table 5: Check the appropriate region of the HR diagram corresponding to each description below. Description Upper Left Upper Lower Right Right Lower Left Large Blue stars are found at the: Small Red stars are found at the: Small Blue stars would be found at the: Really Large Red stars are found at the: Check show isoradius lines. Note that at each point on a green line, stars have the same value of radius. Use these isoradius lines to check your answers in the table above. Table 6: Fill the table with brief explanation of the location of the described stars referring to the equation L × R²T4. Description Large Blue stars Small Red stars Small Blue stars Really Large Red stars Reason for location For the next exercise you will have to change the luminosity or the temperature of the star in order to keep it on the main sequence, an identify the star's approximate radius. Table 7: Fill the table with the correct values to keep the star on the main sequence. Use To=5800K Temperature (To) Luminosity (L) Radius (R) 0.5 0.7 1 1 1 2 15 6.5 For the last exercise explore the luminosity classification by checking show luminosity classes. The green region (labeled dwarfs V) is known as the main sequence and contains all stars that are fusing hydrogen into helium as their primary energy source. Over 90% of all stars fall in this region on the HR diagram. The other highlighted regions are giants, supergiants, white dwarfs. Move the active cursor up and down each region and explore the different values of, luminosity, temperature and stellar radius. Table 8: Fill the table with statements describing the stars that belong to each class. (Example: Stars in this class have high/low luminosity, high/low temperature, big/small radius) Description Giant Supergiant White dwarf Luminosity, temperature and radius. Final Questions 1. Describe the sizes of stars along the main sequence. What are stars like near the top of the main sequence, the middle, and the bottom? 2. Describe the masses of stars along the main sequence. What can you conclude? 3. Can a star with a radius equal 1000 Ro be on the main sequence? Explain your answer. 4. Which is larger a blue supergiant or a red supergiant? Explain. 5. Which is larger a white dwarf or a red dwarf? Explain.See Answer
  • Q4:Question 5 Outline three competing views for the origin of the Earth's water. Cite appropriate examples that can help to distinguish between the three different views, taking into account any limitations or gaps in our current knowledge.See Answer
  • Q5:Question 1 a. Define the terrestrial age of a meteorite and explain, how this is determined. b. if a meteorite were to be of Martian origin, explain where the oxygen isotope composition of this sample and other Martian samples would appear with respect to the terrestrial fractionation line (TFL) on a plot of 170 versus 180 using figure 9.16 Figure 9.16 A plot of 80 and 8¹% for whole-rock meteorites is shown in Figure 9.16. Compare the scales of this plot with those of Figure 9.15; while astronomical entities display vast variations in oxygen isotopic compositions, those of materials formed within the solar nebula are much less variable (although the small differences which can be measured are of immense importance). Note the line of slope 0.5 representing the TFL. 870% 2 terrestrial fractionation line 17 calcium-aluminium- rich inclusions 2 8180/% bulk meteorites Figure 9.16 Plot of 6¹70 and 5180 for whole-rock meteorite samples. Each different coloured field represents a different type of meteorite group (included on the plot are fields for different groups of carbonaceous chondrites, different types of ordinary chondrites, Martian meteorites, HEDs, and so on). The inset shows the range in oxygen isotopic composition of all bulk meteorite samples and covers a range in 8¹O values from -40 to +20% and in 8¹70 values from -40 to +30%. The region of the main graph is 10 shown by the shaded box in the inset. (Franchi et al., 2001)See Answer
  • Q6:4. (6 pts) Planetary geology a) What is the difference between lithosphere and crust? (2 pts) b) Describe convection in a terrestrial planet. How does it cool the planetary interior? (4 pts)See Answer
  • Q7:3. (2 pts) Manually draw a bound orbit and an unbound orbit around a planet. Mark where the planet is with respect to the orbits.See Answer
  • Q8:2. (6 pts) Formation of the solar system (nebula theory) a) From what you drew for Question 1, you should be able to tell the spin direction of the protoplanetary disk (the disk formed from the collapse and flattening of the original nebula) during the formation of the solar system. What is the spin direction? (2 pts) b) Where is the frost line with respect to the planets' orbits? (2 pts) c) Why are most icy bodies (e.g. icy moons, comets, dwarf planets) found outside the frost line? (2 pts)See Answer
  • Q9:1. (10 pts) Manually draw the layout and patterns of motion of the solar system. Please include the Sun and all planets. Draw the orbits of all planets around the Sun (2 pts) Label the orbit direction and spin direction of all planets. Label the spin direction of the Sun. (2 pts) Label the planets' average orbital distances from the Sun in AU and their orbital periods in Earth years (2 pts) Label the size of the Sun and each planet as compared to Earth's radius (e.g. 0.5 Earth radius, 2 Earth radii,...) (2 pts) Point out the exceptions to the patterns of motion (2 pts). (The sizes and distances do not need to be drawn to scale, which is impossible to do on letter sized paper anyway.) • •See Answer
  • Q10:Problem 4 (10 pts.): Two elliptical orbits share the same central body and apsidal line as shown in below figure. Point A lies at the apogee of orbit 1. Point B lies at the apogee of orbit 2. Perform a Hohmann transfer from point A to point B. All numbers have been non-dimensionalzed such that μ 1. The apogee and perigee of orbit 1 and 2 are given by = = 10 and Respectively. What is the total Av for the maneuver? 11p₁ = 4 √√₁2 = 8 (p2 = 3 Point BSee Answer
  • Q11:Analyze and Interpret 1. Describe the pattern on your graph. 2. The Sun's spectral type is about G2. Use your chart to predict the Sun's absolute magnitude. 3. Vega's spectral type is A0. Predict Vega's absolute magnitude. 4. Predict the absolute magnitude of a star whose spectral type is B5. Conclude and Communicate 5. Summarize how you can use this pattern to predict a main- sequence star's absolute magnitude if you know its spectral type.See Answer
  • Q12:34 A satellite of mass 1 600 kg is orbiting the Earth with radius 2R. R is the radius of the Earth which is equal to 6.37 × 106 m. What is the centripetal force acting on the satellite? [G = 6.67 × 10-¹1 N m² kg-2, mass of the Earth = 5.97 x 1024 kg] A 1744 N B 1806 N C 1960 N D 3 925 NSee Answer
  • Q13:33 A satellite is orbiting at a distance of 4.2 x 106 m from the surface of the Earth. The radius of the Earth is 6.4 x 106 m. What is the ratio of gravitational force on the satellite in orbit/gravitational force on the satellite on the surface of the Earth? A 0.36 B 0.42 C 0.51 D 0.64 Answer give DSee Answer
  • Q14:3)Terrestrial planets grew slowly and the Jovian planets grew quickly.See Answer
  • Q15:2)The inner planets are composed of rock and metal, and the outer planets are rich in low-density gases such as hydrogen and helium.See Answer
  • Q16:1)All the planets in the Solar System revolve in a clockwise motion.See Answer
  • Q17:Please explain to the class the questions below: Are these statements True or False? Justify your answer for one of them. 1. The neap tides occur at the new moon and full moon. 2. Spring tides occur during the new and full lunar phases. 3. Special relativity states the relationship between energy and mass as E = m0c2. 4. There is no gravity in space. 5. Newton's first law of motion is essentially a restatement of Galileo's law of inertia.See Answer
  • Q18:Problem 1. (15 points) Ptolemy vs Copernicus (1) In this problem and the next we will compare how Ptolemy and Copernicus handled the inner (or inferior) and outer (or superior) planets in their respective models of the Solar System. To keep things simple, we will neglect the planets' eccentricities for the purposes of these two problems. (a) As we discussed in class, in Ptolemy's geocentric model of the Solar System the centers of the epicycles for the inferior planets Mercury and Venus are tied to the motion of the Sun, in order to keep these two planets from 'wandering' too far away from the Sun in the sky. The maximum elongations (i.e., angular distance from the Sun) observed for Mercury and Venus are max 22.8° and 46.3°, respectively. Demonstrate that, in the Ptolemaic model, 0 max can be used to estimate the ratio of the radius of the epicycle, E for each planet to that of its deferent, D, but not their absolute values nor their ratios to the Earth-Sun distance. = (b) In the Copernican model, on the other hand, show that the orbital radius of an inferior planet is given by r = R sin max, where R is the Earth's orbital radius, or 1 Astronomical Unit (AU). Use the values of max given above to evaluate r for Mercury and Venus. Give your answers to 3 decimal places. (c) With the help of a diagram, calculate the minimum and maximum distances from the Earth for an inferior planet in the Ptolemaic model in terms of D and the parameter (max. (d) Do the same for the Copernican model, giving your results in terms of R and max. Show that the ratio of minimum to maximum distance is the same for both models. (Do this analytically, rather than numerically.) In this sense, the two models are equivalent, but Copernicus considered the inability to relate the orbital radii of Mercury & Venus to that of the Earth to be a major failing of the old model. Do you agree?See Answer
  • Q19:(a) The Greek astronomer Aristarchus, in the 3rd century BCE, is thought to have been the first person to have deduced the distance from the Earth to the Moon, using observations of lunar eclipses. Aristarchus first observed that the diameter of the Moon was approximately one-third of the diameter of the Earth's shadow, at the distance of the Moon. He also knew that the angular diameters of the Moon and Sun, as seen from the Earth, are almost exactly equal, based on observations of solar eclipses. With the aid of a sketch of the geometry of a lunar eclipse, show that these two observations imply that the physical diameter of the Moon is approximately one-quarter of the diameter of the Earth. (b) Now using the fact that the angular diameter of the Moon is close to 0.5°, or a little under 0.01 radians, estimate the distance of the Moon in units of the Earth's diameter ᎠᏯ . (c) About 19 centuries later, the Italian-French astronomer Giovanni Domenico Cassini attempted to estimate the distance to the Sun by combining observations of the planet Mars when it was closest to the Earth, against the background of distant stars, from two widely-separated places on Earth. (He used data from Paris and French Guyana in South America, having sent out an expedition for this purpose.) From these data he calculated that the difference in the direction to Mars would have been approximately 40 arcseconds, if it had been possible to observe it from the Earth's North and South poles simultaneously. [Recall that there are 3600" in 1°, or 206, 265" in one radian.] Assuming that the distance to Mars at the time was 0.5 AU, use this result to estimate the distance to the Sun (i.e., 1 AU) in terms of the Earth's diameter De. In fact, both of these estimates were quite accurate, for their times, and each became the standard value used by later astronomers for a century or more. Nowadays, we know the distance to the Moon accurate to a few centimeters, thanks to laser retro-reflectors left on its surface by the Apollo missions. The AU was not measured accurately until the advent of radar astronomy and interplanetary spacecraft in the 1960s, though many more attempts were made in the interim, mostly using transits of Venus to gauge the diameter of the Sun.See Answer
  • Q20:Consider a metric in a D-dimensional space. Evaluate the following expressions.See Answer
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"After using their service, I decided to return back to them whenever I need their assistance. They will never disappoint you and craft the perfect homework for you after carrying out extensive research. It will surely amp up your performance and you will soon outperform your peers."

Olivia

"Ever since I started using this service, my life became easy. Now I have plenty of time to immerse myself in more important tasks viz., preparing for exams. TutorBin went above and beyond my expectations. They provide excellent quality tasks within deadlines. My grades improved exponentially after seeking their assistance."

Gloria

"They are amazing. I sought their help with my art assignment and the answers they provided were unique and devoid of Original work. They really helped me get into the good books of my professor. I would highly recommend their service."

Michael

"The service they provide is great. Their answers are unique and expert professionals with a minimum of 5 years of experience work on the assignments. Expect the answers to be of the highest quality and get ready to see your grades soar."

Richard

"They provide excellent assistance. What I loved the most about them is their homework help. They are available around the clock and work until you derive complete satisfaction. If you decide to use their service, expect a positive disconfirmation of expectations."

Willow

TutorBin helping students around the globe

TutorBin believes that distance should never be a barrier to learning. Over 500000+ orders and 100000+ happy customers explain TutorBin has become the name that keeps learning fun in the UK, USA, Canada, Australia, Singapore, and UAE.