Calculate the size of the Schwarzschild radius for the Sun. Choose the option below that most closely matches your answer. Select one: O a. 20 km O b. 1 km O C. 3 m O d. 3 km

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White Dwarf Size II. The white dwarf, Sirius B, contains 0.98 solar mass, and its density is about 2 x 106 g/cm?. Find the radius of the white dwarf in km to three significant digits. (Hint: Density = mass/volume, and the volume of a 4 sphere is Tr.) 3 km Compare your answer with the radii of the planets listed in the Table A-10. Which planet is this white dwarf is closely equal to in size? I Table A-10 I Properties of the Planets ORBITAL PROPERTIES Semimajor Axis (a) Orbital Period (P) Average Orbital Velocity (km/s) Orbital Inclination Planet (AU) (106 km) (v) (days) Eccentricity to Ecliptic Mercury 0.387 57.9 0.241 88.0 47.9 0.206 7.0° Venus 0.723 108 0.615 224.7 35.0 0.007 3.4° Earth 1.00 150 1.00 365.3 29.8 0.017 Mars 1.52 228 1.88 687.0 24.1 0.093 1.8° Jupiter 5.20 779 11.9 4332 13.1 0.049 1.30 Saturn 9.58 1433 29.5 10,759 9.7 0.056 2.5° 30,799 60,190 Uranus 19.23 2877 84.3 6.8 0.044 0.8° Neptune * By definition. 30.10 4503 164.8 5.4 0.011 1.8° PHYSICAL PROPERTIES (Earth = e)…

4.) The sun, Earth, and Jupiter are aligned in a straight line. Using the average distances from table 11.1 determine the following: a.) what is the distance between Earth and Jupiter in uniters of metres? (show all work) b.) what is the gravitational attraction between Earth and Jupiter in units of Newton's? (show all work)  Object Avg. Radius (m) Mass (kg) Mean sun to planet distance (m) Sun 6.96 x 108 1.99 x 1030 --- Earth  6.38 x 106 5.97 x 1024 1.50 x 1011 Jupiter 7.15 x 107 1.90 x 1027  7.78 x 1011

Mean anomaly A satellite is in an orbit with a semi-major axis a of 8,500 km and an eccentricity e of 0.1. The satellite's eccentric anomaly at time t, is E, 26 d 12 m 46.2 s. Calculate (to the nearest 0.1 s) the satellite's mean anomaly at t2, which is half an hour after t II. Assume GM = 3.986005 x 1014 m³/s² for your computations. Provide units for intermediate and final results!

Four research teams measured the rotation period of a newly detected neutron star, and what each team wrote in its team notebook is shown in the table below. Suppose a later and more reliable measurement gives 0.250 s for the period of the same star. Decide which of the earlier measurements was the most accurate. and which was the most precise. most precise measurement what was written most accurate team in the notebook measurement "0.270st 1.0% "0.25s "0.290s t0.002s" D. "between 0.19s and 0.23s

Star A and Star B are a bound binary at a distance of 20 pc from the Earth. Their separation is 30 AU. Star A has a mass twice that of Star B. The orbital period of the binary is 100 years. Assume the stars orbit in circular orbits. a. What is the parallax of Star A, in units of arcsec? Assume parallax is measured from the Earth. For part a, ignore the presence of the binary companion. b. What is the angular separation we would observe between Star A and Star B, in units of arcsec? If we compare multiple images of this star system taken across different months and years, which source of motion will be the dominant effect? What is the total mass of the binary system (combined mass of Star A and Star B)? Provide your answer in both kg and solar masses. c. d. What is the distance from Star A to the center of mass of the binary system?

5. A planet of mass m is located on a line equidistant from two identical stars of mass M, located at I = +d, as shown. a) Obtain the equation of motion of the planet. b) Describe the motion (in words). M M

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Pointers: 1. Use 6 decimals for the value of K when solving applications. 2. Format of answer: Provide 2 decimals and place a space before the unit. Example: 123.45_m 3. No unit for population 4. When writing equations with e, provide no space and write exp. Example: u=70-52exp(-0.29t) OBJECTIVES: 1. Determine the velocity of escape of a particle on Ganymede considering g-6.1x10^-3 miles/s^2. The acceleration of gravity at surface is 0.12g and the size of Ganymede is roughly 3560miles. From what pattern was Bernoulli's differential equation derived from? In Bernoulli's DE, the value of n should not be equal to 0 or 1. What is the end De, if n =0? 2. 3. 4. In the following DE, (3x+6y+2)dx-(2x+4y)dy, what should be the first substitution? 5. In the following DE, (3x+6y+2)dx+(2x+4y)dy, what method can be used? 6. What is the integrating factor for the homogenous DE, (dz/dx)+zcot x = -x PROBLEM SOLVING 1: A substance from outdoors with temperature of 18 degrees Celsius was brought inside…