Φ(r) GM (r² +r²)¹/2
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The Plummer sphere is a model for some star clusters, and it has the gravitational potential as given in the provided image. M and rp are both constant.
What is the density profile ρ(r)? When the Plummer sphere is observed from a large distance along the z axis, what is its surface density, Σ(R), where R is the distance from the center?
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- The typical core-collapse supernova has an energy budget of about 1046 J. This energy comes from the gravitational potential energy of an inner core with mass Mic, which collapses from an initial radius of 5 x 106 m down to the final radius of 50 km. Estimate Mic, in solar masses, for this to be a realistic energy source of the core-collapse supernova. You may assume that the density before the collapse is uniform. Discuss briefly how a Type la supernova is different from a core-collapse supernova from a massive star?The most mass of our Milky Way is contained in an inner region close to the core with radius Ro. Because the mass outside this inner region is almost constant, the density distribution can be written as following (assume a flat Milky Way with height zo): { r Ro Po, p(r) = 0, (a) Derive an expression for the mass M(r) enclosed within the radius r. (b) Derive the expected rotational velocity of the Milky Way v(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: Vobs (r) = VGT Po z0 Ro 5/2 1+e-4r/Ro 4 Draw the expected and observed rotational velocity into the plot below:Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer. and and Very very grateful!
- If theta dot is the slew rate, what would be the maximum slew rate? How would you differentiate theta dot to get theta double dot?Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer. and and Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer. and and Very very grateful!
- Use the Widmark Equation, , to solve this question. Recall that r = 0.68 for men and r = 0.55 for women. B = percentage of BACN = number of “standard drinks” (A standard drink is one -ounce beer, one -ounce glass of wine, or one -ounce shot of liquor.) N should be at least one.W = weight in poundsr = the distribution rate for alcohol through the body (this value is a constant), for males and for femalest = number of hours since the first drink A male student had four glasses of wine at a party. He weighs 172 pounds. How long will it take before his BAC falls to 0.05? 3.14 hours 3.57 hours 1.00 hours 4.29 hoursPlease do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer. and and Very very grateful!/dsinė A beam of electrons is shot towards a material X with a crystalline structure. A diffraction pattern is observed corresponding to a distance d=0.15 nm. between two adjacent Bragg planes. The electrons are each sent in with a kinetic energy of 51.900000000000006 eV. Part a) Find the de Broglie wavelength in nanometres of an electron incident on the material X.
- As we have been slowly discovering more and more about the atoms we have encountered several different models of the atoms. All of these models have issues. One of the most common issues is the scale of the subatomic particles. Like the image below The proton in this model is too large. Given the following measurement, how many protons would need to set side-by-side to to equal the width of a hydrogen atom? The radius of a proton is 0.5636 fm (Femtometer). The diameter of a hydrogen atom is 7.5 Angstroms. must be written in Scientific noation.What diameter telescope is needed to resolve the separation between an Earth-like planet and its star at 550 nm if the linear separation between them is 1 AU and the star system is 4 pc from Earth? (Give your answer in m.) mUse Wien's Law to calculate the peak wavelength of light coming from the Sun. Assume T=5800 K for the surface temperature of the Sun. Wein's displacement law says that the blackbody temperature and peak wavelength multiplied together give a constant of 0.29 cm-K. (K is degrees Kelvin). Convert the wavelength from part A into a frequency. The product of wavelength and frequency for electromagnetic radiation is a constant, the speed of light (c), 3 x 10^10 cm/s.