GM + C cos 0 2 (παb)
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Derive Kepler’s third law of planetary motion from Eqs 12.37 and 12.43.
Reference to Equation 12.37:
Reference to Equation 12.43:
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- Nothing can escape the event horizon of a black hole, not even light. You can think of the event horizon as being the distance from a black hole at which the escape speed is the speed of light, 3.00×10^8 m/s, making all escape impossible. What is the radius of the event horizon for a black hole with a mass 3.5 times the mass of the sun?Around 2.5 centuries ago, several physicists of the time came up with the notion of a dark star. This was a star so dense, with so much gravity, that not even light could escape. The calculations used Newtonian mechanics. In class, we calculated the escape speed from the surface of the earth or the distance from the sun, and the mass of the planet or star. Here, the process is partially reversed. Calculate the dark star radius from the mass of the star and the escape speed. Answer in kilometers. c = 3*108 m/s M = 3.2*1030 kg G = 2/3 * 10-10 N*m2/kg2Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is V = 240 km/s and the orbital period of each is 12.1 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 x 1030 kg.) solar masses XCM M
- A 61 kg object experiences a gravitational field of size 2.9 N/kg. Calculate the gravitational force on the object. (Please answer to the fourth decimal place - i.e 14.3225)Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is V = 210 km/s and the orbital period of each is 11.5 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 x 1030 kg.) solar masses M XCM MImagine a particular exoplanet covered in an ocean of liquid ethane. At the surface of the ocean, the acceleration of gravity is 7.60 m/s2, and atmospheric pressure is 8.80 ✕ 104 Pa. The atmospheric temperature and pressure on this planet causes the density of the liquid ethane ocean to be 620 kg/m3. (a) What force (in N) is exerted by the atmosphere on a disk-shaped region 2.00 m in radius at the surface of the ocean? ______________ N (b) What is the weight, on this exoplanet, of a 10.0 m deep cylindrical column of ethane with radius 2.00 m? (Enter your answer in N.) _______________ N (c) What is the pressure (in Pa) at a depth of 10.0 m in the ethane ocean? ____________________ Pa
- The supermassive black hole at the center or our galaxy (Sagittarius A*) has a mass equal to 4.3 million Suns (the mass of the Sun is 1.99 × 1030 kg). The distance from Sgr A* to Earth is 7,940 parsecs, where one parsec is equal to 3.09 × 1016 m. (a) What is the gravitational force that Sgr A* exerts on a 75 kg person on Earth, in units of Newtons? Hint: use Newton's law of universal gravitation. (b) Suppose the same person is sitting 1.0 meter away from a paperclip with a mass of 1.0 grams. What is the gravitational force that the paperclip exerts on the person? (c) Compare the forces from parts (a) and (b). Which is greater?Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is |v| 190 km/s and the orbital period of each is 12.9 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 x 1030 kg.) solar masses M XCM MI have tried 16.7x10^3, 16.7x10^4, and 1.365x10^8 and those are all wrong for the first part. I know that the second part is 14.3 hr. I need to know the km/s. Thank you!!