Prove that the Earth is spherical by using the equations of analytical mechanics.
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Q: Around 2.5 centuries ago, several physicists of the time came up with the notion of a dark star.…
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Q: Calculate the dark star radius from the mass of the star and the escape speed. Answer in…
A: Mass , M = 2.4*1030 kg To find = radius
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- 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/kg2An exotic planet Vogsphere is known to have a mass that is 1/81 that of the Earth and a radius 0.25 that of the Earth. Astrophysicist Trillian built a rocket and decided to leave the planet and never to return. Given that the escape speed from the Earth is 11.2 km/s, with what speed must Trillian achieve his goal?Two binary stars orbit each other as shown below. If the period of both stars is 6.7 x 105s, r1= 9.0 x 1010m and r2= 4.0 x 1010m, determine m2.
- Needs Complete solution with 100 % accuracy.A solid uniform sphere has a mass of 4.00 x 10* kg and a radius of 1.5 m. (Use the following as necessary: r and m. Assume SI units. Do not enter units in your ansWers.) (a) What is the magnitude of the gravitational force due to the sphere on a particle of mass m located at a distance of 1.6 m from the center of the sphere? F = N. (b) What if it is 1.4 m from the center of the sphere? F = N. (c) Write a general expression for the magnitude of the gravitational force on the particle at a distancer 1.5 m from the center of the sphere. F = Additional Materials eBook Powers of TenBased on Kepler's laws and information on the orbital characteristics of the Moon, calculate the orbital radius for an Earth satellite having a period of 1.00h. What is unreasonable about this result?
- An undiscovered planet, many lightyears from Earth, has one moon in a periodic orbit. This moon takes 1810 × 103 seconds (about 21 days) on average to complete one nearly circular revolution around the unnamed planet. If the distance from the center of the moon to the surface of the planet is 255.0 × 106 m and the planet has a radius of 3.30 × 106 m, calculate the moon's radial acceleration ?cac.A certain quaternary star system consists of three stars, each of mass m, moving in the same circular orbit of radius r about a central star of mass M. The stars orbit in the same sense, and are positioned one-third of a revolution apart from each other. Show that the period of each of the three stars is given by the following expression. (Submit a file with a maximum size of 1 MB.) T = 2πt در G(M+ Choose File No file chosen m