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Show that if you estimate a spherical gravitating system as being of constant density equal to...
A satellite of mass m is in a circular orbit of radius R2 around a spherical planet of radius R1 made of a material with density ρ. ( R2 is measured from the center of the planet, not its surface.) Use G for the universal gravitational constant.
A satellite of mass m is in a circular orbit of radius R2 around a spherical planet of radius R1 made of a material with density ρ. ( R2 is measured from the center of the planet, not its surface.) Use G for the universal gravitational constant.A) Find the kinetic energy of this satellite, KExpress the satellite's kinetic energy in terms of G, m, π, R1, R2, and ρ.B) Find U, the gravitational potential energy of the satellite. Take the gravitational potential...
2. Assume the earth is a uniform sphere of mass M and radius R. (Its mass-density...
2. Assume the earth is a uniform sphere of mass M and radius R. (Its mass-density ρ--M/V is therefore constant.) a) Find the force of gravity exerted on a point mass m located inside the earth, as a function of its distance from the earth's centre. (You may make use of results derived in class for a thin spherical shell.) b) Find the difference in the gravitational potential energy of the mass, between the centre of the earth and the...
Consider the expression for potential energy at the surface of a spherical mass GMm R. Р.Е....
Consider the expression for potential energy at the surface of a spherical mass GMm R. Р.Е. where M is the mass and R is the radius of the spherical mass, and m is the mass of some object at the surface. Show that the difference between this potential and that of an object a distance h above the surface is mgh, where g is a constant that is the same for any m or h. Derive an expression for g...
B.2 This question concerns the possible tidal disruption of a spherical moon on a circular orbit of radius r about a ho...
B.2 This question concerns the possible tidal disruption of a spherical moon on a circular orbit of radius r about a host planet. The planet has mass Mp, radius R and mean density pp; the moon has mass M, radius Rm rand mean density Pm You may ignore any forces beyond the moon-planet system. (i) Show that tidal forces lead to a differential acceleration, between the face of the moon closest to the planet and the moon's centre, of amplitude...
Answer the questions below by assuming the spherical mass distribution of dark matter in our Galaxy,...
Answer the questions below by assuming the spherical mass distribution of dark matter in our Galaxy, where the Galactic radius is 100,000 light years, the distance of the solar system from the center is 27,000 light years, and the constant orbital speed of stars is 220 km s1. Use the gravitational constant 6.674 x 10-11 N m2 kg2, light year 9.46 x 1015 m, and solar mass 2.0 x 1030 kg. 1. show the mass of dark matter inside radius...
After our Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a...
After our Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state, in which it has approximately the same mass as it has now but a radius equal to roughly the size of the Earth's radius. (a) Calculate the average density of this white dwarf if the Sun were to collapse to a radius of 6.25 x 10°m. kg/m (b) Calculate the free-fall acceleration at its surface. m/s2 (c) Calculate the gravitational potential...
After our Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a...
After our Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state, in which it has approximately the same mass as it has now but a radius equal to roughly the size of the Earth's radius. (a) Calculate the average density of this white dwarf if the Sun were to collapse to a radius of 6.18 x 10 m. O kg/m3 (b) Calculate the free-fall acceleration at its surface. Cm/s2 (c) Calculate the...
I just need from part 2 and on A rod of total length L 5m is...
I just need from part 2 and on
A rod of total length L 5m is positioned upside down (that is vertically). Its lower end is at L 0 coordinate and its higher end is at y JL 5m coordinate. The mass of the rod is not uniformly distributed and it has position dependent mass density given by the formula por 2y2 1 ml where y is the coordinate of a rod point essentially the distance of the point from...
3questions in total please *Problem 6.66 You stand on a spherical asteroid of uniform density whose...
3questions in total please
*Problem 6.66 You stand on a spherical asteroid of uniform density whose mass is 2.5 x 1016 kg and whose radius is 11 km (11 x 103 m). These are typical values for small asteroids, although some asteroids have been found to have much lower average density and are thought to be loose agglomerations of shattered rocks. You want to figure out how fast you have to throw the rock so that it never comes back...
Question 1 (10 marks) (a) (4 marks) Recall that the gravitational potential energy for two masses...
Question 1 (10 marks) (a) (4 marks) Recall that the gravitational potential energy for two masses is Ug-GMm Use this fact to show that the virial theorem holds for a mass m, executing uniform circular motion about a much larger mass M (b) (3 marks) The potential energy of a collection of N particles each of mass m in a region with radius R can be written as Use this expression to derive a mass estimate for the virialized system...
2. Assume the earth is a uniform sphere of mass M and radius R. (Its mass-density ρ--M/V is therefore constant.) a) Find the force of gravity exerted on a point mass m located inside the earth, as a function of its distance from the earth's centre. (You may make use of results derived in class for a thin spherical shell.) b) Find the difference in the gravitational potential energy of the mass, between the centre of the earth and the...
Consider the expression for potential energy at the surface of a spherical mass GMm R. Р.Е. where M is the mass and R is the radius of the spherical mass, and m is the mass of some object at the surface. Show that the difference between this potential and that of an object a distance h above the surface is mgh, where g is a constant that is the same for any m or h. Derive an expression for g...
B.2 This question concerns the possible tidal disruption of a spherical moon on a circular orbit of radius r about a host planet. The planet has mass Mp, radius R and mean density pp; the moon has mass M, radius Rm rand mean density Pm You may ignore any forces beyond the moon-planet system. (i) Show that tidal forces lead to a differential acceleration, between the face of the moon closest to the planet and the moon's centre, of amplitude...
Answer the questions below by assuming the spherical mass distribution of dark matter in our Galaxy, where the Galactic radius is 100,000 light years, the distance of the solar system from the center is 27,000 light years, and the constant orbital speed of stars is 220 km s1. Use the gravitational constant 6.674 x 10-11 N m2 kg2, light year 9.46 x 1015 m, and solar mass 2.0 x 1030 kg. 1. show the mass of dark matter inside radius...
After our Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state, in which it has approximately the same mass as it has now but a radius equal to roughly the size of the Earth's radius. (a) Calculate the average density of this white dwarf if the Sun were to collapse to a radius of 6.25 x 10°m. kg/m (b) Calculate the free-fall acceleration at its surface. m/s2 (c) Calculate the gravitational potential...
After our Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state, in which it has approximately the same mass as it has now but a radius equal to roughly the size of the Earth's radius. (a) Calculate the average density of this white dwarf if the Sun were to collapse to a radius of 6.18 x 10 m. O kg/m3 (b) Calculate the free-fall acceleration at its surface. Cm/s2 (c) Calculate the...
I just need from part 2 and on
A rod of total length L 5m is positioned upside down (that is vertically). Its lower end is at L 0 coordinate and its higher end is at y JL 5m coordinate. The mass of the rod is not uniformly distributed and it has position dependent mass density given by the formula por 2y2 1 ml where y is the coordinate of a rod point essentially the distance of the point from...
3questions in total please
*Problem 6.66 You stand on a spherical asteroid of uniform density whose mass is 2.5 x 1016 kg and whose radius is 11 km (11 x 103 m). These are typical values for small asteroids, although some asteroids have been found to have much lower average density and are thought to be loose agglomerations of shattered rocks. You want to figure out how fast you have to throw the rock so that it never comes back...
Question 1 (10 marks) (a) (4 marks) Recall that the gravitational potential energy for two masses is Ug-GMm Use this fact to show that the virial theorem holds for a mass m, executing uniform circular motion about a much larger mass M (b) (3 marks) The potential energy of a collection of N particles each of mass m in a region with radius R can be written as Use this expression to derive a mass estimate for the virialized system...
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