Consider a satellite in elliptical orbit around a planet of mass M, and suppose that physical units are so chosen that GM D 1 (where G is the gravitational constant). If the planet is located at the origin in the xy-plane, then Explain the equations of motion of the satellite?

In this problem, you are going to explore three different ways to determine the gravitational constant G.  a) By observing that the centripetal acceleration of the Moon around the Earth is ac = 2.66 × 10-3 m/s2, what is the gravitatonal constant G, in cubic meters per kilogram per square second? Assume the Earth has a mass of ME = 5.96 × 1024 kg, and the mean distance between the centers of the Earth and Moon is rm = 3.81 × 108 m.   b) Measuring the centripetal acceleration of an orbiting object is rather difficult, so an alternative approach is to use the period of the orbiting object. Find an expression for the gravitational constant in terms of the distance between the gravitating objects rm, the mass of the larger body (the earth) ME, and the period of the orbiting body T.   c) The gravitational constant may also be calculated by analyzing the motion of an object, launched from the surface of the earth at an initial velocity of vi. Find an expression of the gravitational constant…

Consider a satellite in elliptical orbit around a planet of mass M, and suppose that physical units are so chosen that GM D 1 (where G is the gravitational constant). If the planet is located at the origin in the xy-plane, then Explain the equations of motion of the satellite? Let T denote the period of revolution of the satellite. Kepler’s third law says that the square of T is proportional to the cube of the major semiaxis a of its elliptical orbit. In particular, if GM D 1, then?

a square of edge length 20.0 cm is formed by four spheres of masses m1 = 5.00 g, m2 = 3.00 g, m3 = 1.00 g, and m4 = 5.00 g. In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 2.50 g?

It is found that when a particular object with a mass of 0.41 kg is released from rest while immersed within a certain substance, the coefficient of proportionality regarding the resistive force is 0.621 kg/s. What is the magnitude of the resistive force that acts on this mass 1.49 s after being released? Let the resistive force be given by R = -bv  (Assume that the gravitational force also acts)

Here, (G = 6.67×10−11N m2/kg2) is the universal gravitational constant, (M) is the mass of the object,and (r) is its radius. For example, the mass of the Earth is (M = 6×1024kg) and the radius is (r = 6.4×106m). Thus, the surface gravity of Earth is:g=(6.67×10−11×6×1024(6.4×106)2)m/s2= 9.8 m/s2ObjectMassRadiusMercury3.3×1023kg2.4×106mVenus4.9×1024kg6.1×106mMars6.4×1023kg3.4×106mJupiter1.9×1027kg7.0×107mSaturn5.7×1026kg5.8×107mUranus8.7×1025kg2.5×107mNeptune1.0×1025kg2.5×107m ProcedureFor each of the planets listed above, compute the surface gravity in m/s21

A ring of radius 6.5 m lies in the x-y plane, centered on the origin. The portions of the ring in the first and third quadrants have a mass density of 3.6 kg/m, while the portions of the ring in the second and forth quadrants have a mass density of 9.5 kg/m. Find the z component of the gravitational field due to the ring at a point P on the z axis a distance 6 meters from the origin.Use G = 6.673E-11 N m2/kg2.

In introductory physics laboratories, a typical Cavendish balance for measuring the gravitational constant G uses lead spheres with masses of 1.90 kg and 19.0 g whose centers are separated by about 2.60 cm. Calculate the gravitational force between these spheres, treating each as a particle located at the center of the sphere.

In introductory physics laboratories, a typicalCavendish balance for measuring the gravitational constant G uses lead spheres of masses1.68 kg and 14.4 g whose centers are separatedby 2.7 cm.Calculate the gravitational force betweenthese spheres, treating each as a point masslocated at the center of the sphere. Thevalue of the universal gravitational constantis 6.67259 × 10−11 N · m2/kg2.Answer in units of N.