Sally and Sam are in a spaceship that comes to within 13,000 km of the asteroid Ceres. Determine the force Sally experiences, in N, due to the presence of the asteroid. The mass of the asteroid is 8.7 1020 kg and the mass of Sally is 74 kg. For calculation purposes, assume the two objects to be point masses. N?

The center of a moon of mass m is a distance D from the center of a planet of mass M. At some distance x from the center of the planet, along a line connecting the centers of planet and moon, the net force on an object will be zero. Derive an expression for x.

a.) Find the net force on the Moon (mM=7.35×1022kg)(mM=7.35×1022kg) due to the gravitational attraction of both the Earth (mE=5.98×1024kg)(mE=5.98×1024kg) and the Sun (mS=1.99×1030kg)(mS=1.99×1030kg), assuming they are at right angles to each other (Figure 1). Express your answer to three significant figures and include the appropriate units. Fnet= __________ ____________   b.) Determine the direction of the net force. Express your answer to three significant figures and include the appropriate units. θ= ______________ ___________

Tidal forces are gravitational forces exerted on different parts of a object by a second object. Their effects are particularly visible on Earth's surface in the form of tides. To understand the origin of tidal forces, consider Earth-Moon system to consist of two spherical bodies, each with a spherical mass distribution. Let RE be the radius of Earth, m be the mass of the Moon, and G be the gravitational constant. Part B Since the gravitational force between two bodies decreses with distance, the accelaeration a(near) experienced by a unit mass located at the point on the earth's surface closest to moon is slightly different from the acceleration a(far) experienced by a unit mass located at the point on the earth`s surface farthest from the moon. Give a general expresion for the quantity a(near)- a(far).