two particles, of masses m and 2m, are fixed in place on an axis. (a) Where on the axis can a third particle of mass 3m be placed (other than at infinity) so that the net gravitational force on it from the first two particles is zero: to the left of the first two particles, to their right, between them but closer to the more massive particle, or between them but closer to the less massive particle? (b) Does the answer change if the third particle has, instead, a mass of 16m? (c) Is there a point off the axis (other than infinity) at which the net force on the third particle would be zero?

consider particle A of mass mA being somewhere between particle B of mass mB=2000 kg and particleS of mass mc=1000 kg, at just the right distance so that gravitational attraction to particle B and gravitational attraction to particle C are equal. Is this location nearer Particle B or nearer particle C?

Consider two nearly spherical Soyuz payload vehicles, in orbit about Earth, each with mass 9000 kg and diameter 4.0 m. They are initially at rest relative to each other, 10.0 m from center to center. Determine the gravitational force between them and their initial acceleration. Estimate how long it takes for them to drift together, and how fast they are moving upon impact. (5.4 x 10-5 N, 1.7 x 104s, 3.6 x 10-4 m/s)

A planet of mass 5 ⨯ 1024 kg is at location <4 ⨯ 1011, −4 ⨯ 1011, 0> m.  A star of mass 4 ⨯ 1030 kg is at location <−6 ⨯ 1011, 4 ⨯ 1011, 0> m. (a) What is the relative position vector pointing from the planet to the star? (b) What is the distance between the planet and the star? (c) What is the unit vector in the direction of r? (d) What is the magnitude of the force exerted on the planet by the star?(e) What is the magnitude of the force exerted on the star by the planet? (f) What is the force (vector) exerted on the planet by the star? (g) What is the force (vector) exerted on the star by the planet? (Note the change in units.)