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)

What is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable about this result?

Show that the areal velocity for a circular orbit of radius r about a mass M is At=12GMr . Does your expression give the correct value for Earth’s areal vilocity about the Sun?

Check Your Understanding Assume you are in a spacecraft in orbit about the Sun at Earth’s orbit, but far away from Earth (so that it can be ignored). How could you redirect your tangential velocity to the radial direction such that you could then pass by Mars’s orbit? What would be required to change just the direction of the velocity?

Estimate the gravitational force between two sumo wrestlers, with masses 220 kg and 240 kg, when they are embraced and their centers are 1.2 m apart.

Assuming a circular orbit for the Sun about the center of the Milky Way galaxy, calculate its orbital Speed using the following information: The mass of the galaxy is equivalent to a single mass times that at the Sun (or located 30,000 ly away.

Compute directly the gravitational force on a unit mass at a point exterior to a homogeneous sphere of matter.

A Molniya orbit is a highly eccentric orbit of a communication satellite so as to provide continuous communications coverage for Scandinavian countries and adjacent Russia. The orbit is positioned so that these countries have the satellite in view for extended periods in time (see below). If a satellite in such an orbit has an apogee at 40,000.0 km as measured from the center of Earth and a velocity of 3.0 km/s, what would be its velocity at perigee measured at 200.0 km altitude?

Check Your Understanding If we send a probe out of the solar system starting form Earth’s surface, do we only have to escape the Sun?