Chapter 5, Problem 5.5P

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?

An average-sized asteroid located 5.0107km from Earth with mass 2.01013kg is detected headed directly toward Earth with speed of 2.0km/s . What will its speed be just before it hits our atmosphere? (You may ignore the size of the asteroid.)

Show that the period of orbit for two masses, m1 and m2 , in circular orbits of radii r1 and r2 , respectively, about their common center-of mass, is given by T=2r3G(m1+m2) where r=r1+r2 . (Hint: The masses orbit at radii r1 and r2 , respectively where r=r1+r2 . Use the expression for the center-of-mass to relate the two radii and note that the two masses must have equal but opposite momenta. Start with the relationship of the period to the circumference and speed of orbit for one of the masses. Use the result of the previous problem using momenta in the expression for the kinetic energy.)

Check Your Understanding By what factor must the radius change to reduce the orbital velocity of a satellite by one-half? By what factor would this change the period?

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?

Why can a squirrel jump from a tree branch to the ground and nm away undamaged, while a human could break a bone in such a fall?