8. Centripetal Forces & Gravitation

Determine the mean distance from Jupiter for each of Jupiter’s principal moons, using Kepler’s third law. Use the mean distance of Io and the periods given in Table 6–3. Compare your results to the values in Table 6–3.

The Near Earth Asteroid Rendezvous (NEAR) spacecraft, after traveling 2.1 billion km, orbited the asteroid Eros with an orbital radius of about 20 km. Eros is roughly 40km x 6km x 6km. Assume Eros has a density (mass/volume) of about 2.3 x 10³ kg/m³. Estimate the orbital period of NEAR around Eros, as if Eros were a sphere.

Large stars can explode as they finish burning their nuclear fuel, causing a supernova. The explosion blows away the outer layers of the star. According to Newton’s third law, the forces that push the outer layers away have reaction forces that are inwardly directed on the core of the star. These forces compress the core and can cause the core to undergo a gravitational collapse. The gravitational forces keep pulling all the matter together tighter and tighter, crushing atoms out of existence. Under these extreme conditions, a proton and an electron can be squeezed together to form a neutron. If the collapse is halted when the neutrons all come into contact with each other, the result is an object called a neutron star, an entire star consisting of solid nuclear matter. Many neutron stars rotate about their axis with a period of ≈ 1 s and, as they do so, send out a pulse of electromagnetic waves once a second. These stars were discovered in the 1960s and are called pulsars. How many revolutions per minute are made by a satellite orbiting 1.0 km above the surface?