1. Planet A has a period of 1 year and an average distance from the sun of 1.63 × 1011 meters. If the average distance from the sun for planet B is 0.53 × 1011 meters, what is its period to the nearest hundredth of a year? 2. Two objects attract each other gravitationally with a force of when they are 0.25 m apart. Their total mass is 4.0 kg. Find their individual masses. 3. Because the Earth rotates once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this? 4. How long would a day be if the Earth were rotating so fast that objects at the equator were apparently weightless? 5. Jupiter is about 320 times as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can’t survive more than a few g’s. Calculate the number of g’s a person would experience at the equator of such a planet. Use the following data for Jupiter: equatorial rotation Take the centripetal acceleration into account. 6. Astronomers using the Hubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be at a distance of 60 light-years from the core. Deduce the mass of the core, and compare it to the mass of our Sun.