After the NEAR spacecraft passed Mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid Eros, the final destination for the mission. After getting close to Eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 103 m) around the asteroid. So much propellant had been used that the final mass of the spacecraft while in circular orbit around Eros was only 480 kg. The spacecraft took 1.04 days to make one complete circular orbit around Eros. Calculate what the mass of Eros must be. g

Glass is transparent to visibile light under normal conditions; however, at extremely high intensities, glass will absorb most of the light incident upon it. this works through a process known as multiphoton absorption. in this process, several photons are absorbed at the same time. if very intense light whose photons carry 2ev of energy is shined onto a material with a band gap of 4ev, that light can be absorbed through two-photon absorption, because two photons have the right amount of energy to bridge the band gap. what is the minimum number of photons of 800-nm light that are needed to equal or exceed the band gap of fused silica glass

Gather reliable information to brent make his decision. to gather this information, use newspapers, call insurance companies or look at their web sites, and review consumer magazines and web sites. also, look at the manufacturer web site or for information about gas mileage. list the sources you use and take notes.

Global warming will produce rising sea levels partly due to melting ice caps but also due to the expansion of water as average ocean temperatures rise. to get some idea of the size of this effect, calculate the change in length of a column of water 1.00 km high for a temperature increase of 1.00ºc. note that this calculation is only approximate because ocean warming is not uniform with depth. (answer in ×10^{-3} −3 m)