The orbit in space of one body around another, such as a planet around the Sun, need not be circular. In general it takes the form of an ellipse, with the body sometimes closer in and sometimes further out. If you are given the distance 21 of closest approach that a planet makes to the Sun, also called its perihelion, and its linear velocity v1 at perihelion, then any other property of the orbit can be calculated from these two as follows a) Kepler's second law tells us that the distance &2 and velocity v2 of the planet at its most distant point, or aphelion, satisfy l202 - L1v1. At the same time the total energy, kinetic plus gravitational, of a planet with velocity v and distance r from the Sun is given by where m is the planet's mass, M-1.9891 x 1030 kg is the mass of the Sun, and G 6.6738 x 10-11 m3 kg 1 s-2 is Newton's gravitational constant. Given that energy must be conserved, show that v2 is the smaller root of the quadratic equation 2 2GM Once we have v2 we can calculate £2 using the relation l2- L1v1/v2.

answer(a) occurs after your prediction;

a  social news website  is an  internet  website  that features  user-posted stories. such stories are ranked based on popularity, as voted on by other users of the site or by website administrators. users typically comment online on the news posts and these comments may also be ranked in popularity. since their emergence with the birth of  web 2.0, social news sites have been used to link many types of information, including news, humor, support, and discussion. all such websites allow the users to submit content and each site differs in how the content is moderated. on the  slashdot  and  fark  websites,  administrators  decide which articles are selected for the front page. on  reddit  and  digg, the articles that get the most votes from the community of users will make it to the front page. many social news websites also feature an online comment system, where users discuss the issues raised in an article. some of these sites have also applied their voting system to the comments, so that the most popular comments are displayed first. some social news websites also have a  social networking  function, in that users can set up a user profile and follow other users' online activity on the website.