ASTR1000 Summer 2016 Assignment 1 Due: Tuesday, May 24 QUESTION 1 (3 points Question An asteroid orbiting the Sun has a perihelion distance of 4 astronomical units, and an aphelion distance of 12 astronomical units. a) What is the value of the semi-major axis? b) What is the eccentricity of the orbit? c) How long will it take the asteroid to make one complete orbit? QUESTION 2 (3 points): The Andromeda galaxy has an angular diameter along its long axis of 5.0 degrees. Its distance from us is about 2.2 million light-years. What is the linear diameter of the Andromeda galaxy? Give your answer in light-years. QUESTION 3 (3 points): The asteroid Cochine is a spherical rock with a radius of 20 km and a mass of 9.6 x 1016 kg. Calculate the escape velocity of Cochine in m/s. Some NHL players have a slapshot that exceeds 160 km/h (about 45 metres/second). If a player were on Cochine, could he shoot a puck fast enough so that it would escape from Cochise? QUESTION 4 (3 points): During the latter half of the 19th century, some astronomers thought that there might be a planet orbiting the Sun inside the orbit of Mercury. It was even given a name, Vulcan. We now know that there is no planet inside the orbit of Mercury, but if Vulcan did exist and had an orbit that was one-quarter the size of Mercury’s orbit, how many days would it take to orbit the Sun? Assignment 2 Due: Tuesday, June 7 QUESTION 1 (3 points): a) Given that the Sun is 150,000,000 km from Earth, how long does it take light to travel to the Earth from the Sun. Give your answer in minutes (min) b) The Cassini spacecraft currently in orbit about Saturn sends its data to Earth using radio waves. Assume that Saturn is at its closest approach to Earth. How long does it take the signals to reach Earth from Saturn? Give your answer it minutes (min). QUESTION 2 (3 points): A regular incandescent lightbulb radiates most strongly at a wavelength of 3000 nm. a) How hot is the filament? Give your answer in Kelvins (K) b) In which part of the spectrum does it emit the most radiation: visible, or infrared (heat)? QUESTION 3 (3 points): Assume Jupiter’s orbit is circular, and that the Earth is at the closest point it its orbit to Jupiter. You observe Callisto, the outermost large moon of Jupiter and notice that as it moves from its greatest distance from Jupiter on one side, to the greatest distance on the other side is 0.34 degrees. What is that distance in km? Assume Callisto’s orbit is circular; what is the semi-major axis of its orbit. QUESTION 4 (3 points): While observing Callisto, you notice that it takes it takes 16.7 days to make one orbit around Jupiter. Using the semi-major axis of its orbit from Question 3 to calculate the mass of Jupiter using Newton’s version of Kepler’s third law. Remember that in equations that contain, “G”, the gravitational constant, “a” has to be in metres and “P” has to be in seconds. Assignment 3 Due: Thursday, June 23 QUESTION 1 (3 points): Given that Pluto’s mass is 1.3 x 1022 kg and its radius is 1.1 x 106 metres. What is its average density? Give your answer in kg/m3. Using these units, the density of water is 1000 kg/m3 and iron is about 7000 kg/m3. Do you think that Pluto has a large core of iron like the Earth? QUESTION 2 (3 points): Seismic waves are partly reflected when they cross a boundary such as that between the “solid” mantle and the liquid outer core. Suppose a P wave has a constant speed of 8 km/s. 700 seconds after an earthquake near the surface, a seismograph at the site of the earthquake detects a reflected P wave. How far below the surface is the mantle–core boundary? Give your answer in km QUESTION 3 (3 points): Kinetic energy is the energy contained in an object because of its relative velocity to an observer. It is calculated quite easily as: € E = 1 2 mv 2 where m is the mass (in kg); v is speed (in m/s) and E is the energy (in joules). What is the energy of impact of a comet made of ice (density is 1000 kg/m3) if it has a radius of 1 km and strikes the Earth at 30 km/s. Give your answer in megatons of TNT (million of tons of TNT). One megaton of TNT has an energy equal to 4 x 1015 joules HINT: Remember to make sure your units are in kilograms, metres, and seconds HINT: mass = density multiplied by volume. For a spherical object, the volume is € 4 3 × π × r 3 where r is the radius QUESTION 4 (3 points): Repeat question 3 but with three changes: a) the impacting object is the same comet as in question 3, but it hits Earth head-on at 60 km/s. b) the object is an asteroid of the same size, but made of rock with a density of 4000 kg/m3 that hits the Earth at 30 km/s c) the asteroid in part b) hitting the Earth head-on at 60 km/s. NOTE: You do not have to completely redo the calculation you did in the previous question if you look at the formula for kinetic energy and see how energy is related to changes in mass and velocity.