Topic: Discuss astronomical latitude and longitude and how these can be determined Primary Aim: Give students enough information for them to be able to make a latitude and longitude of some location on campus. The results will be handed on Monday October 10. Discussion So far students should know what the different types of latitude and longitude are and that astronomical latitude is measured relative to the local gravity vector. The discussion today is how to make measurements that will allow latitude and longitude to be determined. Start this discussion with thoughts about what the stars do when you watch them at night. The trace circles in the sky and the circles are centered on the rotation axis projected into space. If the angle between the rotation axis and the direction of gravity could be measured then the latitude can be determined (at least relative to an equator plane defined to be perpendicular to the rotation axis. Since polar motion is only about 10 meters, this method in principle can determine your latitude within 10 meters. In the Northern hemisphere there is a star near the rotation axis (the North Star). When this star is observed, the radius of the circle that it maps out is very small. In the southern hemisphere, there is no such star. So one method of determining latitude is to pick a star. When it is at its highest elevation, note the angle between the star and the direction on gravity. Wait 12-hours until the star is at its lowest elevation angle and measure the elevation angle again. The average of the two angles will be the elevation of the rotation axis, which is a direct measure of the latitude. Stars that remain above the horizon are called circum-polar stars. (The stars in this category depend on your latitude.) The above technique only words in winter unless a telescope is used. (It is easy to see stars during day light with a telescope. Also in places like Boston it can be difficult to see the stars . To make life easy, the positions on many stars have been measured by astronomers, basically be measuring how far they are away from the rotation axis. (Actually they appear to change their positions with time because the rotation axis moves in space due to the gravitational torque on the equatorial bulge by the sun and moon. Many stars are also close enough that we can see them move (called proper motion). The coordinates of stellar objects are given in an equator-based system called right ascension (like longitude except the X-axis is given by the intersection of the equator plane and orbit plane of the Earth: The latter is called the ecliptic), and declination (like latitude). So when a star whose coordinates are known, the elevation angle of the star at its highest or lower point can be used to determine latitude To determine longitude, you need know the time when the star crosses the meridian. The meridian crossing time of stars are tabulated for Greenwich and the time difference tells you the longitude (in time units which can be multiplied by 15 to get degrees). There is a very good star to use and this is the sun. Its declination changes through out the year because of the tilt of the Earth’s equatorial plane (figure again in 12.215 Lec 05). There is however two special times when the sun is very easy to use: The fall and spring equinoxes. The fall equinox occurs on Sep 23: a day when there are no classes. At the equinoxes, the sun is in the equator plane of the earth and so its declination is zero. A simple measure of the elevation angle to the Sun at its highest elevation is a direct measure of the latitude (90 minus the elevation angle is the latitude). The longitude is reasonably easy the get if the time is know when the sun reaches its highest point. Nominally this would be 12:00 noon but when your time is corrected for the Boston time zone, it will not be exactly this value due to the longitude difference from Greenwich. An important correction here is the equation of time (12.215 notes), which cause noon at Greenwich to vary –14 to +16 minutes around the clock time noon. This needs to be corrected for.