# Phys 1830: Lecture 3 Previous Class: What are Outreach Images This Class: Scient

## Phys 1830: Lecture 3 Previous Class: What are Outreach Images This Class: Scient

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The Vastness of the Universe How do we scientifically know the sizes of astronomical objects How do we make measurements on the sky The Vastness of the Universe: Angular Size Eclipse of the sun by the moon Valleys on moon Baileys Beads Sun has ejections of loops of gas, called prominences The sun in addition to the moon have a similar angular diameter Oscar Martin Mesonero (OSAE/SAROS Group) Angular Diameter As the moon orbits the Earth it sometimes aligns with the sun causing the shadow of the moon to fall on the Earth The angular diameter is the angle between one side in addition to the other of an object. This is not the same as the linear diameter.

Angular Diameter The linear diameter of the moon in addition to the sun are very different. Question: Lets try a prediction. If the Earth was much closer to the sun, when they were aligned our moon would appear to more than cover all of the sun. cover a fraction of the sun. cover the same amount of the sun that it does now. Total Solar Eclipse Because the angular sizes are similar we can see the atmosphere of the sun during an eclipse. http://www.saros.org/ has an animation http://antwrp.gsfc.nasa.gov/apod/ap090726.html Copyright Koen van Gorp Copyrighted images will be removed on posted powerpoints.

Why do we use angular measurements Point a camera at the night sky. Open the shutter as long as several hours. The result is that the stars leave their trail across the sky. http://www.cfht.hawaii.edu/HawaiianStarlight/monthlysequence-0904.html Angular Measurements. Measuring the size of the moon means that we measure an arc giving us an angular diameter. Angular Measurements. Measuring the distance between stars means that we measure an arc. These arcs lead to the concept of Celestial Sphere

The Concept of Celestial Sphere All objects are at the same very large distance from the Earth such that they are projected on to an imaginary celestial sphere. Measurements on the Celestial Sphere Measurements are angular There as long as e we use units of arc Units of Arc Complete circle = 360 degrees 1 degree = 60 minutes of arc = 60 (arcmin) 1 arcmin = 60 seconds of arc = 60 (arcsec)

Relationship between time in addition to angular sizes: The Earth rotates 360 degrees in 24 hours (such that it looks like the sky rises in addition to sets). The Earth rotates 15 deg/hr in addition to 15 arcsec/sec of time. Measure the time from the sky: Can determine the exposure time: 135 deg (visually roughly 1/3 of a circle) [135 deg/360 deg] 24 hr = 9 hr Practise! Look at the images in this lecture in addition to estimate from the arcs on the sky, the length of time of the exposure. Angular Measurement: At arms length, your thumb (or a penny) is about 1-2 degrees wide. Estimate the angular size of this image of the moon using your thumb.

Angular Measurement: Which part of the room estimates the larger size Back of room Front of room Middle of room Angular Measurement: Given objects with the same linear size, this implies that if an object appears to have a smaller the angular size, then it is further away. Linear Measurements How do we go from angular measurements on the sky to knowing the linear diameters of planets, as long as example, or the distances between stars Distance Geometry

Linear Measurements: Geometry Draw 2 imaginary circles Circumference = 2 pi Radius Revolution = 360 degrees The fraction of the outer circle covered by the diameter of the object is equal to the fraction of the inner circle covered by the angular diameter. Linear Measurements: Geometry Linear diameter angular diameter — = —- 2 pi R 360 degrees Linear Measurements: Geometry Notice that the radius of the outer circle is equal to the distance to the object: Linear diameter angular diameter — = —- 2 pi Distance 360 degrees

Linear Measurements The linear diameter is: 2 pi Distance linear diameter = — angular diameter 360 degrees Measure the angular diameter Measure the distance Put these in the equation Gives the linear diameter! Re-arrange the equation so the calculated parameter is on the left. How many people found this easy Easy O.K. Hard Would you like to tutor your peers I do not know how to re-arrange an equation. True False