応用天文学

Math is the language of science, and with it, astronomers can describe many aspects of how the Universe functions.  In this ongoing class, students will get to apply math skills to various astronomical questions such as how distances are calculated, how to use ratios to find sizes of geographical features of other planets and moons, and how we can calculate travel times and communication times to the planets in the Solar System.

PREREQUISITES: This is an intermediate to advanced class. Students are encouraged to bring a calculator to class. However, they should also have a solid foundation in multiplication, division, and algebra because we will use these skills often to manipulate of equations and solve for variables. While geometry, angles, and some trigonometric functions will be discussed and utilized, it will be at a basic level.

Each week, students will be guided through the mathematical steps astronomers use and will gain an appreciation for their practical value. Classes are not built upon previous material and students are welcome to join at any time. For each class, students will be provided with a worksheet to follow along with during class. **Some questions on the worksheet will be left for students to get additional practice outside of class.**

The class schedule is a follows:

Topic 1: Distances (Tuesday, February 11)
-Scientific notation
-Units of measurements used in astronomy and conversion factors
-Scaling

Topic 2: Angles (Tuesday, February 18)
-Earth’s tilt vs. other planets’ tilts
-The Moon’s phases

** No Class Tuesday, February 25**

Topic 3: Scales and Ratios (Tuesday, March 4)
-Find sizes of lunar craters and maria
-Find height of ejected material
-Using significant figures and taking averages

Topic 4: Mass and Weight (Tuesday, March 11)
-Calculating your weight on other worlds
-Algebraic manipulation to isolate a variable

Topic 5: Time and Stellar Location (Tuesday, March 18)
-Earth time vs. other planet’s time
-Converting to military time
-How to calculate a star's rise time

Topic 6: Apparent Magnitude: Observations and Calculating Δm (Tuesday, March 25)
-History of the magnitude system
-How modern astronomers use apparent magnitude
-Negative numbers

Topic 7: Apparent Magnitude: Brightness and Big Batch Processing (Tuesday, April 1)
-Negative numbers
-Logarithmic functions
-Using an astronomical database
-How to use a spreadsheet for large data batches

Topic 8: Absolute Magnitude (Reading a Star Chart and Calculating) (Tuesday, April 8)
-How to use a star chart to determine magnitudes
-Apparent magnitude vs Absolute magnitude
-Negative numbers
-Logarithmic functions
-Using an astronomical database
-How to use a spreadsheet for large data batches
-How to calculate percentage error in your measurements

Topic 9: Geometry in the Solar System: Inferior Planets (Tuesday, April 15)
-Inferior vs. superior planets
-Diagramming maximum elongation
-Copernican method to find distance to inferior planets (using geometric functions)

Topic 10: Geometry in the Solar System: Superior Planets (Tuesday, April 22)
-Inferior vs. superior planets
-Diagramming opposition, conjunction, and quadrature
-Copernican method to find distance to inferior planets (using geometric functions)

Topic 11: Kepler’s 1st Law (Tuesday, April 29)
-Ellipses
-Focal point and semi-major axis
-Eccentricity

Topic 12: Kepler’s 2nd and 3rd Laws (Tuesday, May 6)
-Proportions
-Graphing

Topic 13: Newton Extends on Kepler's 3rd Law of Motion (Tuesday, May 13)
-Algebraic manipulation of equations
-Calculating masses

Topic 14: Orbital Velocities (Tuesday, May 20)
-Recognize forces that keep bodies (like satellites) in motion
-Become familiar with the orbital velocity formulas
-Calculate the needed velocity for various situations

**No Class June 3 or June 10**

Topic 15: Escape Velocities (Tuesday, June 17)
-Recognize forces that keep bodies (like satellites) in motion
-Become familiar with the  escape velocity formulas
-Calculate the needed velocity for various situations

Topic 16: Travel Times in the Solar System (Tuesday, June 24)
-How spacecraft travel from Earth to other bodies in the Solar System
-How long communication takes from the spacecraft back to Earth

Topic 17: Black Holes: Schwarzchild Radius and Tidal Forces (Tuesday, July 1)
-Calculating constraints for non-rotating black holes
-Comparison of strength and size between stellar mass black holes and supermassive black holes