Beginning in March 2011 Bob Roeth will be starting a series of presentations on Astronomy related mathematics. These talks will be held periodically on the fifth Tuesday of the month (when there is one).

The first session on March 29th will cover the following (time permitting):

- Spherical Aberration with concave spherical mirrors. This uses the geometry of triangles, parallels and parallelograms along with the laws of reflection.
- Use of Conjunctions to determine planetary periods, advance through the civil calendar of the onset of retrograde motion. This is just arithmetical and treats the orbits as circles – they are very close to circular except for Mercury (and demoted Pluto).
- Constructing ellipses – another meaning for ‘envelope’. This is practical and will require using a table with compasses, rule, pencil, eraser if you think you might need one and scissors. Cutting out a couple of paper circles with diameters about 200 mm beforehand could save time. The least well known method to be tested is surprising and simple but the maths needed to show that it should produce an ellipse is quite daunting. We will only look at the practical side.

Below is a list of the topics which may be covered as the series progresses. This list may be revised throughout the year, so please have a look and let us know of any topics which you may have a particular interest in. This feedback will help in deciding which topics will be covered in future sessions.

Note: These topics are not in any particular order

1. Eccentricity calculations with a simple calculator with square roots and with a scientific calculator having Sines and Cosines from trigonometry,

2. Newton’s invention of Gravity,

3. Easy ellipse mathematics,

4. How close was Ptolemy’s orbit to the ellipse when he used the equant?

5. Constructing ellipses – another meaning for ‘envelope’,

6. Sundial maths, shadow paths and the Equation of Time,

7. L1,L2 and L3 e.g., SOHO ‘at’ L1,

8. Combining magnitudes e.g., Venus and Jupiter in very close conjunction in 2BC and 6BC,

9. Co-orbital Janus and Prometheus in Saturn’s family of satellites,

10. Horseshoe orbits, The Interplanetary Highway of cheap Solar System Tours (cheap on fuel – EXPENSIVE IN TIME).

11. Gravity Assist e.g., the Pioneers and/or VEEGA, Jupiter’s effect on orbiting junk,

12. Spherical Aberration with concave spherical mirrors,

13. Sagittal calculations for spherical mirrors in the stage before parabolising,

14. Calculations relating to the Calendars,

15. Kepler’s mathematics,

16. Use of Conjunctions to determine planetary periods, advance through the civil calendar of the onset of retrograde motion,

17. Estimating the declination of the Sun from the day-number in the year.

We hope to see you there.

Peter Nosworthy

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