## Unit 28

Ok, so deriving Kepler’s Laws of Planetary Motion relied on Kepler having 40 years of astronomical data from which to draw his conclusions. Later putting it on a firm mathematical footing needed one Isaac Newton to reinforce it with calculus.

I have neither 40 years of data nor a Sir Newton to draw on between now and next week. đź™‚

The alternative is therefore Unit 28 of MST209.

But Unit 28 requires your calculus to be in tip-top condition – not so much the skills of doing it, as some rarely-used rules to be applied at various stages of the derivation.

I thought my calculus was quite good, but, at one third the way into the unit, with all exercises tried, and some failed, I have a lonnnnnng list of questions to ask my tutor on Monday.

I suspect he’ll groan internally when I phone him, since I’ve phoned five times in the past week already about fairly abstract thoughts on previous units, all of which have been borne by my propensity for making solutions to questions more involved than they need be (I once submitted two pages of a proof, which came back with his proof, in agreement, which was about five lines long).

But he’s a jolly good egg, with patience far in excess of mine, so all will be ok.

In the meantime, soldier on, I shall, with the aim to have Unit 28 finished by 11:59pm on Monday night, the TMA in the post, and the CMA submitted via the course’s electronic system.

Tuesday evening can then be spent catching up on things for work, before Wednesday marks the start of MST209 exam revision proper.

Chris FinlayUnderstanding how Newton’s inverse square law explains Kepler’s laws of planetary motion is one of the major achievements of classical physics. Of course a bit like quantum physics whilst we know that gravity obeys an inverse square law (or at least until we take into account General relativity) doesn’t mean that we know what gravity actually is and in a way we don’t have to. What matters is that it gives the correct predictions of planetary motion a remarkable achievement linking calculus, analytical geometry and Newton’s laws of motion. It wasn’t for nothing that the poet Alexander Pope said

“Nature and Nature’s laws lay hid in night:

God said, “Let Newton be!” and all was light.”

Glad you’ve made a real effort to understand all this especially given TMA deadlines and exams this could well be an optional extra. Just like the continutiy but non differentiability of the blancmange function is in M208. This is what maths and physics are really about

Best wishes Chris

September 17, 2011 at 10:39 PM

oumathsHi Chris,

Many thanks for your input.

I find it quite intriguing that such motion can be so accurately modeled.

I had quite a few assumptions about a) what maths would be needed to ensure such models hold and b) what roles certain variables would play – some of which held, but some of which has been a bit of an eye-opener.

Oddly, at the outset of this course, I had a preference to study mathematical modeling in a purely engineering environment and found the physics difficult to penetrate and appreciate.

Now that the reading for MST209 is almost complete, I find myself thinking about shifting one of my two degree choices toward a hybrid physics/applied maths Open degree, in tandem with a meat-and-potatoes named maths and stats degree for good measure.

I think I need to choose from two of MS324, SM358 and M248 for next year. If I feel that the MST209 exam has gone well, I might just sign up for both level three courses and continue to leave the statistics in the background for now. Of course, at the snail’s pace with which I digest information, that would lead to a 30-40 hour per week study commitment. For every hour the OU suggests as a guideline for study time, I have a multiplier of roughly 2 to 2.2.

September 17, 2011 at 11:11 PM

Chris FinlayM248 whilst OK isn’t really mathematical in that a lot of the basic ideas aren’t really justified, Ok it gives a good overview of the basic techniques and how to use them but it’s a bit thin on the ground mathematically. So I would suggest although it would be quite demanding MS324 and SM358 for next year. It will one of the most intellectually stimulating 9 months in your life. Then MS326 and the electromagnetism course and the Relativistic universe course ( I don’t know the code numbers). That way you would have a grasp of the main theories of physics, classical mechanics, Maxwell’s equations and general relativity and a good grounding in the mathematical techniques used to apply them.

In terms of statistics it might be better to do the royal statistical society exams

http://membership.rss.org.uk/main.asp?page=1793

Which are probably more rigorous than the OU courses

That would free up more points to pursue other OU maths courses.

September 18, 2011 at 1:26 PM