Aphelion, brought to you by Kepler

Today is Aphelion Day. 

Not a date you will see on many calendars or one requiring a public holiday.

You won’t notice any changes or spectacular sights, but today we are as far from the sun as we get.

In fact at 04.30 British Summer Time this morning the Earth was 3,106,600 miles or 4,999,630 Kilometres further from the Sun than it was at it’s closest point.  That’s a shade over 392 Earth diameters further away, which appears to be quite a huge difference.  But then our average distance to the Sun would fit almost 12,000 Earth diameters.

The very existence of a difference in distance may strike you as odd.  It turns out that a perfectly circular orbit is not what we get when we look at the planets.  When we moved from the Aristotelian model to the Copernican model we were getting a more realistic model of our Solar System, the Earth was not at the centre and the planets orbited the Sun.  But it wasn’t right.  The observations didn’t match.  Prediction was not borne out in the sky.  Of course that is the very essence of the scientific method.

Johannes Kepler is the hero of the piece.  The man who saved the new model of our universe.  He was an astrologer and teacher in a seminary at a time when distinctions between religion, beliefs, arts and science were blurred.  He was a strong believer in divine influence, the power of the stars over human affairs and that both could be understood through reason.  This was not unusual for the time, in this respect Kepler was pretty mainstream.

Johannes Kepler

Kepler. Looking a bit ruff.

What made him divisive was something that today we take for granted. 

He married Astronomy and Physics. 

For many of his contemporaries this was abhorrent.  400 years later Astronomy is perhaps the most famous branch of physics and certainly one of the most popular.  At the birth of the 17th Century though Astronomy, not fully divorced from Astrology was a liberal art and Physics was a natural science and never the twain shall meet.  He was even dismissed Galileo.

His laws of planetary motion are in many respects very simple and have that most prized of physics qualities ‘elegance’.

Law 1

The orbit of a planet is an ellipse with the Sun at one of two foci.

Kepler's first law

It ain’t a circle! Kepler’s First Law

In other words orbits are not circular and have no single centre.

 Law 2

A line joining the planet and Sun sweeps out equal areas during equal intervals of time.

Kepler's Second Law

Weee! Can you feel the acceleration? after today Earth is speeding up… Kepler’s Second Law

 This points out that the orbital speed is different at different points.  Right now Earth is moving a bit slower that it is when it is closer to the Sun. In the diagram Earth covers the distance between the highlighted points (A-B, C-D)  in the same time.

Law 3

The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

 Usually expressed as P2=KA3 where P is the orbital period, K is a constant (which can be ignored if you select your units very carefully…) and A is the semi-major axis.

Semi-major what now?  Well in essence that is what today is about.  This is the distance between the planet at its furthest and the ‘middle’ of the elipse, which equates to our average difference from the Sun. 

 Which is a lot closer than we are today.


About astronomersden

Daddy, Hubby, Teacher and when ever I get the chance Astronomer.
This entry was posted in Aphelion, Astronomy, Kepler, Sun, The Astronomer's Den and tagged , , , , , . Bookmark the permalink.

3 Responses to Aphelion, brought to you by Kepler

  1. tychogirl says:

    “Semi-major what now?” I love it! Awesome post as always.

  2. Pingback: Hairy Stars | astronomersden

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