Earth Radius Measurements for the Spring Equinox March 20 2004
The year has been declared as The Year of Scientific Awareness. The year also contains a rare and significant Astronomical event that Edmund Halley (of the comet fame) described as a "sight that is by far, the noblest astronomy affords..." – The Transit of Venus on the 8th of June 2004. By observing this event students countrywide can make their own measurements of the Earth –Sun distance.
That is still a few months ahead, but, they will also need to make some related observations that will help them to arrive at this deeply significant measurement.
Venus in the sky! This is difficult to miss these days – the most brilliant object in the western sky after sunset. On the 23rd and 24th of February, it will have a close conjunction with the crescent Moon – one of the most inspiring views in the sky! Students could get a feel for the changing position of Venus in the sky, over the next month – and see Venus elevated to the maximum angular distance that it can achieve on the 29th of March. Our rich Astronomical heritage can be used to measure this maximum angular distance of Venus from the Sun – students of Delhi and Jaipur can use the Jaiprakas Yantra of Jantar Mantar to make these measurements, while students from other locations within the country could use alternate simple methods to view the changing position of Venus in the sky, over the next one month.
Let us chose the 20th of March, The spring Equinox for 2004, for a wonderful country wide collaboration for allowing students from all corners of the country – every interested student from every city, town and village of India – to make their own measurement of the Radius of the Earth, using very simple equipment and method. The radius of the Earth is an important ingredient going into the calculation of the Earth-Sun distance, using transit observations.
Bring along your neighborhood cricket club stumps, a piece of string, a stone and a scale and we are set to measure the dimensions of the Earth!
Very simple geometry will be used for this measurement – exactly as had been used by Eratosthenes - all the way back in the 3rd century BC!
On the date chosen – 20th of March – we are just moving away from the northern hemisphere winter, so we know that the rays of the Sun fall in our regions inclined at some angle. This is the angle that needs to be measured – this activity, in fact, is part of the Xth standard Physics Activities mentioned in the NCERT textbooks. So, students sweating it out on their desks, for the exams, take just ten minutes out of that and be in the Sun, on the 20th of March to appreciate the power of this textbook activity!
One needs only to fix the cricket stump – exactly vertical – in the ground. Use a Plumbline made from string and stone to ensure that the stick is vertical.
Those with more time to spare for this activity can start marking the end of the shadow of this stump from morning till evening – one will see the shadow shortening slowly – going to a minimum sometime near, but, not quite the exact, noontime, and lengthening again.
It is the time of the minimum shadow that is of importance – at this time, measure, as accurately as possible, the length of the shadow. The time to do this will be different for different locations – for every city town and village of India – the time to do this experiment is given at the bottom of this page. Measure also the length of the stick above the ground. The two lengths are enough to give the angle at which sunrays are falling at your location at that instant.
Use the following figure –
One
needs to know the distance AB – perpendicular distance to a latitude at which
the Sun rays are falling perpendicular, giving rise to no shadow at the same
instant that we are measuring the shadow at our location.
The Distance AB, for the 28th
of Febraury, is the perpendicular distance from any location in India, to the Equator.
Check back at this site
For other activities, the time and distance for different locations in India, activities at other times and much more!
The timings and the distance AB for every city, town and village of India, for the 20th of March 2004, will be found at the links below!
(Caution - I just checked that some of the links below may not have been correctly uploaded and may contain older data meant for the 28th of Feb. ANyone wishing to do these measurements for the 20th of March - do mail to rathnasree@yahoo.co.uk to obtain the relevant information)
[A] [B] [C] [D] [E] [F] [G] [H] [I] [J] [K] [L] [M] [N] [O] [P] [Q] [R] [S] [T] [U] [V] [W] [XYZ]
An explanation of what is involved in the estimation of these numbers will be added shortly.
Check here for making the distance and time calculation yourself, for a date of your choice.