To build and to measure: an easy way to understand

Leonarda Fucili1, Simon Garcia Garcia2, Giuliano Casali3

"EAAE Summerschools" Working Group

1S.Media "U. Foscolo" Roma

3ITCG "P. Baffi" Fregene

#### Project

The Workshop was born by the collaboration of the Italian and Spanish authors, exchanging ideas, methodology, data and photos at a distance.

Introduction

Watching the Sun with opportune filters, you can see it like a disc with a definite outline; the measure of its apparent diameter is almost an half degree, quite the same of a full Moon diameter: the Sun, which is 400 times bigger than the Moon is, for a nice coincidence, 400 times farther.

About the distances, they change a little bit, according to Earth and Moon different positions in their orbits. It is for this reason that you can see the Moon bigger (perigee) or smaller (apogee). When Earth, Moon and Sun (in this order) are aligned on the "nodes line", which is the intersection line between the plane of lunar orbit and the plane of Earth's orbit, you can observe the well known phenomenon of Solar Eclipse, that could be total (the Moon is in perigee) or anular (the Moon is in apogee).

The Solar Eclipse of 11th August 1999, let us to measure

- Lunar diameter during the Eclipse and the distance between Earth and Moon

- Sun angular diameter

- Moon angular diameter

and to make experiments. The most significant that you can do, on our opinion, is to build a "scale model" of the Eclipse, using the founded measures.

For convenience, in the usual didactic procedure, you could easily use the averadge of the measures, making recourse to different types of scale, according to your needs (may be you have a small place to work).

Preliminaries

During the night between the 8th and the 9th of May 1999 we took pictures of the Moon, both in Athens (Greece) and in Murcia (Spain). The two cities are almost at the same latitude. The purpose was to investigate how far is the Moon from the Earth with parallax.

Methodology and results will be shown during the workshop.

Distance to the Moon

We are going to calculate the distance to the Moon watching it from two or more places on the surface of the Earth, comparing its position in relation to the stars.

First we fix coordinates of the observation places and the directions in which we see the Moon from each place.

The needed data to find out the distance to our satellite are: Latitude and Longitude of the observation place; straight rise and declination of the observation place; universal time; day, month and year of the observation.

The procedure can be visual or photographic. In the case of night photography we will use 50 to 200 mm lenses and 400 ISO film with ½ to ¼ sec exposure.

If we take advantage of the Sun eclipse we will use long focal lenses (200 mm or more) and slower film with adecuate exposure (very short).

#### The Solar Eclipse "In Miniature"

Activities

Having directly observed the 11th August Solar Eclipse for the whole length, we will start to build an "in miniature model", to bring back on the Earth what happen in the space during that phenomenon.

The realization could seem very easy, because it is reassuring to have at layout "measures"! Indeed you have to consider many variables. For example:

- Is the scale that you want to use according to the choosen place?

- How do you think to really realize the models of the Sun and of the Moon?

- How do you measure big distances?

- How do you fix or anchor the "point of view"?

- How do you build steady supports (doing one's best)?

- In which way the depressions or the elevations of the ground could create disturb to the demonstration?

If you want to use a 1:750.000.000 o 1:500.00.000 scale, look at these data:

 Real diameters Diameters 1:750.000.000 Scale Diameters 1:500.000.000 Scale Sun: 1.392.000 Km Earth: 12.756 Km Moon: 3.476 Km 186 cm 1,7 cm 0,46 cm 278 cm 2,55 cm 0,69 cm

 Distances (average) Distances 1:750.000.000 Scale Distances 1: 500.000.000 Scale Earth-Sun: 149.000.000 Km Earth-Moon: 384.390 Km 198 cm 50,6 cm 299 cm 76 cm

You have to pay attention at the choice of the scale, not only for the selected place, but to avoid to have, both the models of the Sun and Moon, too small; so

- Pratically realize the model;

- Discover that a little ball/moon (diameter = 1 cm) can obscure a disc/sun (diameter almost 3 m);

- Leave an empty space between Moon and Sun (about 300 m);

- Go all over that space with eyes and on foot.

All these things help us to understand whose are the spatial relationships between celestial bodies during a Solar Eclipse, much better than reading in a book a "cool" serie of numbers, or simply knowing data.

You can also put Mercury and Venus between Earth and Sun. If you want to place Mars, Jupiter and Saturn, you have to put them respectively at 450 m, at 1,5 Km and, almost, at 3 Km far from the Sun.

Even in little scale, it is very difficult to go all over interplanetaria spaces!

To build the model you need long time. A long time to fill in with manual action of the students but, during the workshop you can:

- Tell them stories from Mythology and from popular traditions, connected with the Eclipse;

- Read the reports of ancient scientist.

In the past there lot of interesting data and forecast of Solar and Lunar Eclipses were collected. You can consider them a significant foundation for the history of Astronomy.