8/7/2019 tp1_long_distances

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Physics : First practical session

How can we measure long distances ?

I. How can we measure the Earths radius ?

1. The observations made by Eratosthenes

In 205 B.C., the Greek astronomer Eratosthenes, at the time Director of the Great Library of Alexandria in Egypt, proposed a purely

geometrical method to measure the radius of the Earth.

He started by using the observation of shadows made at two different places, Alexandria and Syene ( now Aswan ) distancedapproximately 800 km apart ( distance estimated in relation to the time taken by a caravan of camels to connect the two towns ! ) atthe time of the Summer solstice and at noon local solar time.

On that date and at that precise time in the northern hemisphere, the Sun reaches its highest position in the year above the horizon.However, Eratosthenes noticed differences from one place to another. In Syene, the Sun is at the vertical, so much so that its rays

reach the bottom of a well ! In Alexandria, on the other hand, the Sun is no longer at the vertical, and vertical objects have a very

shallow shadow. Eratosthenes set about measuring the shadow of an obelisk whose height he knew, and used this information todeduce the angle of the sun's rays from the vertical : he found 7.2.

2. Questions

a. Can you describe the shadow of vertical objects in Aswan at the time of the Summer solstice and at noon local solar time ?

b. Would you observe the same shadows in Alexandria ?

c. Draw a diagram to explain this difference.

d. Deduce from that a method to determine the Earths radius.

II. How can we measure distances in the Universe ?

1. The light year unit

Astronomers use light years to measure vast distances in space.

a. According to you, why do astronomers use another unit than meter ?

b. What can a light year represent ?

c. Light moves at a speed of about 300,000 km per second. Give a rough estimate of this speed in meter per second.

d. Express one light year ( l.y. ) in meter.

e. The Milky Way is about 150,000 light-years across. Express the diameter of this galaxy in meter.

2. How do astronomers measure the distance from Earth to Moon ?The method consists in emitting a laser beam from the Earths ground. This light signal is reflected by the surface of the Moon and

goes back to the Earth where it is received.The first laser reflector was positioned on the Moon in 1969 by the Apollo 11 astronauts. And now, by beaming laser pulses at the

reflector, scientists are able to determine the roundtrip travel time of the laser beam and obtain the Earth-Moon distance.

a. Knowing that the laser signal takes 2.56 s to carry out its roundtrip travel, determine the Earth-Moon distance in meter.

b. Is it interesting to express this distance in light year ?

3. How far away is the Sun ?

History : Aristarchus of Samos, an early Greek astronomer ( about 310 to 230 BC ), was the first to suggest that the Earth revolvedaround the Sun. Moreover, he was the first person to do the measurement of the Sun-Earth distance. Eratosthenes ( 276-194 BC )

also measured the distance between Earth and Sun. And the first scientific measurement of the Earth-Sun distance was made by

Cassini in 1672 by parallax measurements of Mars ( he observed Mars from two places simultaneously ).Nowadays we consider that the average distance between the Earth and the Sun is 149,597,870.691 kilometres.

The Astronomical Unit( AU ) is the mean distance between the Earth and the Sun. It is used to indicate distances within our solarsystem. The Earth orbits at a distance of 1 AU from the Sun.

a. Give an estimate value ( with 2 significant figures ) of 1 AU in meter.

b. Express one light year in astronomical unit.

c. The distance between the Sun and Pluto is about 6 billion km. Show that Pluto is about 40 times as far from the Sun as the Earth is.

III. To go further

Sometimes we can hear When we view distant objects in space, we are looking back in time.

Try to explain this sentence.

christophe RAVEL Lyce Victor Hugo Besanon