MONTH: August VOLUME: I ISSUE NO: 2015-1

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Theme of the Month:

Inside Highlights:

MADHYAM

Printed under Gifted Education Abhiyaan An initiative by the office of principal Scientific

Advisor to the Government of India

MONTH: August VOLUME: I ISSUE NO: 2015-1

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The Earth and the Moon to Scale

Did you ever come across Fascinating Questions Like?

We all have seen drawings or sketches in books that show the earth and the moon

together in the same view, but in reality they are far away from each other.

Similarly, you all know that moon is smaller than

the earth but how much small? Half the size, one

tenth the size, one hundredth the size ……..

Can you recall any drawing which can help you to

make this comparison more realistic?

This is possible only by creating properly scaled

drawings; you will get more precise idea of what

their sizes are! All you will need is a compass, a

metric ruler, and a calculator.

The adjacent photo was taken by the Voyager 1 spacecraft on September 18,

1977 at a distance of 7 million miles from the Earth and it has not been

edited in any way.

“Can we determine the

relationship between Sun and

the moons from other

planets and their distances

from the Sun just by

calculating the ratios?

How can we scale diameters

of Earth and Moon?

How can we scale their

distances from each other?

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Let’s know about the distance between Earth and its Moon.

The distance between the center of Earth and its Moon is 384,000 kilometers.

More precisely, average distance between the Earth and the Moon is 384,403 km.

Why have we taken ‘average’ distance?

Facts you may need to answer the question:

Moon is continuously moving around the Earth in an elliptical path.

Moon is not at a constant distance from the centre of the Earth.

Watch the Youtube video: one year of the moon is 2.5 minutes, released by

Goddard Space Flight Centre Scientific Visualization Studio (2011) and answer the

following questions:

How will you describe the movement of Moon mathematically?

The radius of the Moon is 1,737 kilometers and the radius of Earth is 6,371

kilometers. Based on this information, answer the following questions:

a) What is the ratio of Earth's radius to the Moon's radius?

b) Can you tell about how many times bigger the Earth is than Moon? (to the

nearest whole number)

c) Use a radius of 1 centimeter for the moon disc; draw two circles that

represent this size difference between the Earth and the Moon using ruler and

compass.

Think over:

Ancient Greeks used simple geometry, radius of the Earth and measuring the

shadows of the object when placed before the Sun to calculate nearly approximate

distance of moon from the centre of the Earth.

(Read more on it and send us at least two questions which emerged in your mind)

Sources: https://www.nasa.gov/pdf/377727main_Lunar_Math.pdf

http://www.spaceupdate.com/

https://www.youtube.com/user/eplanetarium

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Lunar Laser Ranging Experiment

Today we will talk about the modern technology used by the scientists to measure

the distance between moon and the earth with millimeter precision. It is done by

measuring the time taken by light to travel between LIDAR station at retro-

reflectors placed on the moon.

This method is known as Lunar Laser Ranging Experiment.

To know more about it you must read the following excerpts:

The Lunar Laser Ranging Retro-reflector Experiment was deployed on Apollo 11, 14

and 15. It consists of a series of corner cube reflectors, which are a special type

of mirrors with the property of always reflecting an incoming light beam back in

the direction from where it came from (Refer Fig I). These reflectors can be

illuminated by laser beams aimed through large telescopes on the Earth. The

reflected laser beam is also observed with the telescope, providing a measurement

of the round-trip distance between the Earth and the Moon. (Source: Apollo 11 Mission; Lunar and Planetary Institute, Houston/ http://www.lpi.usra.edu/)

Figure I

Let’s understand this process by knowing each term.

What is Laser?

Laser is an electronic device that emits narrow, intense beam of light through

optical amplification. It is an acronym of Light Amplification of Stimulated

Emission of Radiation.

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What is Retro-reflector?

Retro-reflector is a surface or a device that reflects light back to its original

source with least amount of scattering.

How does Lunar Laser Ranging Retro-reflector (LLRR) Experiment works?

Lunar Laser Ranging Retro-reflector is a two feet wide panel of 100 mirrors

arranged as corner-cube reflectors directed towards the Earth. When a laser

beam from a high powered telescope placed on the Earth is send to the LLRR, kept

at the Moon, mirrors of the instruments redirect the beam of light and send it

back to the same point on the Earth.

What is a corner cube reflector?

Corner cube reflector is a set of three mutually perpendicular reflective surfaces

placed to form the corner of a cube. It works as a retro-reflector.

(refer figure II)

Figure (II)

Discussion:

Light takes just over one second to travel 186,000 miles per second to travel from

space to earth.

Through LLRR data scientists concluded that light takes only 1.3 seconds

(approximate) to reach from Moon to Earth. Now, it was easy to know the distance between Moon and Earth. The closest distance is 363,104 km or 225,622 miles and farthest distance is 406,696 km or 252,088 miles.

Sources: http://www.bbc.co.uk/education/clips/zhxmhyc

http://www.fromquarkstoquasars.com/

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Important findings of Lunar Laser Ranging Experiment:

Moon has a liquid core.

Moon is gradually receding from the Earth.

For Advanced Reading:

Article tilted, ‘The Lunar Laser Ranging Experiment’ by Pl. Bender et.al

(Web-source: physics.ucsd.edu/~tmurphy/apollo/doc/Bender.pdf)

Let us learn to make a Corner Cube Recto-reflector:

Material:

Three 2” x 2” glass mirrors

A cubic box slightly larger than the size of the glass (let us take a plastic

cubic box of size 2.5” x 2.5” x 1.5”

Double side tape

Steps to make:

Clean the surface of the glass using glass cleanser.

Neatly place double tape at the back of the mirror.

Insert the mirror inside the box.

Similarly, insert the second mirror on the adjacent inner wall of the box

using double tape.

Again, insert the third mirror on the other adjacent inner wall of the box

using double tape.

Mirrors should be placed such that they form corner of a cube.

(source: makezine.com/projects/)

Your Corner Cube Retro-reflector is ready.

Now you can beam the laser light and note your observations.

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Things to do and submit

Q 1) Collect more information about Apollo 11 Lunar laser Retro-reflector

Experiment and write at least five facts about it.

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Q 2) Write the names of three working observatories collecting data through

lunar laser retro-reflector technique?

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Q 3) During the home made Corner Cube Retro-reflector, what will happen if

glasses are not placed at exact right angled?

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Q 4) Use your own home made Corner Cube Retro-reflector to measure distance

between different locations around your home. Compare it by measuring again with

meter-tape. Summarize your results based on the observations.

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Q 5) What were some ancient methods of calculating the distance between Earth

and Moon?

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Q 6) Why do we measure average distance between Earth and Moon?

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Q 7) In the above discussion, we have talked about two units of measurement - km

and miles. Write a mathematical relation between the two.

Your feedback: Information given: _______________________________________________

Sources mentioned: _______________________________________________

Activities discussed:______________________________________________

Questions asked: _______________________________________________

Any other: _______________________________________________

RESEARCH TEAM

Geetu Sehgal , Jyoti Batra,

Uzma Masood, Ritu

Verma,Meenakshi

Gifted Education Abhiyaan Project Team

Dr. Jyoti Sharma

Prof. Pankaj Tyagi

Prof. Shobha Bagai

Prof. Bibhu Biswal

Email id: giftededucationcic@gmail.com