Problems 1-1. Because the distances between the planets are much larger than pla

Question

Problems 1-1. Because the distances between the planets are much larger than planetary sizes, very few diagrams or models of the Solar Sys- tem are completely to scale. However, imag- ine that you are asked to give an astronomy lecture and demonstration to your niece's second-grade class, and you decide to illustrate the vastness and near emptiness of space by constructing a scale model of the Solar System using ordinary objects. You begin by selecting a (1-cm-diameter) mar ble to represent the Earth. (a) What other objects can you use, and how far apart must you space them? (b) Proxima Centauri, the nearest star to the Solar System, is 4.2 light years dis- tant; where, in your model, would you place it?

Explanation / Answer

(a)This is a near impossible task.

First we begin with 1cm diameter Earth. That means the actual diameter of 12,742 km is reduced to 1 cm. So the scale is 1:1,27,42,00,000. (1km = 100,000cm)

On the same scale:

Actual diameter of the sun = 13,91,900 km

Scaled diameter of Sun = 13,91,900 / 12,742 = 109.2 cm

Actual diameter of the Mercury = 4,866 km

Scaled diameter of Mercury = 4,866 / 12,742 = 0.38 cm

Actual diameter of the Venus = 12,106 km

Scaled diameter of Venus = 12,106 / 12,742 = 0.95 cm

Actual diameter of the Mars = 6,760 km

Scaled diameter of Mars = 6,760 / 12,742 = 0.53 cm

Actual diameter of the Jupiter = 1,42,984 km

Scaled diameter of Jupiter = 1,42,984 / 12,742 = 11.22 cm

Actual diameter of the Saturn = 1,16,438 km

Scaled diameter of Saturn = 1,16,438 / 12,742 = 9.138 cm

Actual diameter of the Uranus = 46,940 km

Scaled diameter of Uranus = 46,940 / 12,742 = 3.68 cm

Actual diameter of the Neptune = 45,432 km

Scaled diameter of Neptune = 45,432 / 12,742 = 3.56 cm

Finding objects of these sizes are not that difficult. We can use marbles or cardboards to make the spheres with the calculated diameters. But the problem is the distance between these objects. Let's find out how they fit into this scale.

Orbit radius of mercury = 5,79,50,000 km

Scaled orbit radius of mercury = 5,79,50,000 / 12,742 = 4547.95 cm = 45.4795 m

Orbit radius of venus = 10,81,10,000 km

Scaled orbit radius of venus = 10,81,10,000 / 12,742 = 8,484.53 cm = 84.84 m

Orbit radius of Earth = 14,95,70,000 km

Scaled orbit radius of Earth = 14,95,70,000 / 12,742 = 11,738.34 cm = 117.38 m

Orbit radius of Mars = 22,78,40,000 km

Scaled orbit radius of Mars = 22,78,40,000 / 12,742 = 17881.02 cm = 178.81 m

Orbit radius of Jupiter = 77,81,40,000 km

Scaled orbit radius of Jupiter = 77,81,40,000 / 12,742 = 61068.90 cm = 610.689 m

Orbit radius of Saturn = 1,42,70,00,000 km

Scaled orbit radius of Saturn = 1,42,70,00,000 / 12,742 = 111991.83 cm = 1119.918 m

Orbit radius of Uranus = 2,87,03,00,000 km

Scaled orbit radius of Uranus = 2,87,03,00,000 / 12,742 = 225262.91 cm = 2252.629 m

Orbit radius of Neptune = 4,49,99,00,000 km

Scaled orbit radius of Neptune = 4,49,99,00,000 / 12,742 = 353154.92 cm = 3531.549 m

Thus we can see that if we are to build this model the object representing neptune must be placed at a distance of 3.5 km from the object representing Sun. Or in other words our model would have a radius of 3.5 km.

(b) Here, there is a factual error in the question, nearest star to solar system is Alpha Centuary A. Proxima centuary is the third nearest star to solar system.

Light year is the distance light travels in one year.

1 light year is approximately 9.461 x 1012 km.

Therefore 4.2 ly = 4.2 x 9.461 x 1012 = 39.7362 x 1012 km

That is Proxima Centuary is at a distance of 39.7362 x 1012 km from our solar system

Scaled distance of Proxima Centuary = 39.7362 x 1012 / 12,742 = 3.1185 x 109 cm = 3.1185 x 104 km = 31,185 km

Thus, proxima centuary must be placed at a distance of 31,185 km from our model of solar system if we follow the scale

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