Scaling Activity Introduction

We begin by creating a scaled-down map of the classroom to familiarize students with scaling and distance on a very familiar level. We continue by scaling the size of the solar system and continue this model out to the edge of the local group. Also, in another model the distance to the edge of the known universe is scaled to a comprehensible size by setting the distance between the Sun and the Earth to the thickness of a sheet of paper. It is presumed that students have some knowledge of the planets and workings of the solar system, and also a general idea of the scale of the solar system. This exercise builds on this knowledge and extends it to scale the universe including the nearest star to the Sun, the distance to the center of our galaxy, the diameter of the galaxy, the distance to the next galaxy, the diameter of the local group and the distance to the edge of the known universe.

Tables I, II & III, which are to be used in the activities which follow, show statistics of the planets in metric units, Earth units, and scaled units, respectively. The scaled units are calculated based upon scaling the diameter of the Sun to 3 inches. This convenient size is demonstratable in a large classroom, and also familiar to students as ordinary objects, like oranges or tennis balls. It also allows for conceivable scaled distances to astronomical objects. The first two tables are included mainly for reference and comparison, and to encourage familiarization with scientific units.

Table I. Astronomical Object Properties in metric units

	Mass (kg)	Equatorial Diameter (km)	Distance from Sun (10⁶ km)	Rotation Period (days)	Orbital period (years)
Sun	1.99 x 10³⁰	1390000	0
Mercury	3.30 x 10²³	4,880	58	59	0.241
Venus	4.87 x 10²⁴	12,100	108	243	0.615
Earth	5.97 x 10²⁴	12,756	150	1	1
Mars	6.42 x 10²³	6,790	228	1.03	1.88
Jupiter	1.90 x 10²⁷	142,984	778	0.4	11.86
Saturn	5.69 x 10²⁶	120,536	1427	0.4	29.46
Uranus	8.66 x 10²⁵	51,118	2871	0.7	84.01
Neptune	1.02 x 10²⁶	48,528	4497	0.6	164.8
Pluto	1.31 x 10²²	2,300	5910	6.4	248
Proxima Centauri			40500000
Distance to Center of Galaxy			2.5 x 10¹¹
Diameter of Galaxy			9 x10¹¹
Distance to Andromeda			2 x 10¹³
Diameter of Local Group			3 x 10¹³

Table II. Astronomical Object Properties in Earth Units (based on Earth mass and diameter)

	Mass (M_e)	Equatorial Diameter (D_e)	Distance from Sun (AU)	Rotation Period (days)	Orbital period (years)
Sun	333000	109	0
Mercury	0.06	0.38	0.39	59	0.241
Venus	0.81	0.95	0.72	243	0.615
Earth	1	1	1	1	1
Mars	0.11	0.53	1.52	1.03	1.88
Jupiter	317.9	11.2	5.2	0.4	11.86
Saturn	95.18	9.4	9.54	0.4	29.46
Uranus	14.5	4.0	19.19	0.7	84.01
Neptune	17.1	3.8	30.06	0.6	164.8
Pluto	0.002	0.18	39.5	6.4	248
Proxima Centauri			270000
Distance to Center of Galaxy			1600
Diameter of Galaxy			6000
Distance to Andromeda			140000
Diamter of Local Group			200000

Table III. Astronomical Object Properties in Scaled Units (based upon scaling the diameter of the Sun to 3 inches)

	Mass	Equatorial Diameter (Scaled Inches)	Distance from Sun (Scaled inches)	Rotation Period (days)	Orbital period (years)
				0
Sun		3	0
Mercury		0.011	10 ft.	59	0.241
Venus		0.026	19 ft.	243	0.615
Earth		0.027	27 ft.	1	1
Mars		0.015	41 ft.	1.03	1.88
Jupiter		0.31	140 ft.	0.4	11.86
Saturn		0.26	260 ft.	0.4	29.46
Uranus		0.11	520 ft.	0.7	84.01
Neptune		0.10	810 ft.	0.6	164.79
Pluto		0.0050	1100 ft.	6.4	247.69
Proxima Centauri			1400 miles
Distance to center of galaxy			8400000 miles
Diameter of galaxy			31000000miles
Andromeda			730000000 miles
Diameter of Local Group			1000000000 miles

Because this exercise concentrates on distance scale, you may want to begin the lesson with an exercise demonstrating the relative masses and radii of the planets. For a good example of this comparison, consult the New Jersey Science Curriculum Framework in the list of learning activities for standard 11 under Planet Gravities. This exercise uses relative numbers of pennies in empty soda cans to represent the weight of a full soda can on other planets. The number of pennies in each can changes based upon how massive the particular planet is and how big its radius is.

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