Diameter of planets and their distance from the Sun in kilometers (km): Planet Diameter (km) Distance from Sun (km) Sun 1,391,400 Mercury 4,879 57,900,000 Venus 12,104 108,200,000 Earth 12,756 149,600,000 Mars 6,792 227,900,000 Jupiter 142,984 778,600,000 Saturn 120,536 1,433,500,000 Uranus 51,118 2,872,500,000 Neptune 49,528 4,495,100,000 If the Sun is a soccer ball of diameter 20 cm, then What will be the diameter of the Earth? How far away will the Earth be from the Sun in this scale
The Correct Answer and Explanation is:
Scaled Diameter and Distance of the Earth
Given:
- Actual diameter of the Sun = 1,391,400 km
- Scaled diameter of the Sun (soccer ball) = 20 cm
- Actual diameter of Earth = 12,756 km
- Actual distance of Earth from the Sun = 149,600,000 km
1. Scaled Diameter of Earth:
To find the scaled diameter, we calculate the ratio of the real Sun to the model Sun and apply that to Earth’s diameter: Scale factor=20 cm1,391,400 km=201,391,400 cm/km\text{Scale factor} = \frac{20\, \text{cm}}{1,391,400\, \text{km}} = \frac{20}{1,391,400} \, \text{cm/km} Scaled diameter of Earth=12,756×201,391,400=255,1201,391,400≈0.1833 cm\text{Scaled diameter of Earth} = 12,756 \times \frac{20}{1,391,400} = \frac{255,120}{1,391,400} \approx 0.1833\, \text{cm}
So, the scaled diameter of Earth is approximately 0.183 cm, or about 1.83 mm.
2. Scaled Distance of Earth from Sun:
Scaled distance=149,600,000×201,391,400\text{Scaled distance} = 149,600,000 \times \frac{20}{1,391,400} =2,992,000,0001,391,400≈2151.5 cm=21.52 meters= \frac{2,992,000,000}{1,391,400} \approx 2151.5\, \text{cm} = 21.52\, \text{meters}
So, the scaled distance from Earth to the Sun is approximately 21.5 meters.
Explanation
Scaling celestial distances and sizes helps us better understand the vastness of our solar system, which is otherwise hard to grasp. In this exercise, the Sun is represented by a soccer ball with a diameter of 20 cm. Using this model, we applied a consistent scale ratio to determine both the size and distance of Earth from the Sun.
The real diameter of the Sun is about 1.39 million kilometers, while Earth’s diameter is approximately 12,756 km. Dividing Earth’s diameter by the Sun’s gives us the proportion of their sizes. When we multiply this ratio by 20 cm (the diameter of our model Sun), we find Earth would be about 0.183 cm—or just under 2 mm—on this scale. This is roughly the size of a pinhead, which highlights just how small Earth is compared to the Sun.
Next, we looked at Earth’s distance from the Sun, which is nearly 150 million kilometers. Using the same scaling factor, this translates to a distance of about 21.5 meters on our model—roughly the length of a school bus. This huge gap, even on a reduced scale, emphasizes the emptiness of space and the vast distances that separate planets from the Sun and from each other.
Overall, this scaled model helps us visualize the disproportion between planetary sizes and their spacing. Earth, though seemingly large to us, is minuscule compared to the Sun and spaced incredibly far away in cosmic terms. This realization can deepen our appreciation of both the precision of celestial mechanics and the immense scale of our solar system.
