Question

In order to conceptualize the size and scale of Earth and Moon as they relate to the solar system, complete the following: a. Approximately how many Moons (diameter \(=3474\) kilometers) would fit side- by-side across the diameter of Earth (diameter = \(12,756\) kilometers \() ?\) b. Given that the Moon's orbital radius is 384,798 kilometers, approximately how many Earths would fit side-by-side between Earth and the Moon? c. Approximately how many Earths would fit side-by-side across the Sun, whose diameter is about 1,390,000 kilometers? d. Approximately how many Suns would fit side-by-side between Earth and the Sun, a distance of about 150,000,000 kilometers?

Short answer

a. 3.67 Moons b. 30.16 Earths c. 109 Earths d. 107.91 Suns.

Step-by-step solution

Calculate Moons across Earth's Diameter

To determine how many Moons can fit across Earth's diameter, we divide Earth's diameter by the Moon's diameter: \[\text{Number of Moons} = \frac{12,756 \text{ km}}{3,474 \text{ km}} \approx 3.67\]Thus, approximately 3.67 Moons can fit across Earth's diameter.

Calculate Earths between Earth and Moon

To find out how many Earths can fit between Earth and the Moon, we divide the distance between Earth and the Moon by Earth's diameter:\[\text{Number of Earths} = \frac{384,798 \text{ km}}{12,756 \text{ km}} \approx 30.16\]Therefore, approximately 30.16 Earths can fit side-by-side between Earth and the Moon.

Calculate Earths across the Sun's Diameter

To determine how many Earths fit across the Sun's diameter, divide the Sun's diameter by Earth's diameter:\[\text{Number of Earths} = \frac{1,390,000 \text{ km}}{12,756 \text{ km}} \approx 109.0\]So, approximately 109 Earths can fit side-by-side across the Sun.

Calculate Suns between Earth and the Sun

To find out how many Suns fit between Earth and the Sun, divide the distance from Earth to the Sun by the Sun's diameter:\[\text{Number of Suns} = \frac{150,000,000 \text{ km}}{1,390,000 \text{ km}} \approx 107.91\]Therefore, approximately 107.91 Suns can fit side-by-side between Earth and the Sun.

Key concepts

Earth and Moon size comparison

To understand how the Earth and Moon compare in size, let's first look at their diameters. Earth has a diameter of approximately 12,756 kilometers. In contrast, the Moon's diameter is significantly smaller, at about 3,474 kilometers.

When we try to imagine these celestial bodies side-by-side, it might be useful to visualize how many Moons could fit across the Earth’s diameter. By dividing Earth's diameter by the Moon's diameter, we calculate:

• \[\text{Number of Moons fitting across Earth} = \frac{12,756 \text{ km}}{3,474 \text{ km}} \approx 3.67\]

This means approximately 3.67 Moons could fit along a single line spanning the diameter of the Earth. This comparison highlights not only the relative sizes of the Earth and the Moon but also aids in visualizing the scale of these celestial objects in a straightforward manner.

Orbital radius calculation

The Moon orbits Earth at a distance known as the orbital radius, which is roughly 384,798 kilometers. This space might seem vast, but it proves manageable when broken down by comparing it to the size of Earth.

To visualize this, we calculate how many Earths could fit in a line between Earth and the Moon by dividing the orbital radius by Earth's diameter:

• \[\text{Number of Earths fitting between Earth and Moon} = \frac{384,798 \text{ km}}{12,756 \text{ km}} \approx 30.16\]

This result shows that approximately 30.16 Earths could fit between Earth and the Moon. Such comparisons help us to mentally bridge the vast distances in space with our understanding of Earth's size.

Sun's diameter comparison

When we consider the Sun's size in relation to Earth, it is crucial to note the Sun's enormous diameter of about 1,390,000 kilometers. This staggering measurement can be more comprehensible when compared to Earth's diameter of 12,756 kilometers.

By calculating how many Earths could line up across the Sun's diameter, we divide the Sun's diameter by Earth's diameter:

• \[\text{Number of Earths across the Sun} = \frac{1,390,000 \text{ km}}{12,756 \text{ km}} \approx 109.0\]

This calculation indicates that approximately 109 Earths could fit side-by-side across the Sun. Understanding this comparison provides a clearer picture of the vast scale difference between Earth and the Sun, illustrating the Sun’s massive presence in our solar system.

Distance between Earth and the Sun

The Earth orbits the Sun at a significant distance of about 150,000,000 kilometers. To put this distance into perspective, we can consider how many Suns could fit between the Earth and the Sun.

Since the Sun's diameter is about 1,390,000 kilometers, we can compute how many Suns fit by dividing the distance from Earth to the Sun by the Sun's diameter:

• \[\text{Number of Suns fitting between Earth and Sun} = \frac{150,000,000 \text{ km}}{1,390,000 \text{ km}} \approx 107.91\]

Thus, approximately 107.91 Suns could align between Earth and the Sun. This comparison serves as a compelling visual representation of the vast spatial distances within our solar system, showcasing the immense scale that separates these celestial bodies.