Which of these pairs of objects has the smallest number of powers of ten difference in their sizes?
Select one:
a. Earth's moon's diameter and Earth diameter
b. Diameter of Earth and diameter of the solar system
c. Proton and a carbon atom
d. Star diameter and galaxy diameter
e. Adult human being and a typical cruise ship
To determine the pair of objects with the smallest number of powers of ten difference in their sizes, we can compare the sizes of each pair:
a. Earth's moon's diameter and Earth's diameter:
The diameter of the Earth is approximately 12,742 kilometers (1.27 × 10^4 km).
The diameter of the Moon is approximately 3,474 kilometers (3.47 × 10^3 km).
The difference in size is approximately one power of ten (10^4 - 10^3).
b. Diameter of Earth and diameter of the solar system:
The diameter of the Earth is approximately 12,742 kilometers (1.27 × 10^4 km).
The diameter of the solar system is difficult to define as it encompasses many objects and distances.
c. Proton and a carbon atom:
The size of a proton is approximately 1.6 x 10^-15 meters (1.6 × 10^-15 m).
The size of a carbon atom is approximately 0.15 nanometers (1.5 × 10^-10 m).
The difference in size is approximately five powers of ten (10^-15 - 10^-10).
d. Star diameter and galaxy diameter:
The size of a star can vary greatly depending on the specific star being considered. Similarly, the size of a galaxy can also vary significantly. Therefore, it is challenging to provide a direct comparison without specific objects.
e. Adult human being and a typical cruise ship:
The size of an adult human being can vary, but on average, we can consider a height of approximately 1.7 meters (1.7 × 10^0 m).
The size of a typical cruise ship can also vary, but let's consider a length of 300 meters (3 × 10^2 m).
The difference in size is approximately two powers of ten (10^0 - 10^2).
Based on the comparisons, the pair with the smallest number of powers of ten difference in their sizes is option ** - Earth's moon's diameter and Earth's diameter.
To determine which pair of objects has the smallest number of powers of ten difference in their sizes, we need to compare the sizes of each object and calculate the difference in their sizes in terms of powers of ten.
a. Earth's moon's diameter and Earth diameter: To compare the sizes of these two objects, you can research their respective measurements. Once you have their diameters, calculate the ratio of the larger diameter to the smaller one. If this ratio is close to 1, it indicates that there is a small difference in sizes, which means they have the smallest number of powers of ten difference in their sizes.
b. Diameter of Earth and diameter of the solar system: Comparing the diameter of the Earth to the diameter of the entire solar system is not a straightforward comparison, as the solar system consists of multiple celestial bodies. Therefore, it may not be appropriate to compare them directly in terms of powers of ten difference in their sizes.
c. Proton and a carbon atom: A proton is a subatomic particle, while a carbon atom consists of multiple protons. Therefore, in terms of sizes, a carbon atom would be larger than a single proton.
d. Star diameter and galaxy diameter: To compare the sizes of a star and a galaxy, you would need specific measurements for each. Generally, galaxies are significantly larger than individual stars, so there would likely be a considerable number of powers of ten difference in their sizes.
e. Adult human being and a typical cruise ship: Comparing the size of an adult human being to that of a typical cruise ship may require measurements of both objects. Calculate the ratio of the larger size to the smaller one to determine the powers of ten difference between them.
Without specific measurements, it is challenging to determine the exact answer. It is recommended to research the sizes of the objects in question and calculate the ratios to determine the smallest number of powers of ten difference in their sizes.