(a) If the Earth had retained hydrogen and helium in the same proportion to the heavier elements that exist elsewhere in the universe, what would its mass be? Give your answer as a multiple of the Earth's actual mass. Explain your reasoning. (b) How does your answer to (a) compare with the mass of Jupiter, which is 318 Earth masses? (c) Based on your answer to (b), would you expect Jupiter's rocky core to be larger, smaller, or the same size as the Earth? Explain your reasoning.

Understanding the mass of Earth is vital to comprehending the fundamental characteristics of our planet and its ability to retain an atmosphere. The actual mass of Earth is approximately 5.97 x 10^24 kilograms. This mass includes a variety of elements, but primarily iron, oxygen, silicon, and magnesium which form the bulk of its inner structure. Earth's atmosphere is relatively thin and contains only trace amounts of hydrogen and helium. In contrast to giants like Jupiter, Earth's smaller gravitational pull means it cannot retain these light gases in significant amounts.

Imagine a scenario where Earth could keep hydrogen and helium in the same ratio as found in the rest of the universe; our planet's mass would balloon to an estimated 50 times its current size! This colossal increase would be discovered by applying the compositional percentages of the universe to Earth's makeup: if 98% of its mass were hydrogen and helium, like the universal abundance, the mass of Earth would mirror that of a mini gas giant rather than the terrestrial planet we call home.

The retention of hydrogen and helium in planetary atmospheres is a topic that fascinates many students of astronomy and planetary science. These two elements are the most abundant in the universe, yet Earth holds only tiny amounts of them. Planets with substantial gravitational clout, like Jupiter and Saturn, are able to hold onto these gases, giving them thick atmospheres composed mainly of hydrogen and helium.

To comprehend why Earth cannot retain these gases as Jupiter does, one must consider Earth's smaller size and lower escape velocity. Earth's gravity is not strong enough to prevent these light gases from escaping to space. Over geological time, any primordial hydrogen and helium would have been stripped away by solar winds or never captured by Earth's gravity during its formation. This fundamental concept explains why Earth's atmosphere is markedly different from that of gas giants, which are enveloped in these lightweight, abundant elements.

Jupiter, the largest planet in our solar system, has a total mass of about 318 times that of Earth. This massive size allows it to retain light gases such as hydrogen and helium, making up most of its composition. However, despite its huge mass, the size of Jupiter's core relative to Earth is a point of curiosity.

It is believed that Jupiter's core is not proportionally large when considering the planet's overall size. The core is composed of heavier elements similar to those found on Earth but accounts for only a fraction of the gas giant's mass. Based on calculations comparing the hypothetical mass of an Earth retaining hydrogen and helium to Jupiter's actual mass, it would follow that Jupiter's rocky core should be smaller than that of Earth. This deduction aligns well with observations and theoretical models which suggest that Jupiter's core is enveloped by a vast mantle of metallic hydrogen surrounding the core, leading to its extensive mass.