Why do smaller worlds retain less of their internal heat?

Short Answer

Expert verified
Smaller worlds retain less of their internal heat because of their larger surface area to volume ratio. The larger surface area relative to volume means there's a bigger 'outlet' for the heat to escape, leading to quicker cooling and a faster slowdown of geochemical activity.

Step by step solution

01

Understand Scale Impact

First, it's important to understand the general principle: All celestial bodies start with a certain amount of internal heat from their formation. Over time, each world loses heat through its surface area. However, if the volume is large (i.e., for a larger planet), there will be more heat to lose, and it will take longer.
02

The Surface Area to Volume Ratio

The key is in the surface area to volume ratio: as a sphere grows larger (increasing diameter), its volume increases far quicker than its surface area. This means smaller bodies have a larger surface area relative to their volume, providing a larger 'outlet' for heat to escape, resulting in quicker cooling.
03

Result of Quicker Cooling

As a result of quicker cooling, smaller celestial bodies lose their internal heat faster compared to larger worlds. Because of that heat loss, geologic activity (which is fueled by internal heat) slows down and can even stop, thus they retain less of their internal heat.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Surface Area to Volume Ratio
The principle of the surface area to volume ratio is critical to comprehending why smaller celestial bodies have trouble retaining internal heat. Imagine a simple cube. As its edges grow from 1 unit to 2, its surface area increases by a factor of 4 (from 6 to 24 square units), but its volume shoots up by a factor of 8 (from 1 to 8 cubic units).

This exponential difference is even more pronounced in spherical objects like planets. While the surface area of a sphere scales with the square of the radius, the volume scales with the cube of the radius. Consequently, smaller bodies, having a higher surface area relative to their volume, dissipate internal heat more rapidly through their surfaces.

In celestial terms, this translates to smaller planets and moons losing heat much faster than their larger counterparts. The planet's initial heat – from formation or radioactive decay – will escape more efficiently if the 'exchange window' (the surface area) is larger relative to the entire 'house' (the volume).

Easy to remember is that a high surface area to volume ratio leads to faster cooling, making it a challenge for small worlds to cling on to their cozy warmth.
Planetary Geologic Activity

Heat as the Engine of Planetary Dynamics

Planetary geologic activity is largely driven by internal heat. On Earth, this includes phenomena such as volcanism, tectonic shifts, and the movement of continental plates. Internal heat is not only a byproduct of the formation process but also comes from the decay of radioactive elements within the core.

Influence of Size on Geological Activity

Larger planets with substantial internal heat enjoy prolonged geological activity. This activity contributes to an evolving landscape – think of the resurfacing of Venus or the continuous volcanic activity on Jupiter's moon Io. On smaller celestial bodies, the rapid loss of internal heat due to a higher surface area to volume ratio limits such activities. Over geological timescales, the lack of internal heat results in a frozen landscape where changes become rare, essentially halting the dynamism that characterizes living planets.

Thus, the scale of geologic activity is a testament to a body's ability to retain heat, modifying landscapes and potentially aiding in the development of complex ecosystems.
The Cooling of Celestial Bodies

The Inexorable Chill of Space

Like a hot cup of tea on a cold day, celestial bodies are perpetually losing heat to their surroundings – in this case, the near-absolute-zero temperature of space. Over time, this results in celestial body cooling, an inevitable consequence of thermodynamics.

Rate of Cooling Across Different Scales

Smaller worlds with a high surface area to volume ratio cool and solidify quickly after their formation. Earth’s moon, with its barren surface riddled with ancient craters, stands as a testament to this phenomenon, having lost much of its internal heat billions of years ago. Larger planets, such as Earth or gas giants like Jupiter, retain heat much more efficiently and therefore are geologically active even billions of years after their formation.

This gradual loss of heat affects not only the geologic activity but also the potential for hosting life, as stable, warm environments tend to be more hospitable. In essence, how long a celestial body retains its primeval warmth can shape its identity and destiny in the cosmic landscape.

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Most popular questions from this chapter

Use the Stamy Night Enthusiast TM program to examine the Jovian planets Jupiter, Saturn, Uranus, and Neptune. Select each of these planets from the Solar System submenu in the Favourites menu. If you desire, you can remove the image of the astronaut's feet by selecting Feet in the View menu. Position the mouse cursor over the planet and click and drag the image to examine the planet from different views. Describe each planet's appearance. Which has the greatest color contrast in its cloud tops? Which has the least color contrast? What can you say about the thickness of Saturn's rings compared to their diameter?

What is an asteroid? What is a trans-Neptunian object? In what ways are these minor members of the solar system like or unlike the planets?

Use the Deep Space Explorer \({ }^{T M}\) program to examine the Jovian planets Jupiter, Saturn, Uranus, and Neptune. In the left-hand part of the window, under the heading Solar System select Explore. Then click on the name of each planet to view it in detail. You can zoom in and zoom out using the buttons at the upper left of the window (an upward-pointing triangle and a downward- pointing triangle). You can also rotate the planet by putting the mouse cursor over the image of the planet or asteroid, holding down the mouse button, and moving the mouse. (On a two-button mouse, hold down the left mouse button.) Describe each planet's appearance. Which has the greatest color contrast in its cloudtops? Which has the least color contrast? What can you say about the thickness of Saturn's rings compared to their diameter?

What are the asteroid belt, the Kuiper belt, and the Oort cloud? Where are they located? How do the objects found in these three regions compare?

Suppose Mars Global Surveyor had discovered magnetized regions in the lowlands of Mars. How would this discovery have affected our understanding of the evolution of the Martian interior?

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