14 Gravitational Theory - Law of Universal Gravitation and Tidal Forces

 

Learning Outcomes

• State and explain Newton’s law of universal gravitation;
• Use the gravitational formula to calculate the force between two masses;
• Explain the origin of tidal forces due to gravitational interactions between the Earth, Moon, and Sun;
• Calculate the tidal forces exerted by the Moon and the Sun on the Earth’s oceans;
• Describe the role of tidal forces in generating tides and their effects on the marine environment; and
• Analyze and articulate the implications of the gravitational theory in the context of marine biology.

Newton’s Law of Universal Gravitation: A Force That Shapes Our Oceans

You might not immediately think of gravity when you think about the ocean, but this fundamental force is crucial in shaping marine environments in ways you may not realize. While gravity is often associated with objects falling to the ground, it’s actually a universal force that affects everything—right down to the movement of the ocean's tides and even the behavior of marine life!

Isaac Newton's Law of Universal Gravitation, formulated in the late 17th century, describes the attractive force that every object with mass exerts on every other object with mass. The key here is that gravity affects all things, from the smallest plankton to the largest whale, and from ocean waves to the tides that shape coastlines.

Key Ideas About Gravity 

1. Gravity Is Always Attractive: Gravity pulls objects together. This is why your body is held to the Earth’s surface, and why the Earth, in turn, pulls on the Moon, keeping it in orbit. It’s a constant force that’s at work wherever there’s mass.

2. The Role of Mass: The more massive an object, the stronger its gravitational pull. For example, the gravitational pull of the Earth is much stronger than that of a small fish, because Earth is so much more massive. But even small objects like fish or plankton are affected by gravity—though on a much smaller scale.

3. The Importance of Distance: Gravity is a distance-sensitive force. The further apart two objects are, the weaker the force between them becomes. For instance, the gravitational pull between two fish in the ocean is much weaker than the pull between Earth and the Moon, simply because they are much farther apart. In fact, if you double the distance between two objects, the force of gravity becomes one-quarter as strong. This is why the Earth’s gravitational effect on the oceans is so much stronger than the pull of individual sea creatures on one another.

How Gravity Affects the Ocean 

One of the most obvious ways gravity plays a role in marine biology is through the tides. The gravitational pull of the Moon (and to a lesser extent, the Sun) causes the oceans to bulge out in certain areas, creating high and low tides. This process is crucial for many marine species, influencing feeding, breeding, and migration patterns.

Consider the tidal pools where marine organisms live. These habitats are heavily influenced by the ebb and flow of tides, which are directly caused by the Moon’s gravitational pull on the Earth. The variation in water depth exposes different species to varying levels of light and air, impacting the creatures that live there.

Gravitational Forces Beyond Earth 

Gravity also plays a role in how ocean currents move. For example, Earth's rotation combined with gravity causes the ocean to behave differently at various latitudes, affecting currents that distribute heat and nutrients across the globe. These currents, like the Gulf Stream, are critical in regulating climates and providing food for marine life.

The same gravitational forces that affect Earth also influence the entire solar system. The interactions between Earth, the Moon, and the Sun create regular, predictable patterns in tides, which are vital for marine life that depends on tidal rhythms.

A Historic Breakthrough 

Newton’s law of universal gravitation fundamentally changed our understanding of the natural world. Before Newton, many phenomena—like why objects fall toward the Earth or why the planets stay in their orbits—were observed but not fully understood. Newton’s insight was that every mass in the universe exerts a gravitational pull on every other mass, and that this force is a key driver in everything from the formation of galaxies to the movement of ocean tides.

In short, gravity is not just a force that holds us on the ground—it's a force that shapes the very nature of our oceans and the life within them. It controls the tides, influences currents, and plays a role in the behavior of marine organisms, all of which are critical to marine ecosystems. Understanding how gravity works can help us better comprehend these oceanic patterns and how they influence the survival and behavior of marine species. 

Statement of the Law 

The basic equation for Newton’s Law of Universal Gravitation is:

Where:

• 𝐹 is the gravitational force between two objects,
• 𝑚₁ and 𝑚₂ are the masses of the two objects,
• 𝑟 is the distance between the centers of these objects,
• 𝐺 is the gravitational constant, a tiny number that tells us how weak gravity is compared to other forces in nature, approximately 6.674 × 10⁻¹¹ N•m²/kg²

Real-World Examples and Applications 

Let's see how this formula works in practice, especially when we consider larger objects like planets or satellites. But we’ll also look at small-scale examples that you could relate to marine life.

Example 1: Gravitational Force Between Two Small Objects

Let’s imagine we are calculating the gravitational force between two small objects in the ocean, such as two fish. Suppose one fish weighs 5 kg and the other weighs 10 kg, and they are separated by a distance of 2 meters (about the length of a small boat). Using the formula, we can calculate the gravitational force between them.

So, the gravitational force between the two fish is incredibly small—about 0.000000000834 Newtons. This is why we don’t notice this force in daily life! But, when it comes to larger objects like planets or satellites, gravity’s effect becomes far more noticeable.

Example 2: Gravitational Force Between Earth and a Satellite

Now, let's consider a much larger-scale situation that impacts ocean phenomena: the gravitational pull between Earth and a 1000-kg satellite orbiting our planet typically about 300 km for Low Earth Orbit (LEO). This force influences tides and ocean currents, and understanding how it works can help explain marine biology events that depend on these factors.

This means the gravitational force between Earth and the satellite is more than 4 meganewtons. This is a significant force compared to the small fish example earlier, and it's exactly the type of force that helps keep satellites in orbit—and also creates the tidal forces in the ocean that influence marine life.

Example 3: Gravitational Force Between Two Small Masses

Finally, let’s consider another small-scale example. Let’s calculate the gravitational force between two objects that are very close to each other, like two small creatures in the ocean, say a couple of small 50-g crabs 10 cm apart.

The force between these two crabs is 16.7 piconewtons—again, very small compared to the Earth-satellite interaction, but still a real force at play between any objects with mass.

Understanding gravitational forces like these can help marine biologists explain and predict oceanic phenomena. For example, the forces between the Earth and the Moon create the tidal cycles that many marine organisms rely on for feeding and reproduction. The distance between Earth and the Moon, as well as their respective masses, influences how high or low the tides will be, which can impact everything from the feeding patterns of marine mammals to the health of coral reefs.

Gravitational forces also help shape the movements of large ocean currents that distribute heat, nutrients, and oxygen throughout the oceans, playing a crucial role in the health of marine ecosystems. By understanding these forces, you can better appreciate how the Earth’s dynamic systems—shaped by gravity—affect marine life.

Problem Set

Problem 1: Tidal Force Between the Moon and Earth

Context: The Moon exerts a gravitational pull on Earth's oceans, causing tides. The gravitational interaction between the Moon and Earth is responsible for the bulges in the ocean that create high and low tides.

Question: Calculate the gravitational force between the Earth and the Moon.

Problem 2: Gravitational Force Between Two Fish

Context: Two fish are swimming in close proximity to one another. Despite being small in mass, they still exert a gravitational force on each other, though it's incredibly small compared to the forces involved in ocean tides.

Question: Calculate the gravitational force between the two fish.

Problem 3: Gravitational Interaction Between Two Large Whales

Context: Two large marine creatures, such as whales, swimming near each other in the ocean, will exert a gravitational force on each other. This force is negligible compared to tidal forces but is still part of the universal gravitational interactions.

Question: Calculate the gravitational force between the two whales.

Problem 4: Gravitational Force Between Two Small Crabs

Context: Two small crabs in the intertidal zone of a beach exert a very tiny gravitational force on each other, though it's not noticeable at the scale of everyday interactions.

Question: Calculate the gravitational force between the two crabs.

Problem 5: Influence of Tides on Intertidal Zone Organisms

Context: Organisms in the intertidal zone experience varying levels of exposure to air and water due to the changing tides. The gravitational force from the Moon causes these tidal cycles.

Question: Calculate the gravitational force between Earth and the Moon, which is responsible for tidal cycles affecting marine life in the intertidal zone.

Problem 6: Gravitational Force and Ocean Circulation

Context: Ocean currents are influenced by gravitational forces from the Moon and the Sun. These currents distribute nutrients that are essential for marine life, such as phytoplankton.

Question: Calculate the gravitational force between Earth and the Sun. How does this force contribute to ocean circulation patterns?

Problem 7: Gravitational Force Between Earth and a Large Submarine

Context: A large submarine in the ocean is subject to Earth's gravitational pull, just like any other object with mass. Understanding gravitational forces is important for underwater navigation and communication.

Question: Calculate the gravitational force between Earth and the submarine.

Tidal Forces: The Gravitational Dance Between Earth, Moon, and Sun

As marine biology students, you already understand the importance of tides to ocean ecosystems. Tides affect everything from the feeding behavior of intertidal organisms to the migration patterns of marine animals. The cause of tides is a fascinating interplay of gravitational forces between the Earth, Moon, and Sun, and these forces create the rhythmic rise and fall of sea levels that we call tides.

Let’s dive into how these tidal forces originate, how they operate, and why they are crucial for life in the ocean.

The Gravitational Influence of the Moon

The Moon is the primary driver of Earth's tides. Even though the Moon is only about 1/80th the mass of Earth, its gravitational pull on Earth’s oceans is significant, causing the water to "stretch" in response.

• As the Moon orbits the Earth, it pulls on the water in the oceans, causing a bulge of water on the side of Earth that faces the Moon. This bulge creates a high tide in that area.  
• On the opposite side of Earth, there is another bulge, even though the Moon’s gravitational force is weaker there. Here’s why: as the Moon pulls on Earth itself (because Earth and the Moon both orbit a common center of mass), the Earth gets "pulled" slightly toward the Moon, but the water doesn’t move with it. This causes a second high tide on the far side of Earth.

Tidal Bulges: How Earth Experiences Two High Tides

• Near-side Bulge: This is the high tide on the side of Earth facing the Moon, where the gravitational pull is strongest.
• Far-side Bulge: This is the high tide on the opposite side, where the gravitational pull is weaker but the Earth’s own motion causes the water to lag behind.

As Earth rotates, different regions pass through these bulges, creating the cycle of two high tides and two low tides every 24 hours. This regular pattern has profound effects on marine life, such as the availability of food in tidal zones, and the timing of reproduction for many coastal species.

The Role of the Sun: Adding Complexity to the Tides 

Although the Moon is the main player, the Sun also has an influence on tides. Despite being about 27 million times more massive than the Moon, the Sun’s gravitational pull is weaker because it is much farther away—about 390 times farther from Earth than the Moon.

• When the Earth, Moon, and Sun align (during full moons and new moons), their combined gravitational forces create higher spring tides. These tides have higher high tides and lower low tides, which occur because the tidal bulges from both the Sun and the Moon reinforce each other. These strong spring tides can be especially significant for marine organisms, as they expose or submerge large portions of the intertidal zone.
• During neap tides, which occur when the Earth, Moon, and Sun form a right angle (during first and third quarter moons), the Sun’s gravitational pull partially cancels out the Moon's. This results in lower high tides and higher low tides. Neap tides are less extreme and have a smaller tidal range. This can affect organisms that rely on the most extreme tidal changes for feeding or breeding, such as certain species of crabs or mollusks.
  
  
  

Summary of Tidal Forces and Their Impact

The origin of tidal forces can be summarized through a few key points:

1. Differential Gravitational Pull: The difference in gravitational pull exerted by the Moon (and the Sun) creates tidal bulges on Earth. The varying strength of gravity across Earth's surface causes the water to move and form high and low tides.  
2. Earth's Rotation: As Earth rotates on its axis, different regions pass through these tidal bulges. This creates the regular cycle of two high tides and two low tides each day, with the timing and size of these tides affected by the Moon's position.
3. Interaction with the Sun: The Sun’s gravity affects the tides, creating spring tides (when the Earth, Moon, and Sun are aligned) and neap tides (when the Moon and Sun are at right angles). These variations in tidal range can influence marine ecosystems in different ways, from nutrient cycling to animal behavior.

Why Tides Matter for Marine Biology

Tidal forces are essential for understanding the rhythms of life in the ocean. Many marine species have evolved to rely on the changes in tidal conditions:

• Intertidal Zones: Organisms living in the intertidal zone (the area between high and low tide) must adapt to extreme conditions of exposure and submersion. These organisms, such as barnacles, sea anemones, and crabs, rely on the regular ebb and flow of the tides to access food, shelter, and mating opportunities.
  
  
  
• Nutrient Distribution: Tides also help distribute nutrients throughout the ocean. The movement of water during high and low tides stirs up nutrients from the seabed, making them available to marine plants and plankton—key components of the marine food web.

  

  From the academic paper The influence of tide-brought nutrients on microbial carbon metabolic profiles of mangrove sediments

  
  
• Breeding and Feeding Cycles: Many marine species, including fish and invertebrates, time their breeding and feeding cycles with the tides. For example, some fish release their eggs during specific tidal conditions, while shorebirds may time their feeding to coincide with low tides, when more food is exposed on the shore.

  

  From the academic paper Tri-Spine Horseshoe Crab Aquaculture, Ranching and Stock Enhancement: Perspectives and Challenges

  
  

By understanding how tidal forces work, marine biologists can better predict the behavior of these species and how they might respond to changes in tidal patterns, whether due to natural events (like lunar eclipses or El Niño) or human-induced changes (like coastal development or climate change).

Key Takeaways

• Tidal forces are caused by the gravitational interaction between the Earth, Moon, and Sun, leading to the rise and fall of sea levels (tides).
• Spring tides occur when the Earth, Moon, and Sun align, creating higher high tides and lower low tides.
• Neap tides happen when the Sun and Moon form a right angle, leading to lower high tides and higher low tides.
• These tidal patterns are critical for many marine species and ecosystems, influencing feeding, reproduction, and nutrient cycling.

Understanding the science behind tidal forces not only enriches our knowledge of the ocean’s behavior but also helps us understand the delicate balance that sustains marine life.

Tidal Force Calculation

The formula for the tidal force 𝐹ₜ  exerted by a celestial body on Earth is:

where:

𝐺 is the gravitational constant (6.674 × 10⁻¹¹ N•m²/kg²),

𝑚 is the mass of the celestial body (either the Moon or the Sun),

𝑟 is the radius of Earth (approximately 6.371 × 10⁶ m),

𝑑 is the distance from Earth to the celestial body (about 3.84 × 10⁸ m for the Moon, and 1.5×10¹¹ m for the Sun).

Tidal Force from the Moon

The Moon, despite being much smaller than the Sun, exerts a significantly stronger tidal force on Earth’s oceans. Here's why:

This means that for every kilogram of mass on Earth, the Moon pulls with a force of about 1.101 × 10⁻⁶ N.

Tidal Force from the Sun

The Sun, despite its enormous size and mass, has a weaker tidal effect on Earth’s oceans because it is much farther away.

So, while the Sun’s tidal force is significant, it’s only about half as strong as the Moon's tidal force.

Tidal Forces and Their Profound Role in Marine Biology

The tidal forces generated by the gravitational pull of the Moon and the Sun have far-reaching implications, not only for the physical environment of Earth's oceans but also for the life forms that inhabit them. Understanding these forces is essential for marine biologists, as they shape everything from nutrient cycling to species behavior, and even global climate patterns. Here's a deeper look into how these gravitational interactions influence marine ecosystems:

Gravitational Dynamics of Tides

1. Tidal Generation: The pull of the Moon and Sun creates tidal forces that cause sea levels to rise and fall in a regular cycle known as the tides. The Moon has a more powerful influence on tides than the Sun, despite its smaller size, simply because it is much closer to Earth. This gravitational interaction leads to the formation of tidal bulges—regions of Earth's oceans where the water level is higher due to the gravitational pull of these celestial bodies. These bulges move as Earth rotates, causing two high tides and two low tides each day, with a periodicity of about 12 hours. 

   Tides influence the entire marine environment, determining when coastal ecosystems are submerged or exposed. These regular shifts affect not only the physical environment but also the biological processes that sustain marine life. 

2. Tidal Currents: As tides rise (flood tide) and fall (ebb tide), they create powerful tidal currents that move through the oceans and along coastlines. These currents are key to:

• Sediment Transport: Tidal movements help shape coastal landforms by moving sediments, which can create or erode beaches, estuaries, and tidal flats.
• Nutrient Cycling: Tidal currents mix waters, redistributing nutrients that are vital for marine life. This process is especially important for the productivity of coastal and estuarine ecosystems, where nutrients are constantly cycled between deep and shallow waters. 

Ecological Impacts of Tidal Forces

1. Intertidal Zone Dynamics: The intertidal zone, where the ocean meets the land, is one of the most biologically productive and ecologically important areas on Earth. However, it is also one of the most challenging environments for organisms to inhabit. Species in this zone must cope with extreme conditions: regular submersion in seawater followed by exposure to air. Organisms such as crabs, mollusks, and sea stars have evolved remarkable adaptations—like strong anchoring mechanisms, thick shells, or the ability to retain moisture during low tide—to survive these shifts.

2. Nutrient Availability: Tides are crucial for nutrient cycling in marine ecosystems. High tides bring nutrients from deeper waters into coastal areas, supporting primary production by phytoplankton, the foundation of the marine food web. When the tide recedes, it exposes nutrient-rich sediments, making them available for bottom-dwelling organisms such as worms, clams, and certain fish species. This constant turnover of nutrients supports a wide variety of marine life, ensuring healthy ecosystems along coastlines.

3. Estuarine Ecosystems: Tidal forces play a major role in creating dynamic estuaries—areas where freshwater from rivers mixes with saltwater from the ocean. These estuaries are incredibly productive and serve as vital nurseries for many marine species, providing shelter and food for young fish and other organisms. The fluctuating salinity and nutrient availability due to tides create a complex and ever-changing habitat, supporting a wide range of biodiversity. The mixing of fresh and saltwater during tidal cycles helps maintain the delicate balance required for estuarine ecosystems to thrive.

4. Species Distribution and Behavior: Tides strongly influence the distribution and behavior of marine species. For example, many fish species spawn during specific tidal conditions, when the movement of water helps disperse their eggs and larvae over large areas. Similarly, intertidal organisms such as mollusks, barnacles, and seaweeds time their feeding and reproductive activities to match the tidal cycles, ensuring their survival and maximizing their chances for growth.

5. Climate Regulation: Tidal forces also play an important role in regulating Earth's climate. By driving oceanic circulation patterns, tidal currents contribute to the mixing of ocean waters, which helps distribute heat across the planet. This ocean circulation, driven in part by tidal forces, influences weather patterns, stabilizes climate systems, and affects global climate change. The oceans act as a massive heat reservoir, and tidal forces help maintain this critical balance.

Human Implications and Resource Management

1. Coastal Resource Management: For marine biologists and coastal resource managers, understanding tidal dynamics is essential for ensuring sustainable practices. Knowledge of tidal cycles is key for activities like fishing, shellfish harvesting, and habitat restoration. Effective management of coastal resources depends on an understanding of how tides affect water quality, nutrient levels, and species behavior.

2. Impact on Coastal Communities: Coastal communities, particularly those relying on fishing, tourism, and recreation, are directly impacted by tidal patterns. Predictable tidal cycles support fishing activities, allowing for optimal harvest times, and are essential for the operation of tidal-powered energy systems. Conversely, changes in tidal regimes, such as those caused by climate change or human activities (like damming), can disrupt local economies and ecosystems, making it essential for marine biologists to monitor these changes.

3. Pollution and Contaminant Dispersion**: Tidal currents also influence how pollutants are spread through coastal waters. Understanding these patterns is vital for managing pollution, especially in estuarine and nearshore environments, where ecosystems are most vulnerable. Tides can carry contaminants from land into the sea and help disperse them throughout the coastal zone, impacting water quality and marine life. This is an important consideration for marine biology, as pollution can affect the health of marine organisms and the sustainability of entire ecosystems.

Newton's law of universal gravitation, which governs the tidal forces of the Moon and Sun, plays a central role in shaping marine ecosystems. These tidal forces are fundamental in driving the biological processes that support life in the ocean, influencing everything from nutrient cycling to species behavior. The dynamics of tides have profound ecological, economic, and environmental implications, affecting coastal ecosystems, marine biodiversity, and even global climate patterns. For marine biologists, understanding the physics of tidal forces is essential to understanding and preserving the delicate balance of life in Earth's oceans.

Discussion: Ecological Significance of Tidal Forces

Objective:

This exercise is designed to test your understanding of the role of carbohydrates in plants and their importance in agriculture. You will be asked to apply your knowledge of carbohydrate functions in plant growth, energy storage, structural support, and soil health to real-world agricultural scenarios.

Instructions:

• Read the following scenario and answer the questions based on your understanding of tidal forces in marine biology.
• Use your knowledge of physics of tides, intertidal zone ecology, and tidal influences on species behavior and distribution to address the questions thoroughly.

 Scenario:

You are a marine biologist tasked with conducting a study on a coastal ecosystem that includes a large intertidal zone, an estuary, and a nearby fishing community. The area is known for its biodiversity and is home to various species of fish, mollusks, and invertebrates. Over the past few years, however, the local fishing community has noticed shifts in the availability of certain species and a decline in overall productivity. This appears to be linked to changes in tidal patterns caused by both natural fluctuations and human activities that have altered the coastline.

Your goal is to evaluate how tidal forces influence the health and sustainability of the ecosystem, the behavior and distribution of species, and the local fishing industry.

Proposed Benoni-Maac Bridge and Mahinog Boulevard 

Questions:

Group 1 

Tidal Forces and Species Behavior

Question: Tidal forces strongly influence the timing of biological activities, such as spawning, feeding, and migration. How do tidal cycles affect the distribution and behavior of intertidal organisms, such as barnacles, mussels, and seaweeds?

Answer Prompt: Consider how tidal movements influence the availability of habitat (e.g., exposed or submerged), feeding opportunities, and reproductive timing for these organisms. Use examples of specific species where possible.

Group 2 Tidal Currents and Nutrient Cycling

Question: Tidal currents play a crucial role in the mixing and redistribution of nutrients. How do tidal movements contribute to nutrient cycling in estuarine and coastal ecosystems?

Answer Prompt: Explain how the ebb and flow of tides help circulate nutrients from deeper waters to shallower zones and how this affects primary producers like phytoplankton and benthic organisms.

Group 3 Intertidal Zone Dynamics

Question: The intertidal zone experiences extreme environmental conditions, such as alternating submersion and exposure. How do organisms living in this zone, like crabs and mollusks, adapt to these shifting conditions?

Answer Prompt: Discuss the physiological and behavioral adaptations these organisms have evolved to cope with desiccation, temperature changes, and the mechanical stress of tidal currents.

Group 4 Tides and Estuarine Ecosystems

Question: Estuarine ecosystems are particularly sensitive to changes in tidal patterns due to the mixing of freshwater and saltwater. How do tidal forces influence salinity gradients and the availability of nutrients in estuaries, and why is this important for juvenile fish and invertebrate species?

Answer Prompt: Consider how the fluctuating salinity and nutrient availability in estuaries are critical for the survival and development of many marine species. Explain how tidal actions shape these environments.

Group 5 Impact of Tidal Changes on Coastal Communities

Question: Over the years, human activities such as damming rivers, coastal development, and climate change have altered local tidal patterns. How might these changes affect coastal ecosystems and local fishing industries?

Answer Prompt: Discuss how changes in tidal regimes might disrupt nutrient cycling, species distribution, and breeding patterns, and how this could lead to declines in fish populations and shellfish harvests.

Group 6 Managing Coastal Resources Based on Tidal Knowledge

Question: Based on your understanding of tidal dynamics, propose a management strategy that could help restore or enhance the health of the coastal ecosystem and the productivity of local fisheries.

Answer Prompt: Consider how an understanding of tidal forces could guide the restoration of habitats (e.g., seagrass beds, tidal marshes) or the regulation of fishing practices to ensure sustainable harvests. Justify your recommendations based on the ecological roles of tides.

Evaluation Criteria:

• Understanding of Tidal Dynamics: Do your responses show a clear understanding of how tidal forces affect marine ecosystems, including species behavior, nutrient cycling, and ecosystem structure? 5pts
• Application to Ecological Context: Can you apply your knowledge of tidal forces to real-world ecological and management challenges, such as species distribution or coastal resource management?  5pts
• Scientific Rationale: Are your explanations grounded in established biological and physical principles, with logical reasoning supporting your proposed strategies or solutions? 5pts