Mass And Density Of Earth

Edited By Vishal kumar | Updated on Jul 02, 2025 07:14 PM IST

Understanding the mass and density of the Earth is crucial not just for scientists, but for anyone curious about how our planet supports life. The Earth's mass determines the gravitational force that holds everything from oceans to the atmosphere in place, while its density reveals how matter is distributed throughout the planet. Imagine standing on the ground; the force you feel pulling you down is a direct result of the Earth's mass. This gravitational pull allows us to walk, build structures, and even keep our atmosphere intact. In daily life, these concepts explain why we don't float off into space or why the air we breathe remains around us. By exploring Earth's mass and density, we gain insights into the very forces that shape our world.

This Story also Contains

What is the Mass of the Earth?
Soρ=3g4πGRρ=5478.4 kg/m3What is Inertial Mass?
What is Gravitational Mass?
What is Mass (m)?
What is Weight (W)?
Solved Examples Based on Mass and Density of Earth
Summary

Mass And Density Of Earth

What is the Mass of the Earth?

Using Newton’s law of gravitation we can estimate the mass of the earth
$\begin{aligned} M = \frac{g R^{2}}{G} ≃ 10^{25} kg \\ M \to mass of earth \end{aligned}$

$G \to$ Gravitational constant
What is the Density of Earth?

$As g = \frac{4}{3} π ρ G R$
Where $ρ$ is the density of the earth

$\begin{aligned} _{So} ρ = \frac{3 g}{4 π G R} \\ ρ = 5478.4 kg / m^{3} \end{aligned}$
What is Inertial Mass?

Also known as the mass of material of the body which measures its inertia.

From Newton’s second law of motion

$\begin{aligned} F = m_{i} a \\ {So}_{i} = \frac{F}{a} \\ Where \\ m_{i} \to inertial mass \\ F \to external force \\ a \to a c c^{n} \end{aligned}$

Gravity has no effect on inertial mass.
Inertial mass is independent of the size, shape, and state of the body.

What is Gravitational Mass?

It is mass which determines the gravitational pull acting upon it.

Let $F =$ gravitational pull on a body of mass applying Newton's law of gravitation

We have

$F = \frac{G M m_{g}}{R^{2}}$
So we get

$m_{g} = \frac{F}{G M / R^{2}} = \frac{F}{I}$
Where $m_{g} =$ Gravitational mass
$I \to$ Gravitational field intensity

Tip-Spring balance measures gravitational mass.

What is Mass (m)?

1. It is the quantity of matter contained in the body.
2. Its SI unit- Kg
3. Its dimension is $[M]$
4. It is a scalar quantity.
5. It Can never be zero
6. Its value does not change with g.

What is Weight (W)?

1. It is an Attractive force exerted by the earth on anybody.
2. S.I. Unit: Newton or Kg - wt
3. Dimension- $[M L T^{- 2}]$
4. It is a vector quantity
5. It changes its value according to the value of $g$
6. At $\infty$ and at the centre of the earth $g = 0$ , So W is equal to zero there.

Solved Examples Based on Mass and Density of Earth

Example 1: Average density of the earth

1) is directly proportional to g

2) is inversely proportional to g

3) does not depend on g

4) is a complex function of g

Solution:

Density of Earth

$ρ = \frac{3 g}{4 π G R}$

$ρ \to$ density of earth

$g \to 9.8 m / s^{2}$

$G \to$ Gravitational constant
wherein

$\begin{aligned} ρ = 5478.4 kg / m^{3} \\ As g = \frac{G M}{R^{2}} \Rightarrow M = \frac{g R^{2}}{G} \\ ρ = \frac{mass}{volume} = \frac{M}{\frac{4}{3} π R^{3}} \\ density \\ ρ = \frac{g R^{2} / G}{\frac{4}{3} π R^{3}} \\ ρ = \frac{3 g}{4 π G R} \Rightarrow ρ α g \end{aligned}$
Hence, the answer is the option 1.

Example 2: Which one statement is incorrect?

1) Gravity has no effect on the inertial mass of the body.

2) Inertial mass is independent of size, and shape.

3) Inertial mass measured by spring balance.

4) It is conserved when two bodies combine physically or chemically.

Solution:

Inertial mass

Mass of material of body which measures its inertia.

Gravity does not affect inertial mass.
wherein

$\begin{aligned} F = m_{i} a \\ m_{i} = \frac{F}{a} \\ m_{i} \to the inertial mass \\ F \to external force \\ a \to a c c^{n} \end{aligned}$

The inertial mass is measured by physical balance, not by spring balance.

Hence, the answer is the option 3.

Example 3: Which one statement is incorrect?

1) Gravitational mass is defined as the gravitational pull experienced by the body in the gravitational field.

2) Gravitational mass measured by spring balance

3) The dimensional formula of gravitational field intensity is $[L T^{- 2}]$

4) Gravitational mass is measured by applying Newton's law of gravitation

Solution:

Gravitational mass

$\begin{aligned} m_{g} & = \frac{F}{G M / R^{2}} = \frac{F}{I} \\ m_{g} & = Gravitational mass \end{aligned}$

$I \to$ Gravitational field intensity
wherein
Mass which determines the gravitational pull acting upon it,

$F = \frac{G M_{e} m_{g}}{R^{2}} or m_{g} = \frac{F}{\frac{G M}{R^{2}}} = \frac{F}{I}$
If $l = 1$ , then $m_{g} = F$

Hence gravitational mass is defined for unit field intensity.

Hence, the answer is the option 1.

Example 4: Which one of the statements is incorrect regarding mass?
1) It is a scalar quantity
2) The value of mass does not depend on gravity
3) The mass of a body is given by

$m = \frac{m_{o}}{(1 - \frac{v^{2}}{c^{2}})}$

here symbol have their usual meaning.
4) mass can never be zero.

Solution:

Mass

Quantity of matter contained in the body

$S . I . \to [K g]$

dimension $[M]$
wherein
(i) Value does not change with g
(ii) Can never be zero
(iii) Scalar quantity

$m = \frac{m_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$
Hence, the answer is the option 3.

Example 5: Regarding weight (w) which is correct?

(i) Its value changes with g

(ii) At the centre of the earth weight is maximum

(iii) The unit is kg-wt

(iv) It is a vector quantity

1)Only (i) and (iv)

2) Only (i), (iii) and (iv)

3) Only (ii) and (iii)

4) All of the above

Solution:

Weight (W)
The attractive force exerted by the earth on anybody.
S.I. Unit: Newton or Kg - wt

Dimension $[M L T^{- 2}]$ wherein
(i) Value changes with g
(ii) at $\infty$ and at centre of earth $g = 0$
(iii) Vector quantity

At the centre of the earth, $g = 0$
Hence, weight $= 0$
Hence, the answer is the option (2).

Summary

The Earth contains is estimated to be made up of 5.97 × 10²⁴ kg. A big portion of this mass is iron (nearly 32%), oxygen (30%) and then silicon (15%) followed by magnesium at 14%, while the remaining make up the rest. In its core, there are high concentrations of heavy metals hence it has a high mass density, about 5.52 grams per cm3 as opposed to most planets that fall within our solar system. The reason behind its high density is that there are many heavy elements in the mantle and crust of Earth.

Frequently Asked Questions (FAQs)

1. How does Earth's mass contribute to its ability to retain an atmosphere?

Earth's mass is crucial for retaining its atmosphere. The planet's gravitational force, determined by its mass, must be strong enough to prevent atmospheric gases from escaping into space. Lighter elements like hydrogen can escape more easily, while heavier gases like nitrogen and oxygen are more readily retained. This is why massive planets tend to have thicker atmospheres, while smaller bodies like the Moon have virtually no atmosphere.

2. How does Earth's mass affect its orbit around the Sun?

Earth's mass plays a crucial role in its orbit around the Sun. According to Kepler's laws of planetary motion, the period of Earth's orbit depends on both its mass and the Sun's mass. If Earth were more massive, it would orbit closer to the Sun for the same orbital period. The current mass of Earth, combined with its distance from the Sun, results in our 365.25-day year.

3. How does Earth's mass influence the orbits of artificial satellites?

Earth's mass directly influences the orbits of artificial satellites through gravitation. The force of gravity, which depends on Earth's mass, keeps satellites in orbit. The velocity required for a stable orbit (orbital velocity) is determined by Earth's mass and the satellite's distance from the center of Earth. Satellites closer to Earth must move faster to maintain orbit due to the stronger gravitational pull.

4. How does Earth's mass affect the escape velocity from its surface?

Earth's mass directly determines the escape velocity from its surface. Escape velocity is the minimum speed an object needs to break free from a planet's gravitational pull. It's calculated using the formula: v = √(2GM/R), where G is the gravitational constant, M is the mass of Earth, and R is Earth's radius. For Earth, this velocity is about 11.2 km/s. A more massive Earth would have a higher escape velocity.

5. How do tides on Earth relate to its mass and the mass of the Moon?

Tides on Earth are primarily caused by the gravitational interaction between Earth and the Moon. The strength of this interaction depends on the masses of both bodies and the distance between them. Earth's greater mass exerts a stronger gravitational pull on the Moon, but the Moon's gravity is still strong enough to cause the oceans to bulge. The Sun also contributes to tides, but to a lesser extent due to its much greater distance despite its enormous mass.

6. Why doesn't Earth's rotation affect its overall mass or density?

Earth's rotation doesn't affect its overall mass because rotation is a motion, not a property that adds or subtracts matter. However, rotation does affect Earth's shape, causing a slight bulge at the equator. This shape change causes minor variations in density across the planet's surface (the equator is slightly less dense than the poles), but the total mass and average density remain constant.

7. What is the relationship between Earth's mass, volume, and density?

The relationship between Earth's mass, volume, and density is expressed by the equation: Density = Mass / Volume. Earth's mass is approximately 5.97 × 10^24 kg, and its volume is about 1.08 × 10^21 m³. Dividing mass by volume gives the average density of 5.51 g/cm³. This relationship holds true for any object, not just Earth.

8. How would Earth's mass and density be different if it were made entirely of water?

If Earth were made entirely of water while maintaining its current size, its mass and density would be significantly lower. Water has a density of 1 g/cm³, so Earth's average density would decrease from 5.51 g/cm³ to 1 g/cm³. Its mass would reduce to about 1.08 × 10^24 kg, roughly 18% of its current mass. This would dramatically affect its gravitational field, ability to retain an atmosphere, and many other planetary processes.

9. Why doesn't Earth's mass change significantly over time?

Earth's mass remains relatively constant because the inflow and outflow of matter are nearly balanced. While Earth gains mass from cosmic dust and meteorites (estimated at 40,000 tons per year), it loses a small amount of mass through atmospheric escape (about 50,000 tons per year). These changes are negligible compared to Earth's total mass of 5.97 × 10^24 kg.

10. What would happen to Earth's density if it were twice its current mass but the same size?

If Earth were twice its current mass but maintained the same size, its density would double. The average density would increase from 5.51 g/cm³ to 11.02 g/cm³. This would likely result in a much larger core, higher internal pressures, and potentially different internal structure and composition. Such a planet would have a much stronger gravitational field and would behave differently in terms of plate tectonics and atmospheric retention.

11. How does Earth's density affect its gravitational field?

Earth's density distribution directly affects its gravitational field. The denser core contributes more to the total gravitational force than an equal volume of less dense crust. This is why gravity varies slightly across Earth's surface, being stronger where the crust is thinner or denser material is closer to the surface.

12. What would happen to Earth's mass if it suddenly lost its atmosphere?

If Earth suddenly lost its atmosphere, its mass would decrease by about 5.1 × 10^18 kg. However, this is only about 0.00009% of Earth's total mass. The change would be negligible in terms of Earth's overall gravitational effects, but it would have catastrophic consequences for life on the planet.

13. Why is knowing Earth's mass and density important for space exploration?

Understanding Earth's mass and density is crucial for space exploration because:

14. What evidence supports the idea that Earth's core is denser than its surface?

Several lines of evidence support a denser core:

15. How do scientists measure variations in Earth's density?

Scientists measure variations in Earth's density through several methods:

16. How do we know the mass of Earth?

We determine Earth's mass indirectly using Newton's law of universal gravitation. By measuring the gravitational force Earth exerts on objects (like the Moon or artificial satellites) and knowing their distances, we can calculate Earth's mass. This method doesn't require weighing the planet directly.

17. Why can't we simply weigh the Earth to find its mass?

We can't weigh Earth because weighing requires comparing an object's gravitational attraction to a known standard mass. Earth is the largest object in our immediate environment, providing the gravitational field we use for weighing. There's no larger reference object or scale to weigh Earth against.

18. What is the accepted value for Earth's mass?

The accepted value for Earth's mass is approximately 5.97 × 10^24 kg. This incredibly large number represents about 6 trillion trillion kilograms. It's important to remember that this value is an estimate based on various measurements and calculations, not a direct measurement.

19. How does Earth's mass compare to other planets in our solar system?

Earth is the fifth most massive planet in our solar system. The gas giants (Jupiter, Saturn, Uranus, and Neptune) are more massive, while the terrestrial planets (Mercury, Venus, and Mars) are less massive. For example, Jupiter is about 318 times more massive than Earth, while Mars is only about 0.107 times Earth's mass.

20. What is meant by the average density of Earth?

The average density of Earth is the total mass of the planet divided by its volume. It represents how much mass is packed into a given volume of the planet, considering all its layers from the core to the surface. Earth's average density is about 5.51 g/cm³, making it the densest planet in our solar system.

21. What role does Earth's density play in its internal heat generation?

Earth's density distribution, particularly its dense core, plays a significant role in internal heat generation. The decay of radioactive elements, primarily in the mantle and core, produces heat. Additionally, the high pressure in the dense core maintains its partially molten state, contributing to heat generation through friction and the release of gravitational potential energy as the planet slowly cools and contracts.

22. How does Earth's density compare to that of the Moon?

Earth's average density (5.51 g/cm³) is significantly higher than the Moon's (3.34 g/cm³). This difference is primarily due to Earth's larger size, which allows it to compress its interior more, and its higher iron content, particularly in the core. The Moon's lower density suggests it has a smaller metallic core relative to its size compared to Earth.

23. How does Earth's density affect its magnetic field?

Earth's density distribution, particularly its dense, metallic core, is crucial for its magnetic field. The liquid outer core, composed mainly of iron and nickel, creates Earth's magnetic field through the dynamo effect. Convection currents in this dense, electrically conductive fluid, influenced by Earth's rotation, generate and maintain the magnetic field. Without this dense core, Earth would likely not have a significant magnetic field.

24. What would happen to Earth's density if its core suddenly cooled and solidified?

If Earth's core suddenly cooled and solidified, its density would increase slightly. Solid materials are generally denser than their liquid counterparts due to tighter atomic packing. The outer core would contract as it solidified, potentially leading to a slight decrease in Earth's volume. This would result in a small increase in average density. However, this change would have far-reaching consequences for Earth's magnetic field, heat distribution, and tectonic activity.

25. Why isn't Earth's density uniform throughout its interior?

Earth's density isn't uniform throughout its interior due to several factors:

26. What role does Earth's density play in plate tectonics?

Earth's density distribution plays a crucial role in plate tectonics:

27. How does Earth's density affect seismic wave propagation?

Earth's density significantly affects seismic wave propagation:

28. How does Earth's density compare to the average density of the solar system?

Earth's average density (5.51 g/cm³) is significantly higher than the average density of the solar system, which is estimated to be around 1.4 g/cm³. This difference arises because the solar system's volume is mostly empty space, and its mass is dominated by the Sun, which has a lower density (1.41 g/cm³) than Earth. Earth's high density reflects its composition of heavy elements and internal compression due to gravity.

29. How does Earth's density affect its ability to retain heat?

Earth's density affects its heat retention in several ways:

30. Why is Earth's average density higher than the density of rocks on its surface?

Earth's average density (5.51 g/cm³) is higher than surface rocks (typically 2.7-3.3 g/cm³) because the planet's interior contains denser materials. The core, made primarily of iron and nickel, has a much higher density (about 13 g/cm³ for the outer core and 17 g/cm³ for the inner core). This high-density core significantly increases Earth's average density.

31. How does Earth's density vary from its surface to its center?

Earth's density increases from the surface to the center. The crust has a density of about 2.7-3.3 g/cm³, the mantle ranges from about 3.3-5.7 g/cm³, the outer core is about 10-13 g/cm³, and the inner core reaches about 13-17 g/cm³. This increase is due to greater pressure and heavier elements concentrated in the core.

32. What would happen to Earth's density if all its water suddenly turned to ice?

If all of Earth's water suddenly turned to ice, the planet's overall density would decrease slightly. Ice is less dense than liquid water (0.92 g/cm³ vs 1 g/cm³), so the volume of the planet would increase while its mass remained the same. However, given that water makes up only a small fraction of Earth's total volume, the change in overall density would be minimal, likely less than 0.1%.

33. How does Earth's mass compare to the total mass of all humans on the planet?

The total mass of all humans on Earth is negligible compared to the planet's mass. Assuming an average human mass of 62 kg and a global population of 7.9 billion, the total human mass is about 4.9 × 10^11 kg. Earth's mass is 5.97 × 10^24 kg, making the total human mass only about 0.000000008% of Earth's mass. This comparison illustrates the vast scale difference between planetary and human masses.

34. How does Earth's mass affect the length of a day?

Earth's mass indirectly affects the length of a day through its influence on the planet's rotation. While mass itself doesn't determine rotational speed, it affects Earth's moment of inertia. Events that redistribute Earth's mass, like large earthquakes or melting ice caps, can slightly change the rotation rate and thus the length of a day. However, these changes are typically in the millisecond range and don't noticeably affect our daily lives.

35. What would happen to Earth's density if it captured another moon?

If Earth captured another moon, its overall density would change slightly depending on the moon's size and composition. If the new moon merged with Earth, the planet's mass would increase more than its volume, leading to a slight increase in average density. However, if the moon remained in orbit, Earth's density wouldn't change significantly. The gravitational effects would be more noticeable, potentially affecting tides and orbital dynamics.

36. Why doesn't Earth's mass change when volcanoes erupt?

Earth's mass doesn't change when volcanoes erupt because the material ejected (lava, ash, gases) was already part of Earth's mass before the eruption. Volcanoes merely move matter from the planet's interior to its surface. While the distribution of mass changes slightly, the total mass remains constant. Only processes that add matter from space or allow matter to escape into space can change Earth's total mass.

37. What would happen to Earth's mass if all nuclear fusion on the Sun suddenly stopped?

If all nuclear fusion on the Sun suddenly stopped, Earth's mass would not be directly affected. The Sun's fusion processes don't add or subtract mass from Earth. However, the cessation of solar fusion would have catastrophic indirect effects on Earth, including rapid cooling and the end of photosynthesis, which would dramatically alter Earth's biosphere and potentially its atmospheric composition over time.