Gravitational Field Intensity: Formulas and Solved Examples

Gravitational Field Intensity

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

Gravitational field intensity is a measure of the force exerted by gravity at a particular point in space. It describes how strong the gravitational force is at that point, typically expressed in units of N/kg (Newtons per kilogram). Understanding gravitational field intensity helps us comprehend the influence of gravity on objects, whether they're near the Earth's surface or in space. This concept is essential for explaining why objects fall towards the Earth, how planets orbit the sun, and many other phenomena governed by gravity. This article will delve into the principles of gravitational field intensity, with solved examples to enhance your understanding.

This Story also Contains

What is a Gravitational Field?
What is Gravitational Field Intensity?
Solved Examples Based on Gravitational Field Intensity
Summary

Gravitational Field Intensity

What is a Gravitational Field?

A gravitational field is a region of space surrounding a mass in which another mass experiences a force of attraction. It is a vector field, meaning it has both magnitude and direction, and is represented by the gravitational field strength (denoted by g), which is the force per unit mass exerted on a small test mass placed within the field.

What is Gravitational Field Intensity?

It is the force experienced by a unit mass at a point in the field. It is denoted by I. If the mass of a body is m then I is given by:

I→=F→mI→→ G.field Intensity m→ mass of object f→→ Gravitational Force

More About Gravitational Field Intensity

It is a vector quantity
If the field is produced by a body M the direction of its Gravitational field Intensity is always towards the center of gravity of M.
Unit: Newton kg or ms2
Dimension : [M0LT−2]

Solved Examples Based on Gravitational Field Intensity

Example 1: The mass density of a spherical body is given by ρ (r) = kr for r ≤ R and ρ (r)=0 for r > R, where r is the distance from the centre. The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is

Solution:

Given that,

p=mv of spherical body P(r)=kr
mv=kr for inside r⩽R
m=kvr……………..

inside the surface of the sphere, the intensity

I=GmrR3∵I=Fmginside =Gm3Rr or I=mgm=g=GR3kvrr= constant from equation (1) gout =Gmr2

Hence, the answer is the option (1).

Example 2: Which of the following statements about the variation of gravitational field strength is true?

1) It increases as we go above the surface of the earth

2) It increases as we go below the surface of the earth

3) Its magnitude is maximum at the surface of the earth

4) None of the above is true

Solution:

Gravitational field Intensity

It is the force experienced by a unit mass at a point in the field.

It is denoted by I

If the mass of a body is M then I is given by

I→=F→mI→=GMr2r^I→∝1r2

I is maximum at the surface of the earth.

For a test mass gravitational force acting due to earth is mg

So gravitational field strength will be equal to the g value.

So the value of the gravitational field strength is maximum at the surface of the earth.

Hence, the answer is the option (3).

Example 3: What is the unit of gravitational-field Intensity?

1) Unit: Newton kg
2) Unit: ms2
3) Unit : Newton 2 kg
4) Both of A and B

Solution:

If the mass of a body is m then Gravitational-field Intensity I is given by

I→=F→m Unit: Newton kg or ms2

Hence, the answer is the option(4).

Example 4:What is the dimension of Gravitational field Intensity :

1) [M0LT−2]
2) [M1LT−2]
3) [M2LT−2]
4) [M0L3T−2]

Solution:

Gravitational field Intensity I

It is the force experienced by a unit mass at a point in the field.

I→=F→m

The dimension of Gravitational field Intensity is : [M0LT−2]

Hence, the answer is the option(1).

Example 5: What is the effect of increasing the mass of an object on the strength of the gravitational field at a point in space?

1) It increases

2) Decreases

3) Remains constant

4) It depends on the distance from the object

Solution:

The intensity of the gravitational field at a point in space is directly proportional to the mass of the object creating the gravitational field, according to the formula g=Gmr2.

Therefore, increasing the mass of an object will also increase the intensity of the gravitational field at a point in space.

Hence, the answer is the option (1).

Summary

The phenomenon of gravity, or gravitation, is the attraction of all objects with mass or energy, such as galaxies, stars, planets, and lights. Earth's mass is given weight via gravity. The gaseous substance in the cosmos began to gravitationally attract one another to form stars, which then gathered into a galaxy. We can determine the intensity of the gravitational field by measuring the force that a unit mass experiences at any given level in the field. N kg-1 is the SI unit for gravitational field intensity. The intensity of the gravitational field is a scalar quantity.

Frequently Asked Questions (FAQs)

1. What is gravitational field intensity?

Gravitational field intensity, also known as gravitational field strength, is the force experienced by a unit mass placed at a point in a gravitational field. It is a vector quantity measured in newtons per kilogram (N/kg) and represents the strength of the gravitational field at that point.

2. How does gravitational field intensity change with distance from a massive object?

Gravitational field intensity decreases as the distance from a massive object increases. Specifically, it follows an inverse square relationship, meaning that if the distance doubles, the field intensity decreases by a factor of four (2²). This relationship is described by Newton's law of universal gravitation.

3. Is gravitational field intensity the same as gravitational acceleration?

Yes, gravitational field intensity is numerically equal to gravitational acceleration. Both are represented by the symbol 'g' and have the same units (N/kg or m/s²). The key difference is that field intensity is a property of space, while acceleration is the effect experienced by objects in that space.

4. How does the mass of an object affect the gravitational field intensity it experiences?

The mass of an object does not affect the gravitational field intensity it experiences. Gravitational field intensity is a property of space at a given point and depends only on the mass creating the field and the distance from that mass. This explains why objects of different masses fall at the same rate in a gravitational field (ignoring air resistance).

5. Why is the gravitational field intensity on Earth's surface approximately 9.8 N/kg?

The gravitational field intensity of 9.8 N/kg at Earth's surface results from Earth's mass and radius. This value is determined by the equation g = GM/R², where G is the gravitational constant, M is Earth's mass, and R is Earth's radius. The specific combination of Earth's mass and size results in this particular field intensity.

6. What's the difference between uniform and non-uniform gravitational fields?

A uniform gravitational field has the same intensity and direction at all points, like the approximation used for small regions near Earth's surface. A non-uniform field varies in intensity or direction (or both) from point to point, which is the case for most real gravitational fields, especially over larger distances or near irregularly shaped objects.

7. Why do astronauts experience "weightlessness" in orbit despite Earth's gravitational field?

Astronauts in orbit are still within Earth's gravitational field and experience nearly the same field intensity as on Earth's surface. Their apparent weightlessness is due to being in free fall around Earth. Both the astronauts and their spacecraft are falling towards Earth at the same rate, creating the sensation of weightlessness.

8. Can gravitational field intensity be shielded or blocked?

Unlike electromagnetic fields, gravitational fields cannot be shielded or blocked. Gravity penetrates all known materials and there's no known way to create a "gravity shield." This is because gravity is a fundamental property of mass and energy, and all matter interacts with gravitational fields.

9. How does the principle of equivalence relate to gravitational field intensity?

The principle of equivalence, a cornerstone of general relativity, states that the effects of gravity are indistinguishable from the effects of acceleration. This means that a uniform gravitational field is equivalent to a uniformly accelerating reference frame. The gravitational field intensity 'g' is equivalent to the acceleration of such a frame.

10. What's the difference between gravitational field intensity and gravitational flux?

Gravitational field intensity is a vector quantity representing the force per unit mass at a point, while gravitational flux is a measure of the total "flow" of the gravitational field through a given surface area. Flux is calculated by integrating the field intensity over an area and is useful in applying Gauss's law to gravitational fields.

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

Earth's rotation causes a slight reduction in the effective gravitational field intensity, especially near the equator. This is due to the centrifugal effect, which opposes the gravitational force. The difference is small (about 0.3% at the equator) but measurable, and it contributes to the Earth's equatorial bulge.

12. What's the relationship between gravitational field intensity and escape velocity?

Escape velocity is directly related to gravitational field intensity. The escape velocity at a point is equal to the square root of twice the product of the gravitational field intensity and the distance from the center of the mass creating the field. In equation form, v_escape = √(2gr), where g is the gravitational field intensity and r is the distance from the center of mass.

13. How does air pressure relate to gravitational field intensity?

Air pressure decreases with altitude due to gravitational field intensity. The atmosphere is held in place by Earth's gravity, and the pressure at any point results from the weight of the air above it. As you go higher and the gravitational field intensity decreases, there's less air above, resulting in lower pressure.

14. How does gravitational field intensity affect time dilation?

Gravitational field intensity is directly related to gravitational time dilation, a phenomenon predicted by Einstein's theory of general relativity. In stronger gravitational fields (higher field intensity), time passes more slowly relative to regions of weaker fields. This effect, while small on Earth, becomes significant near very massive objects like black holes.

15. How does gravitational field intensity affect the bending of light?

Gravitational field intensity affects the path of light through the principle of gravitational lensing. Stronger gravitational fields (higher field intensity) cause greater bending of light paths. This effect is predicted by general relativity and has been observed in phenomena like Einstein rings and gravitational microlensing.

16. What's the relationship between gravitational field intensity and gravitational waves?

Gravitational waves, ripples in spacetime predicted by general relativity, are produced by accelerating masses. The strength of these waves is related to the change in gravitational field intensity. Rapid changes in very strong gravitational fields, such as those produced by merging black holes, create detectable gravitational waves.

17. How does the concept of gravitational field intensity apply in quantum gravity theories?

In quantum gravity theories, which attempt to reconcile general relativity with quantum mechanics, the classical concept of gravitational field intensity may need to be revised. These theories often describe gravity in terms of quantum fields or discrete units of spacetime, which could lead to a quantized understanding of gravitational fields at very small scales.

18. How does the gravitational field intensity affect the rate of chemical reactions?

While the effect is extremely small under normal conditions, gravitational field intensity can theoretically affect chemical reaction rates. This is because gravity influences the energy levels of molecules, which in turn affects reaction kinetics. However, this effect only becomes significant in extremely strong gravitational fields, such as those near neutron stars or black holes.

19. How does the concept of gravitational field intensity apply to dark matter?

Dark matter, while invisible to direct observation, is detectable through its gravitational effects. The gravitational field intensity in galaxies and galaxy clusters is observed to be stronger than what can be accounted for by visible matter alone. This "extra" field intensity is attributed to the presence of dark matter, helping to map its distribution in the universe.

20. How does gravitational field intensity affect the behavior of quantum particles?

Gravitational field intensity affects quantum particles through phenomena like gravitational quantum states and the gravitational Aharonov-Bohm effect. These effects are typically extremely small and hard to measure, but they become important in understanding how quantum mechanics and gravity interact, especially in strong gravitational fields or at very small scales.

21. How does gravitational field intensity relate to the concept of gravitational redshift?

Gravitational redshift occurs when light moves out of a strong gravitational field. The frequency of the light decreases (shifts towards the red end of the spectrum) as it loses energy climbing out of the gravitational field. The magnitude of this redshift is directly related to the difference in gravitational field intensity between the point of emission and the point of observation.

22. What role does gravitational field intensity play in the formation of galaxies?

Gravitational field intensity plays a crucial role in galaxy formation. Regions of slightly higher density in the early universe had stronger gravitational fields, attracting more matter and growing over time. These growing overdensities eventually became the seeds of galaxies. The ongoing gravitational interactions, determined by the field intensities of various mass distributions, continue to shape galactic structures and clusters.

23. Can gravitational field intensity be negative?

Gravitational field intensity is always positive in magnitude, but it is a vector quantity with a direction. The negative sign is sometimes used to indicate that the force is attractive (pointing towards the center of mass). However, the field intensity itself, representing the strength of the field, is always a positive scalar value.

24. How is gravitational field intensity related to gravitational potential energy?

Gravitational field intensity is related to gravitational potential energy through the concept of work. The work done against gravity (which is equal to the change in gravitational potential energy) when moving an object in a gravitational field is the product of the object's mass, the displacement, and the gravitational field intensity.

25. How does the shape of a planet affect its gravitational field intensity?

The shape of a planet affects its gravitational field intensity distribution. While a perfectly spherical planet would have a uniform field intensity at its surface, real planets are slightly flattened at the poles due to rotation. This causes slight variations in field intensity, with it being slightly stronger at the poles than at the equator.

26. How does gravitational field intensity relate to weight?

Weight is the force experienced by an object due to gravity, and it's calculated by multiplying the object's mass by the local gravitational field intensity. In equation form, W = mg, where W is weight, m is mass, and g is the gravitational field intensity. This relationship explains why an object's weight changes in different gravitational fields, while its mass remains constant.

27. Can gravitational field intensity ever be zero?

In theory, gravitational field intensity can be zero at points where gravitational forces from different sources cancel out exactly. These points are called Lagrange points in space. However, true zero field intensity is practically impossible to achieve in real-world scenarios due to the presence of masses throughout the universe.

28. How does the concept of gravitational field intensity apply to black holes?

Near a black hole, the gravitational field intensity becomes extremely high. At the event horizon, the field intensity is so strong that the escape velocity equals the speed of light. Beyond this point, the classical concept of field intensity breaks down, and general relativity is needed to describe the extreme gravitational effects.

29. Why doesn't the gravitational field intensity inside a hollow sphere change with position?

Inside a hollow sphere, the gravitational field intensity is zero at all points. This is because the gravitational forces from all parts of the sphere cancel out perfectly at every internal point. This result, known as the shell theorem, is a consequence of the inverse square nature of gravity and the symmetry of the sphere.

30. How does the gravitational field intensity vary inside a solid planet?

Inside a solid planet, the gravitational field intensity varies with depth. It increases linearly from the center to the surface, assuming uniform density. At the center, the field intensity is zero. This is different from the behavior outside the planet, where field intensity decreases with distance according to the inverse square law.

31. What role does gravitational field intensity play in tidal forces?

Tidal forces arise from differences in gravitational field intensity across an extended object. For example, the side of the Earth facing the Moon experiences a slightly stronger gravitational field than the center of the Earth, which in turn experiences a stronger field than the far side. These small differences in field intensity create the tidal bulges in Earth's oceans.

32. Can gravitational field intensity be negative in general relativity?

In general relativity, the concept of gravitational field intensity is replaced by spacetime curvature. While the curvature itself isn't described as positive or negative, the effects can be attractive or repulsive. In some exotic scenarios involving negative energy density, gravity could become repulsive, analogous to a negative field intensity in Newtonian gravity.

33. How does the gravitational field intensity of a neutron star compare to that of Earth?

The gravitational field intensity at the surface of a typical neutron star is enormously greater than Earth's – often around 10¹¹ to 10¹² m/s² (compared to Earth's 9.8 m/s²). This extreme field intensity is due to the neutron star's incredibly high density and relatively small radius, resulting in a very strong gravitational field near its surface.

34. Why doesn't the high gravitational field intensity of a black hole tear apart nearby objects through tidal forces?

While black holes do have extremely high gravitational field intensities, tidal forces depend on the difference in field intensity across an object. For very large black holes (supermassive black holes), this difference can be relatively small for nearby objects, allowing them to orbit without being torn apart. Smaller black holes, however, can produce significant tidal forces that can disrupt nearby objects.

35. How does gravitational field intensity relate to the concept of gravitational time dilation?

Gravitational time dilation is directly related to gravitational field intensity. In regions of higher field intensity, time passes more slowly relative to regions of lower intensity. This effect is described by general relativity and has been measured on Earth, where clocks at higher altitudes (experiencing lower field intensity) run slightly faster than those at sea level.

36. Can artificial gravity be created by manipulating gravitational field intensity?

True artificial gravity by manipulating gravitational fields is not currently possible with known physics. However, the effects of gravity can be simulated by acceleration, as described by Einstein's equivalence principle. For example, a rotating space station can create a centrifugal force that mimics gravity, even though it's not altering the actual gravitational field intensity.

37. What's the relationship between gravitational field intensity and the curvature of spacetime?

In general relativity, gravitational field intensity is a manifestation of spacetime curvature. Regions with stronger gravitational fields correspond to greater curvature of spacetime. The degree of curvature determines how objects move through space and time, which we interpret as the strength of the gravitational field.

38. Can gravitational field intensity be used to determine the internal structure of planets?

Yes, variations in gravitational field intensity can be used to infer information about a planet's internal structure. By precisely measuring the gravitational field around a planet, scientists can detect density variations within the planet. This technique, known as gravitational field mapping, has been used to study the interiors of Earth and other planets in our solar system.

39. What's the relationship between gravitational field intensity and gravitational potential?

Gravitational field intensity is the negative gradient (rate of change) of the gravitational potential. In other words, the field intensity at any point is equal to the rate at which the potential changes with distance, pointing in the direction of steepest decrease in potential. This relationship is analogous to that between electric field and electric potential in electrostatics.

40. How does the principle of superposition apply to gravitational field intensity?

The principle of superposition states that the total gravitational field intensity at any point is the vector sum of the individual field intensities produced by all masses in the system. This allows us to calculate complex gravitational fields by breaking them down into simpler components and adding their effects vectorially.

41. Can gravitational field intensity be used to detect exoplanets?

Yes, variations in gravitational field intensity are used indirectly to detect exoplanets. The gravitational field of an orbiting planet causes its star to wobble slightly. This wobble can be detected through precise measurements of the star's position (astrometry) or its spectrum (radial velocity method), allowing astronomers to infer the presence and properties of exoplanets.

42. What's the connection between gravitational field intensity and the equivalence principle?

The equivalence principle, a cornerstone of general relativity, states that the effects of gravity are indistinguishable from the effects of acceleration. This means that a uniform gravitational field (constant field intensity) is equivalent to a uniformly accelerating reference frame. This principle led Einstein to realize that gravity could be described as curvature of spacetime.

43. Can gravitational field intensity be used to test alternative theories of gravity?

Yes, precise measurements of gravitational field intensity can be used to test alternative theories of gravity. Different theories often predict slightly different gravitational fields in extreme conditions. By measuring the gravitational field intensity around very massive or dense objects, or over very large distances, scientists can compare observations with the predictions of various gravitational theories.

44. How does gravitational field intensity affect the propagation of gravitational waves?

While gravitational waves themselves are ripples in spacetime, their propagation can be affected by background gravitational fields. In regions of strong gravitational field intensity, gravitational waves can be bent (similar to gravitational lensing of light) or experience time dilation effects. These interactions are important in understanding gravitational wave signals from extreme astrophysical events.

45. How does the concept of gravitational field intensity apply to the expansion of the universe?

In cosmology, the expansion of the universe is described by the scale factor, which relates to the average gravitational field on cosmic scales. While local gravitational fields cause attraction, the overall expansion of the universe can be thought of as a repulsive effect on the largest scales