The acceleration that a freely falling object experiences due to the gravitational force of a large body is known as acceleration due to gravity. It is measured in m/s2 and expressed as g.
The value of g is determined by the mass of the huge body and its radius. It varies according to the body. The value of g is constant on the Moon.
g is referred to as acceleration due to gravity. It is defined as the constant acceleration produced in a body when it freely falls under the effect of gravity alone.
The SI unit of ‘g’ is m/s2.
It is a vector quantity and is directed towards the center of the earth.
Where G is the universal gravitational constant and its value = 6.673 x 10-11 N m2 Kg-2
M = Earth’s mass = 6 x 1024 kg
r = radius of the earth = 6 kg
The value of g on earth is calculated by using the formula:
g = GM/r2
g = 6.673 x 10-11 x 6 x 1024 / (6)2
g = 9.8 ms-2
Value of Gravity
The Gravity of Earth is denoted by g.
It is the net acceleration that is transmitted to bodies due to the combined effect of gravitation and the centrifugal force (from the Earth's rotation).
Its value near the earth's surface is approx 9.8 ms-2
Ignoring the factors like air resistance and speed of the object and considering the body to be free falling under the influence of gravity.
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Value of g
The Table Below Shows The Value of g At Different Locations From Center of Earth
The same equation like we used for value of g on earth is used for calculating the value of g on the surface of other planets
The Value of g Varies In All The Planets Few of Them Are Described Below
Hence, the value of g varies at different places.
Value of g and its Derivation
SI unit of g = m/s2
It’s the vector quantity that points to the center of the Earth.
G = Universal Gravitational Constant
Its value is 6.673 x 10-11N m2 Kg-2
M = Earth’s mass
= 6 x 1024 kg
r = radius of the earth
= 6 kg
Hence, the formula for calculating the value of g on Earth is:
g = GM/r2
g = 6.673 x 10-11 x 6 x 1024 / (6)2
g = 9.8 ms-2
Value of g on the Moon
The acceleration due to gravity on the surface of the Moon is called the Moon gravity.
Now, for calculating the value of g on the Moon, the mass of the Moon and earth is to be considered.
The mass of the Moon is 1.2% of the mass of the earth which is equal to 7.342 x 1022 kg.
Now, the radius of the Moon = 1.74 x 106 m
Since the formula is
g = GM/r2
Now, putting all the values of G, we can get:
= 6.673 x 10-11 x 7.342 x 1022 /(1.74 x 106 )2
Hence, g(Moon) = 1.625 ms-2
The value of Moon’s gravity = 1.62 ms-2
Therefore, value of g(Moon) = \[\frac {1} {6}\] or 16.7% of g(earth’s surface)
Hence, it can be said that the gravity of the Moon is 5/6, or 83.33%, less than that of the Earth.
Gravity Value and Gravitational Force
It is well known that a person's weight on the Moon is one-sixth that on Earth. The explanation for this is that the gravitational force on the Moon is 6 times less than that on Earth. It's 1.625 ms-2. The weight is also directly based on gravitational acceleration.
The Moon, like all huge objects in the Universe, gravitationally attracts all other massive bodies. Since it is significantly less massive than Earth, the Moon's surface gravity is weaker.
Do You Know?
Let’s discuss some facts related to the same:
You can jump close to your height on the Moon.
Suppose you fire a bullet from a M-16 rifle at a perfect angle, there are high chances that bullet may fall on the other side of the Moon or may even cross it.
You can easily perform activities like backflip, sidekick, 400 560 kicks and so many acrobatics without getting hurt.
You can easily perform acrobatic exercises like somersaults without belly flops, provided there’s a pool on the Moon, because you’ll have a lot of time to adjust or position yourself for the perfect jump while you are in the air.
You can beat Ankita Sharma’s long jump record (8.19 meters) in a single try.
FAQs on Value of g on Moon
1. What is the value of acceleration due to gravity ('g') on the Moon?
The accepted average value for acceleration due to gravity on the surface of the Moon is approximately 1.62 metres per second squared (m/s²). This is about 16.5% of the value on Earth, which is 9.8 m/s².
2. How is the value of 'g' on the Moon calculated using its formula?
The value of 'g' on the Moon is calculated using the universal law of gravitation formula: g = GM/R², where:
- G is the Universal Gravitational Constant (6.674 × 10⁻¹¹ N·m²/kg²).
- M is the mass of the Moon (7.342 × 10²² kg).
- R is the radius of the Moon (1.74 × 10⁶ m).
Plugging these values into the formula gives the result of approximately 1.62 m/s².
3. Why is the Moon's gravity so much weaker than Earth's?
The Moon's gravity is significantly weaker primarily because of its smaller mass and smaller radius compared to Earth. Acceleration due to gravity is directly proportional to the mass of the celestial body and inversely proportional to the square of its radius. Since the Moon's mass is only about 1.2% of Earth's mass, its gravitational pull is substantially less, resulting in a 'g' value that is roughly 1/6th of Earth's.
4. How does an object's weight on the Moon compare to its weight on Earth?
An object's weight on the Moon is about one-sixth (1/6) of its weight on Earth. This is because weight is the product of mass and acceleration due to gravity (W = m × g). Since the Moon's 'g' is 1/6th of Earth's 'g', the resulting weight will also be 1/6th, even though the object's mass remains the same.
5. What is the key difference between 'g' (acceleration due to gravity) and 'G' (Universal Gravitational Constant)?
The key difference is that 'g' is a variable value while 'G' is a universal constant.
- 'g' (acceleration due to gravity): This is the acceleration experienced by an object due to the gravitational pull of a specific celestial body like Earth or the Moon. Its value changes depending on the body's mass and radius. For example, g on Earth is 9.8 m/s², while on the Moon it's 1.62 m/s².
- 'G' (Universal Gravitational Constant): This is a fundamental constant of nature, with a fixed value of 6.674 × 10⁻¹¹ N·m²/kg². It is the same everywhere in the universe and is used to calculate the gravitational force between any two objects.
6. If a person has a mass of 60 kg on Earth, what would their mass and weight be on the Moon?
This is a great example of the difference between mass and weight.
- Mass: The person's mass would remain exactly the same. Mass is the amount of matter in an object and does not change with location. So, on the Moon, their mass is still 60 kg.
- Weight: The person's weight would change significantly. On the Moon, their weight would be calculated as W = 60 kg × 1.62 m/s² = 97.2 Newtons. For comparison, their weight on Earth is 60 kg × 9.8 m/s² = 588 Newtons.
7. Can a person jump high enough to escape the Moon's gravity?
No, a person cannot jump high enough to escape the Moon's gravity. While you can jump much higher on the Moon due to the lower 'g', escaping its gravity requires reaching the lunar escape velocity, which is approximately 2.4 kilometres per second (or 8,640 km/h). This is far beyond the capability of a human jump. Any object that does not reach this speed will eventually be pulled back down to the lunar surface.
8. Does the value of 'g' on the Moon change if you are on a high lunar mountain?
Yes, the value of 'g' on the Moon does change slightly if you are on a high lunar mountain. According to the formula g = GM/R², the acceleration due to gravity is inversely proportional to the square of the distance from the center of the Moon. As you move to a higher altitude (like the top of a mountain), your distance (R) from the Moon's center increases, causing the value of 'g' to decrease slightly. However, this change is very small for typical mountain heights.
