Value of g on Moon: Definition, Derivation and Sample Questions

Moon as well, like other massive objects in the Universe, attracts every other massive body gravitationally. Earth’s surface gravity is about 9.8 m per second per second while Moon’s surface gravity is about 1.6 m per second per second. The Moon’s surface gravity is weaker as it is far less massive than Earth. Here, we will discuss the value of acceleration due to gravity on the Moon along with a few important questions.

What is the Value of g?

The acceleration experienced by a freely falling item due to the gravitational force of a big body is known as acceleration due to gravity and is represented by the SI unit m/s2 as g. The value of g is determined by the mass of the enormous body and its radius, and it varies from one body to the next. On the moon, the value of g is constant.

m/s² is the SI unit of g.

It is a vector quantity that points to the center of the Earth.

G is the universal gravitational constant, with a value of 6.673 x 10^-11N m² Kg^-2.

M = Earth’s mass = 6 x 10²⁴ kg

r = radius of the earth = 6 kg

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

Gravity Value

The Earth's Gravity Is Denoted By g.

It is the net acceleration delivered to bodies as a result of the combined influence of gravitation and centrifugal force (from the rotation of the Earth). It has a value of approximately 9.8 ms^-2 near the earth's surface. Ignoring the constituents such as air resistance and object speed and assuming the body is free-falling under the effect of gravity.

The video below explains this:

Relation Between G And g Detailed Video Explanation:

Value of g

At a certain point, the value of g remains constant. It changes from place to place on the earth's surface due to height and spin.

The value of g at various distances from the center of the Earth is tabulated below.

The same equation that is used to get the value of g on Earth can be used to calculate the value of g on the surfaces of other planets.

The Value of g in All the Planets:

The value of g differs from place to place.

Value Of g on Moon

The value of g is calculated as follows:

The mass of the moon is 1/80 (1.2 percent) of the mass of the Earth, which is 7.342 x 10²² kg.

The radius of the Moon is 1.74 x 10^6 m.

Now, by using the formula:

g = GM/r²

Putting the value of G = 6.673 x 10^-11 Nm² Kg^-2 and M and r in the above equation:

= 6.673 x 10^-11x 7.342 x 10²² /(1.74 x 10⁶ )²

By calculating we get,

g(moon) =1.625 ms^-2 

As a result, the value of g(moon) is 1/ 6 or 16.7% of g(earth's surface).

We can also state that the gravity of the moon is 5/6, or 83.33 percent, less than that of the Earth.

Moon Gravity

Moon gravity can be defined as the acceleration due to gravity on the surface of the moon. The value of Moon’s gravity = 1.62 ms^-2

Moon's Gravitational Force

We all know that the weight of a body on the Moon is 1/6th of that on the Earth. It is because the gravitational force on the moon is 6 times smaller than the gravitational force on the earth, which is 1.625 ms^-2, and also the weight is directly based on gravitational acceleration.

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Things to Remember based on Value of g on Moon

• The acceleration experienced by a freely falling item due to the gravitational force of a massive body is the acceleration due to gravity.
• It is represented by the SI unit m/s² as g. 
• G is the universal gravitational constant, with a value of 6.673 x 10^-11N m² Kg^-2; M = Earth’s mass = 6 x 10²⁴ kg; r = radius of the earth = 6 kg.
• Earth’s surface gravity is about 9.8 m per second per second. 
• The mass of the moon is 1/80 (1.2 percent) of the mass of the Earth, which is 7.342 x 10²² kg.
• On the moon, you can jump close to your height.
• The value of the Moon’s gravity = 1.62 ms^-2
• If you fire a bullet from an M-16 rifle at a perfect angle, there's a good possibility it'll land on the other side of the moon or possibly cross it.

Sample Questions based on Value of g on Moon

Ques. Make a list of facts about the moon. (2 marks)

Ans. The following are some scientifically established facts about the moon:

• The moon's surface is normally dark.
• The moon moves the earth and the tides.
• The moon was formed when an asteroid the size of Mars collided with Earth.

Ques. Gravity is zero at what height? (2 marks)

Ans. Because the value of gravity decreases with height, we would get the value of g as 0 at one-half the Earth's radius.

That is, 9.8 ms^-2 per 3200 km.

Ques. Are You Able To Jump Off The Moon? (2 marks)

Ans. We can, indeed, jump from the moon. Even though we can jump quite high on the moon. To jump off the moon, you must move at speeds of up to 2 kilometers per second to escape the moon's surface.

Ques. What Is the Moon's Temperature? (2 marks)

Ans. One side of the moon lasts around 13.5 days during the day and has 13.5 days of darkness during half nights.

After the sun shines on its surface, the temperature can reach 260° F (127° C), but when the sun sets, the temperature drops to - 280° F (- 173° C).

Ques. The weight of a man on the Earth’s surface is 588 N. calculate his mass by taking g = 9.8 m/s². If the same man is on Moon, his weight would be 98 N. what is his mass on Moon. (2 marks)

Ans. Given, W_e = 588 N, g_e = 9.8 m/s², m = ?

From, W_e = mg_e, m = W_e/g_e = 588/9.8 = 60 kg

Again, W_m = 98N, g_m = ?

Mass on Moon = Mass on the Earth = 60 kg

G_m = W_m/m = 98/60 = 1.63 m/s².

Ques. What is the value of gravitational constant G? (1 mark)

1. On the Earth
2. On the Moon

Ans. a. The value of gravitational constant G on the earth as well as on the moon is 6.67 x 10^-11 Nm²/kg².

The value of G always remains constant irrespective of the location. 

Ques. The gravitational force on the surface of the moon is 1/6th as strong as the gravitational force on the earth. What is the weight of Newton’s 10 kg object on the moon as well as on the earth? (3 marks)

Ans. Given,

Mass of the object (m) = 10 kg

Acceleration due to gravity on the earth = g

Acceleration due to gravity on the moon = g

Now, 

g_m = ge/6 = 9.8/6 = 1.635 m/s²

Weight of an object on earth = W_e = mg_e = 10 x 9.8 = 98 Newton

Weight of an object on moon = W_m = mG_m = 10 x 1.635 = 16.35 Newton.

Ques. One object on the moon’s surface experiences the same gravitational force as the second object on the earth’s surface. Which of the following will be a reasonable conclusion? (2 marks)

1. Both objects will fall at the same acceleration
2. The object on the earth has a greater mass
3. The object on the moon has a greater mass
4. Both the objects will have identical masses.

Ans. The correct answer is option c. The object on the moon has a greater mass.

Explanation: As the acceleration due to gravity is less on the moon’s surface, to have the same gravitational force as the second object on the earth requires the object on the moon to have a larger mass.

Ques. The mass of the moon is about 1.2% of that of the earth. Compared to the gravitational force that the earth exerts on the moon, the gravitational force the moon exerts on earth: (2 marks)

1. Is the same
2. Is smaller
3. Varies with its phase
4. Is greater

Ans. The correct option is a. Is the same.

Explanation: Earth and Moon both exert the same force on each other.

Ques. The gravitational acceleration on the moon’s surface is 1.6 m/s². The radius of the moon is 1.7 x 10⁶ m. find the period of a satellite placed in a low circular orbit about the moon. (2 marks)

1. 1.0 x 10³ s
2. 1.1 x 10⁶ s
3. 6.5 x 10³ s
4. 5.0 x 10⁶ s

Ans. The correct option is c. 6.5 x 10³ s

Explanation: g = v²/r and v = 2????r/T

Ques. The mass of the moon is 7.34 x 10²² kg. If the acceleration due to the moon is 1.4 m/s², the radius of the moon is: (2 marks)

1. 0.56 x 104m
2. 1.87 x 10⁶m
3. 1.92 x 10⁶m
4. 1.01 x 10⁸m

Ans. The correct answer is b. 1.87 x 10⁶m

Explanation: We know,

g = GM/R²

Therefore, R = √GM/g = √6.67 x 10^-11 x 7.34 x 10²²/ 1,4 = 1.87 x 10⁶m.