# Gravitational Acceleration Formula

## Gravitational Acceleration Formula

Students have undoubtedly experienced gravity in real life. After all, the force is what keeps humans’ feet firmly planted on the earth. If one launches a ball into the air in an upward motion. Then it will naturally come down. It is noteworthy that the speed of the ball will be slower when it is moving upwards than when it is moving downward. This is a result of the Gravitational Acceleration Formula caused by the gravitational pull. Students will talk about the acceleration due to the Gravitational Acceleration Formula in this topic. On the Extramarks website and smartphone application, they can read in-depth information regarding the Gravitational Acceleration Formula brought on by gravity.

### Definition:

The acceleration that an object experiences as a result of the gravitational force is known as the Gravitational Acceleration Formula due to gravity. The m/s2 is its SI unit. It has a direction and a magnitude. It is a vector quantity as a result.

The letter g stands in for the acceleration brought on by gravity. Its typical value at sea level on the surface of the earth is 9.8 ms2. The second law of motion and the law of universal gravitation of Newton serve as the foundation for its computation Gravitational Acceleration Formula.

Near the Earth’s surface, the Gravitational Acceleration Formula brought on by gravity is almost constant. However, it varies when near other planets or moons, or when the distance from the Earth is great. These conditions affect the Gravitational Acceleration Formula caused by gravity:

the body’s mass,

distance from the mass’s centre,

The universal gravitational constant is known as Constant G.

g = 𝐺𝑀𝑟2

### Formula:

According to the Gravitational Acceleration Formula, the strength of the forces drawing two bodies together was inversely related to their masses and the distance separating them. Similar to the gravitational force per unit mass of the body experiencing it, Gravitational Acceleration Formula is the specific gravitational force operating on one body in the gravitational field of the other.

Planet mass times planet radius equals the Gravitational Acceleration Formula

The Gravitational Acceleration Formula is given as g = G*M/R2

One possesses

• gravity acceleration or g.
• The gravitational constant is G.
• Planet mass is M.
• The planetary radius is R.

### Derivation:

Newton’s Second Law of Motion and Newton’s Law of Universal Gravitation serve as the foundation for the Gravitational Acceleration Formula caused by gravity. The most Gravitational Acceleration Formula for estimating the acceleration caused by gravity is given by these two laws: g = G*M/R2, where g is the Gravitational Acceleration Formula caused by gravity, G is the universal gravitational constant, M is mass, and R is distance. The remaining portions of this course refine this Gravitational Acceleration Formula, give further insight into what it means, and present real-world examples of how to utilise it to determine the acceleration due to gravity.

### Real Life examples:

Think about a satellite that needs to rotate in the upper atmosphere that surrounds the Earth. Students need to know the gravitational acceleration acting on the object in order to calculate the velocity it must move with in order to stay on its path.

### Solved examples

The Extramarks educational portal provides numerous solved examples related to the designated topic which can be conveniently accessed by students through the Extramarks website as well as the Extramarks Learning App.

#### Example 1:

When an object is placed on the surface of the Earth, and the Moon has a radius of 1.74 106 m and a mass of 7.35 1022 kg, calculate the acceleration caused by gravity.

Solution:

The moon’s radius is 1.74 x 106 metres, or 1740000 metres.

r2 = 3.0276 × 1012m

The moon weighs 7.35 1022 kg.

Students can write, using the formula for the acceleration caused by gravity:

g=GM\s/\sr\s2

When the values are substituted, students obtain,

g=(6.673×\s10\s−\s11\s)(7.35×\s10\s22\s)\s/\s3.0276×\s10\s12

g = (4.905 ×1012)/(3.0276 × 1012)

g = 1.620 m/s2

1.620 m/s2 is the acceleration brought on by gravity.

#### Example 2:

The Earth’s radius is 6.38 x 106 metres. The Earth has a mass of 5.98 x 1024 kg. What acceleration is caused by gravity if a satellite is 250 km above the surface of the Earth in its orbit?

Solution:

Since the satellite is visible at a significant distance from the Earth’s surface, the height cannot be ignored. Students can write, using the first formula,

R=r+h = (6.38 x 106 m) + (250 km)

R = 6 380 000 + 250 000 m

R = 6 630 000 m

The following formula can be used to determine the acceleration brought on by the satellite’s gravity:

g=GM\s/\s(r+h\s)\s2

g=(6.673×\s10\s−\s11\s)(5.98×\s10\s24\s)\s/\s(6630000\s)2

g = (3.9704×1014)/(4.396×1013)

g= 9.031 m/s2