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Gravitational constant given radius of Earth and acceleration of gravity Formula

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Gravitational Constant is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance. Check FAQs

[G] = \frac{[g] \cdot {R M}^{2}}{[Earth-M]}

[G] - Gravitational Constant?R_M - Mean Radius of the Earth?[g] - Gravitational acceleration on Earth?[Earth-M] - Earth mass?

Gravitational constant given radius of Earth and acceleration of gravity Example

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Here is how the Gravitational constant given radius of Earth and acceleration of gravity equation looks like with Values.

Here is how the Gravitational constant given radius of Earth and acceleration of gravity equation looks like with Units.

Here is how the Gravitational constant given radius of Earth and acceleration of gravity equation looks like.

6.7E-11 = \frac{9.8066 \cdot 6371^{2}}{6E+24}

6.7E-11 = \frac{9.8066m/s² \cdot {6371km}^{2}}{6E+24kg}

6.7E-11 = \frac{9.8066 \cdot 6371^{2}}{6E+24}

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Gravitational constant given radius of Earth and acceleration of gravity Solution

Follow our step by step solution on how to calculate Gravitational constant given radius of Earth and acceleration of gravity?

FIRST Step Consider the formula

[G] = \frac{[g] \cdot {R M}^{2}}{[Earth-M]}

Next Step Substitute values of Variables

∴

[G] = \frac{[g] \cdot {6371km}^{2}}{[Earth-M]}

Next Step Substitute values of Constants

∴

[G] = \frac{9.8066m/s² \cdot {6371km}^{2}}{6E+24kg}

Next Step Convert Units

∴

[G] = \frac{9.8066m/s² \cdot {6.4E+6m}^{2}}{6E+24kg}

Next Step Prepare to Evaluate

∴

[G] = \frac{9.8066 \cdot {6.4E+6}^{2}}{6E+24}

Next Step Evaluate

∴

[G] = 6.66502131396554E-11

LAST Step Rounding Answer

∴

[G] = 6.7E-11

Gravitational constant given radius of Earth and acceleration of gravity Formula Elements

Variables

Constants

Gravitational Constant

Gravitational Constant is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance.

Symbol: [G]

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Gravitational Constant

Mean Radius of the Earth

Mean Radius of the Earth is defined as the arithmetic average of the Earth's equatorial and polar radii.

Symbol: R_M

Measurement: LengthUnit: km

Note: Value can be positive or negative.

Formulas to find Mean Radius of the Earth

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Earth mass

Earth mass is the amount of matter contained within the planet, a fundamental parameter in gravitational interactions and celestial mechanics.

Symbol: [Earth-M]

Value: 5.9722E+24 kg

Other formulas in Tide Producing Forces category

Go Gravitational Forces on particles

F g = [g] \cdot (m 1 \cdot \frac{m 2}{r^{2}})

Go Separation of distance between centers of mass of two bodies given gravitational forces

r = \sqrt{\frac{([g]) \cdot m 1 \cdot m 2}{F g}}

Go Distance of point located on surface of Earth to center of Moon

r S/MX = \frac{M \cdot f}{V M}

Go Distance of point located on surface of earth to center of sun

r S/MX = \frac{f \cdot M sun}{V s}

How to Evaluate Gravitational constant given radius of Earth and acceleration of gravity?

Gravitational constant given radius of Earth and acceleration of gravity evaluator uses Gravitational Constant = ([g]*Mean Radius of the Earth^2)/[Earth-M] to evaluate the Gravitational Constant, The Gravitational constant given radius of Earth and acceleration of gravity formula is the constant in Newton's law of gravitation relating gravity to the masses and separation of particles, equal to 6.67 × 10−11 N m2 kg−2. Gravitational Constant is denoted by [G] symbol.

How to evaluate Gravitational constant given radius of Earth and acceleration of gravity using this online evaluator? To use this online evaluator for Gravitational constant given radius of Earth and acceleration of gravity, enter Mean Radius of the Earth (R_M) and hit the calculate button.

FAQs on Gravitational constant given radius of Earth and acceleration of gravity

What is the formula to find Gravitational constant given radius of Earth and acceleration of gravity?

The formula of Gravitational constant given radius of Earth and acceleration of gravity is expressed as Gravitational Constant = ([g]*Mean Radius of the Earth^2)/[Earth-M]. Here is an example- 6.7E-11 = ([g]*6371000^2)/[Earth-M].

How to calculate Gravitational constant given radius of Earth and acceleration of gravity?

With Mean Radius of the Earth (R_M) we can find Gravitational constant given radius of Earth and acceleration of gravity using the formula - Gravitational Constant = ([g]*Mean Radius of the Earth^2)/[Earth-M]. This formula also uses Gravitational acceleration on Earth, Earth mass constant(s).

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