The **gravity equation**, g = G M/r^{2}, states that the acceleration due to gravity (g) is equal to the product of the universal gravitational constant (G) and the mass (M) of the celestial body, divided by the square of the distance between the centers of mass (r). This equation enables the calculation of gravitational acceleration between two objects, utilizing their masses and the distance separating them. It is a fundamental equation in physics that aids in understanding the force of gravity acting between celestial bodies.

## Practice problems

### Problem #1

Calculate the value of gravitational acceleration on the surface of the Earth, given that the mass of the Earth is 5.972 × 10^{24} kg and the radius of the Earth is 6.378 × 10^{3} km. Consider the universal gravitational constant as G = 6.67 × 10^{-11} Nm^{2}/kg^{2}.

**Solution**

Given data:

- Gravitational acceleration on the surface of the Earth, g = ?
- Mass of the Earth, M = 5.972 × 10
^{24}kg - Radius of the Earth, r = 6.378 × 10
^{3}km = 6.378 × 10^{6}m - Universal gravitational constant, G = 6.67 × 10
^{-11}Nm^{2}/kg^{2}

Applying the formula:

- g = G M/r
^{2} - g = (6.67 × 10
^{-11}× 5.972 × 10^{24})/(6.378 × 10^{6})^{2} - g = (39.9 × 10
^{13})/(40.7 × 10^{12}) - g = 0.9803 × 10
- g = 9.81 m/s
^{2}

Therefore, the gravitational acceleration on the surface of the Earth is **9.81 m/s ^{2}**.

### Problem #2

If the mass of Jupiter is 1.898 × 10^{27} kg and the radius of Jupiter is 69.911 × 10^{3} km, calculate the value of gravitational acceleration on the surface of Jupiter. Take the value of the universal gravitational constant as G = 6.67 × 10^{-11} Nm^{2}/kg^{2}.

**Solution**

Given data:

- Mass of the Jupiter, M = 1.898 × 10
^{27}kg - Radius of the Jupiter, r = 69.911 × 10
^{3}km = 69.911 × 10^{6}m - Gravitational acceleration on the surface of the Jupiter, g = ?
- Universal gravitational constant, G = 6.67 × 10
^{-11}Nm^{2}/kg^{2}

Applying the formula:

- g = G M/r
^{2} - g = (6.67 × 10
^{-11}× 1.898 × 10^{27})/(69.911 × 10^{6})^{2} - g = (12.7 × 10
^{16})/(4887.6 × 10^{12}) - g = 0.002598 × 10
^{4} - g = 25.98 m/s
^{2}

Therefore, the gravitational acceleration on the surface of Jupiter is **25.98 m/s ^{2}**.

### Problem #3

What is the value of gravitational acceleration on the surface of Mars, given that the mass of Mars is 6.39 × 10^{23} kg and the radius of Mars is 3.3895 × 10^{3} km? Consider the universal gravitational constant as G = 6.67 × 10^{-11} Nm^{2}/kg^{2}.

**Solution**

Given data:

- Gravitational acceleration on the surface of Mars, g = ?
- Mass of the Mars, M = 6.39 × 10
^{23}kg - Radius of the Mars, r = 3.3895 × 10
^{3}km = 3.3895 × 10^{6}m - Universal gravitational constant, G = 6.67 × 10
^{-11}Nm^{2}/kg^{2}

Applying the formula:

- g = G M/r
^{2} - g = (6.67 × 10
^{-11}× 6.39 × 10^{23})/(3.3895 × 10^{6})^{2} - g = (42.7 × 10
^{12})/(11.5 × 10^{12}) - g = 3.71 m/s
^{2}

Therefore, the gravitational acceleration on the surface of Mars is **3.71 m/s ^{2}**.

### Problem #4

Calculate the value of gravitational acceleration on the surface of the Moon, with the mass of the Moon being 7.342 × 10^{22} kg and the radius of the Moon being 1.7371 × 10^{3} km. Consider the universal gravitational constant as G = 6.67 × 10^{-11} Nm^{2}/kg^{2}.

**Solution**

Given data:

- Gravitational acceleration on the surface of the Moon, g = ?
- Mass of the Moon, M = 7.342 × 10
^{22}kg - Radius of the Moon, r = 1.7371 × 10
^{3}km = 1.7371 × 10^{6}m - Universal gravitational constant, G = 6.67 × 10
^{-11}Nm^{2}/kg^{2}

Applying the formula:

- g = G M/r
^{2} - g = (6.67 × 10
^{-11}× 7.342 × 10^{22})/(1.7371 × 10^{6})^{2} - g = (48.9 × 10
^{11})/(3 × 10^{12}) - g = 16.3 × 10
^{-1} - g = 1.63 m/s
^{2}

Therefore, the gravitational acceleration on the surface of the Moon is **1.63 m/s ^{2}**.

## Related

## More topics

- Free fall equation
- Air resistance formula
- Terminal velocity equation
**Gravity equation**- Inertia formula
- Acceleration formula
- Momentum equation
- Mass formula
- Velocity formula
- Pressure equation
- Kinematic equations
- Friction equation

## External links

- Gravity Equation | Formula, Calculation & Example – Study.com
- Gravity Equation – Universe Today
- How to Calculate Force of Gravity: 10 Steps (with Pictures) – wikiHow
- Gravitational constant – Wikipedia
- The Value of g – The Physics Classroom
- Newton’s law of gravitation | Definition, Formula, & Facts – Britannica
- the earth’s gravity – University College London
- Newton’s Universal Law of Gravitation | Physics – Lumen Learning
- For Newton’s gravitation equation, how do you account for planet size? – Physics Stack Exchange
- What is the formula of gravity? – Quora
- Weight Equation – NASA (.gov)
- Calculating gravitational forces – IOP Spark
- Gravitational Force Calculator – Omni Calculator
- Gravity – Maths Is Fun

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