
The gravity equation, g = G M/r2, 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 × 1024 kg and the radius of the Earth is 6.378 × 103 km. Consider the universal gravitational constant as G = 6.67 × 10-11 Nm2/kg2.
Solution
Given data:
- Gravitational acceleration on the surface of the Earth, g = ?
- Mass of the Earth, M = 5.972 × 1024 kg
- Radius of the Earth, r = 6.378 × 103 km = 6.378 × 106 m
- Universal gravitational constant, G = 6.67 × 10-11 Nm2/kg2
Applying the formula:
- g = G M/r2
- g = (6.67 × 10-11 × 5.972 × 1024)/(6.378 × 106)2
- g = (39.9 × 1013)/(40.7 × 1012)
- g = 0.9803 × 10
- g = 9.81 m/s2
Therefore, the gravitational acceleration on the surface of the Earth is 9.81 m/s2.
Problem #2
If the mass of Jupiter is 1.898 × 1027 kg and the radius of Jupiter is 69.911 × 103 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 Nm2/kg2.
Solution
Given data:
- Mass of the Jupiter, M = 1.898 × 1027 kg
- Radius of the Jupiter, r = 69.911 × 103 km = 69.911 × 106 m
- Gravitational acceleration on the surface of the Jupiter, g = ?
- Universal gravitational constant, G = 6.67 × 10-11 Nm2/kg2
Applying the formula:
- g = G M/r2
- g = (6.67 × 10-11 × 1.898 × 1027)/(69.911 × 106)2
- g = (12.7 × 1016)/(4887.6 × 1012)
- g = 0.002598 × 104
- g = 25.98 m/s2
Therefore, the gravitational acceleration on the surface of Jupiter is 25.98 m/s2.
Problem #3
What is the value of gravitational acceleration on the surface of Mars, given that the mass of Mars is 6.39 × 1023 kg and the radius of Mars is 3.3895 × 103 km? Consider the universal gravitational constant as G = 6.67 × 10-11 Nm2/kg2.
Solution
Given data:
- Gravitational acceleration on the surface of Mars, g = ?
- Mass of the Mars, M = 6.39 × 1023 kg
- Radius of the Mars, r = 3.3895 × 103 km = 3.3895 × 106 m
- Universal gravitational constant, G = 6.67 × 10-11 Nm2/kg2
Applying the formula:
- g = G M/r2
- g = (6.67 × 10-11 × 6.39 × 1023)/(3.3895 × 106)2
- g = (42.7 × 1012)/(11.5 × 1012)
- g = 3.71 m/s2
Therefore, the gravitational acceleration on the surface of Mars is 3.71 m/s2.
Problem #4
Calculate the value of gravitational acceleration on the surface of the Moon, with the mass of the Moon being 7.342 × 1022 kg and the radius of the Moon being 1.7371 × 103 km. Consider the universal gravitational constant as G = 6.67 × 10-11 Nm2/kg2.
Solution
Given data:
- Gravitational acceleration on the surface of the Moon, g = ?
- Mass of the Moon, M = 7.342 × 1022 kg
- Radius of the Moon, r = 1.7371 × 103 km = 1.7371 × 106 m
- Universal gravitational constant, G = 6.67 × 10-11 Nm2/kg2
Applying the formula:
- g = G M/r2
- g = (6.67 × 10-11 × 7.342 × 1022)/(1.7371 × 106)2
- g = (48.9 × 1011)/(3 × 1012)
- g = 16.3 × 10-1
- g = 1.63 m/s2
Therefore, the gravitational acceleration on the surface of the Moon is 1.63 m/s2.
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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