Gravity equation

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Gravity equation
Gravity equation | Image: Learnool

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.

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Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.

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