Question

the value of gravitational constant G on earth is 6.67×10-11 Nm2/kg2 6.67×10-11 Nm2/kg2. what is it's value on the surface of moon?​

Answer 1

The value of Gravitational constant G on the surface moon is also

$6.67$ × $10^{-11} Nm^{2} Kg^{-2}$.

Explanation:

• According to Newton's law of universal gravitation, the attractive force $(F)$ between two point-like bodies is directly proportional to the product of their masses ($m_{1}$ and $m_{2}$) and inversely proportional to the square of the distance, r, between their centers of mass.

⇒ $F=G\frac{m_{1} m_{2} }{r^{2} }$

• In Newton's law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance.    

• In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy-momentum tensor.

• The measured value of the constant is known with some certainty to four significant digits.

• In SI units, its value is approximately $6.674$ × $10^{-11}m^{3}Kg^{-1}s^{-2}$ .
• But it actually represented as $6.67$ × $10^{-11} Nm^{-2} Kg^{-2}$.

• The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant) at denoted by the letter G.

According to the statement, we can find out $G$ is a universal constant.

∴ Its value on the surface of the moon is also $6.67$ × $10^{-11} Nm^{2} kg^{-2}$.  

Answer 2

• The gravitational force acts between any two bodies.

• The gravitational force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them.

      $F= G\frac{m_{1}m_{2} }{r^{2} }$

• The value of G is 6.67 × 10⁻¹¹ Nm²/kg²

• As G is the universal constant, its value anywhere in the universe will remain constant.

• Therefore, the value of G on the surface of the moon will be  6.67 × 10⁻¹¹ Nm²/kg².