Home >> Science & Nature >> Astronomy

How to Calculate Gravitational Constant

Sir Isaac Newton derived a famous equation for calculating the force of gravity between two objects. This equation uses a constant called the Universal Gravitational Constant (G) and it is equal to 6.67 x 10^-11 cubic meters per kilogram per square second. People commonly ask how in the world scientists calculated this number. They did it by using the measured values of gravitation between two objects of known mass. Anyone can do it using his own mass, a relatively simple formula, and some well-known facts about the earth.

Instructions

- 1
  Write Newton's equation for the force due to gravity:
  
  F = (G x m1 x m2)/r^2
  
  F = force of gravity between objects 1 and 2
  G = universal gravitational constant
  m1 = mass of object 1
  m2 = mass of object 2
  r = distance between the centers of objects 1 and 2
  ^ = caret symbol that means "to the power of"
- 2
  Determine your weight in Newtons (N). Your weight is actually the force of gravity between you and the earth. To convert your weight from pounds to Newtons, multiply your weight by 4.45.
  
  Example: If you weigh 150 pounds, then you weigh 150 x 4.45 = 667.5 N
- 3
  Determine your mass in kilograms (kg) by dividing your weight in pounds by 2.2.
  
  Example: If you weigh 150 pounds, then your mass is 150/2.2 = 68.2 kg.
- 4
  Look up the mass and radius of the earth. According to Hypertextbook.com, the mass of the earth is 5.98 x 10^24 kg and the radius of the earth is 6.38 x 10^6 meters (m).
- 5
  Solve Newton's equation for gravity for G, the universal constant.
  
  G = (F x r^2)/(m1 x m2)
- 6
  Plug the values you have calculated so far into the appropriate places in the gravity equation. Let m1 = your mass, m2 = the mass of the earth, and r = the radius of the earth.
  
  Example: G = (667.5 x (6.38 x 10^6)^2)/ (68.2 x 5.98 x 10^24) = 6.67 x 10^-11

Astronomy