The force of gravity is one of the fundamental forces of physics. Its most important aspect is that it is universally valid: all objects have a gravitational force that attracts others. The force of gravity exerted on an object depends on the mass of the bodies examined and the distance that separates them.
Steps
Part 1 of 2: Calculating the Force of Gravity Between Two Objects
Step 1. Define the equation for the force of gravity that attracts a body:
F.grav = (Gm1m2) / d2. In order to correctly calculate the gravitational force exerted on an object, this equation takes into account the masses of both bodies and the distance that separates them. The variables are defined as follows:
- F.grav is the force due to gravity;
- G is the universal gravitational constant equal to 6, 673 x 10-11 Nm2/ kg2;
- m1 is the mass of the first object;
- m2 is the mass of the second object;
- d is the distance between the centers of the objects under examination;
- In some cases you will be able to read the letter r instead of d. Both symbols represent the distance between the two objects.
Step 2. Use the correct units of measure
In this particular equation it is essential to use the units of the International System: the masses are expressed in kilograms (kg) and the distances in meters (m). You will need to make the necessary conversions before continuing with the calculations.
Step 3. Determine the mass of the object in question
For small bodies, you can find this value with a scale and thus determine its weight in kilograms. If the object is large, you will need to find its approximate mass by searching online or by looking at the tables on the last few pages of the physics text. If you are solving a physics problem, this data is usually provided.
Step 4. Measure the distance between the two objects
If you are trying to calculate the force of gravity between an object and planet Earth, then you need to know the distance between the center of the Earth and the object itself.
- The distance from the center to the earth's surface is approximately 6.38 x 106 m.
- You can find these values on the tables in textbooks or online where you are also given the approximate distances from the center of the Earth to objects placed at different altitudes.
Step 5. Solve the equation
Once you have defined the values for the variables, all you have to do is insert them into the formula and solve the math calculations. Check that all units of measurement are correct and well converted. Solve the formula respecting the order of operations.
- Example: Determines the force of gravity exerted on a 68 kg person on the earth's surface. The mass of the Earth is 5.98 x 1024 kg.
- Check once again that all variables are expressed with the right unit of measurement. The mass m1 = 5.98 x 1024 kg, the mass m2 = 68 kg, the universal gravitational constant is G = 6, 673 x 10-11 Nm2/ kg2 and finally the distance d = 6, 38 x 106 m.
- Write the equation: Fgrav = (Gm1m2) / d2 = [(6, 67 x 10-11) x 68 x (5, 98 x 1024)] / (6, 38 x 106)2.
- Multiply the masses of the two objects together: 68 x (5, 98 x 1024) = 4.06 x 1026.
- Multiply the product of m1 and m2 for the universal gravitational constant G: (4, 06 x 1026) x (6, 67 x 10-11) = 2, 708 x 1016.
- Square the distance between the two objects: (6, 38 x 106)2 = 4,07 x 1013.
- Divide the product of G x m1 x m2 for the distance squared to find the force of gravity in newtons (N): 2, 708 x 1016/ 4, 07 x 1013 = 665 N.
- The force of gravity is 665 N.
Part 2 of 2: Calculating the Force of Gravity on Earth
Step 1. Understand the second law of Newton's dynamics, which is expressed by the formula F = ma
This principle of dynamics states that every object accelerates when subjected to a direct force or to a system of forces that are not in equilibrium. In other words, if a force applied to an object is greater than the others acting in the opposite direction, then this object will accelerate according to the direction and direction of the force with greater intensity.
- This law can be summarized in the equation F = ma, where F is the force, m the mass of the object and a the acceleration.
- Thanks to this principle it is possible to calculate the force of gravity exerted on any object on the earth's surface through the known value of the acceleration of gravity.
Step 2. Learn what the gravitational acceleration generated by the Earth is
On our planet the force of gravity causes objects to accelerate at the rate of 9.8 m / s2. When looking at the bodies present on the earth's surface you can use the simplified formula Fgrav = mg to calculate the force of gravity.
If you want an even more exact value, you can always use the formula expressed in the previous section of article F.grav = (GmEarthm) / d2.
Step 3. Use the correct units of measure
In this particular equation you have to use the units of the International System. The mass must be expressed in kilograms (kg) and the acceleration in meters per second square (m / s2). You must perform the appropriate conversions before continuing with the calculations.
Step 4. Determine the mass of the body in question
If it is a small object, you can use a scale to find its weight in kilograms (kg). If you are working with larger objects, then you will need to research their approximate mass online or on tables found in physics textbooks. If you are solving a physics problem, this is usually provided in the description of the problem.
Step 5. Solve the equation
When you have defined the variables, you can insert them into the formula and proceed with the calculations. Make sure once again that all units of measurement are correct: mass must be in kilograms and distances in meters. Proceed to the calculations respecting the order of operations.
- Use the same equation as before to figure out how closely you can achieve the same result. Calculate the force of gravity exerted on a 68 kg individual on the earth's surface.
- Check that all the variables are expressed with the right units of measurement: m = 68 kg, g = 9, 8 m / s2.
- Write the equation: Fgrav = mg = 68 * 9, 8 = 666 N.
- According to the formula F = mg the force of gravity is 666 N, while with the more detailed equation (first part of the article) you have obtained the value 665 N. As you can see the two values are very close.
Advice
- These two formulas lead to the same result, but the shorter one is also simpler to use when examining an object on the planet's surface.
- Use the first formula if you do not know the value of the acceleration due to gravity on the planet or if you are trying to calculate the force of gravity between two very large celestial bodies, such as the Moon and a planet.
