Understanding Gravitational Force
Gravitational force is the attractive force that exists between any two objects with mass. It is the force that keeps planets in orbit around the sun and keeps us on the ground. According to Newton's Law of Universal Gravitation, every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The Gravitational Force Formula
The equation is:
F = G m1m2r2
Where:
- F = Gravitational Force (Newtons)
- G = Gravitational Constant ($6.674 \times 10^{-11} \text{ m}^3 \text{ kg}^{-1} \text{ s}^{-2}$)
- m₁ = Mass of the first object (kg)
- m₂ = Mass of the second object (kg)
- r = Distance between the centers of the masses (m)
How to Use the Calculator
Since gravitational calculations often involve massive numbers (planets) or tiny constants, scientific notation is recommended:
- Select what you are solving for (Force, Mass, or Distance).
- Enter the known values. For planetary calculations, use scientific notation (e.g., Earth Mass = 5.972e24).
- Click Calculate to view the force in Newtons.
Calculation Example: Earth and You
Let's calculate the gravitational force exerted by Earth on a person.
Step 1: Identify variables. $m_1$ (Earth) $= 5.972 \times 10^{24} \text{ kg}$. $m_2$ (Person) $= 70 \text{ kg}$. $r$ (Radius of Earth) $\approx 6.371 \times 10^6 \text{ m}$.
Step 2: Calculate using the formula. The result should be approximately $686 \text{ N}$.
Result: This equates to roughly $70 \text{ kg}$ of weight ($686 / 9.8$), which matches our weight on Earth's surface.
Frequently Asked Questions (FAQ)
What is the value of the Gravitational Constant (G)?
The accepted value is approximately $6.67430 \times 10^{-11} \text{ m}^3 \text{ kg}^{-1} \text{ s}^{-2}$. This extremely small number explains why we don't feel gravitational attraction to everyday objects like furniture or cars—the force is negligible compared to Earth's pull.
Why is the distance squared ($r^2$)?
This is known as the Inverse Square Law. As you move away from a mass, the gravitational pull weakens rapidly. If you double the distance, the force becomes four times weaker.
Is gravity the same everywhere on Earth?
No. Earth is not a perfect sphere; it bulges at the equator. Therefore, gravity is slightly stronger at the poles than at the equator. It also changes with altitude (higher altitude = weaker gravity).
Common Mass References
- Earth: $5.972 \times 10^{24} \text{ kg}$
- Moon: $7.348 \times 10^{22} \text{ kg}$
- Sun: $1.989 \times 10^{30} \text{ kg}$
- Human: $\approx 70 \text{ kg}$