Universal Gravitational Law

Overview

Engineering reference data for Universal Gravitational Law in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Symbol	Description	Unit
$x$	Input value	—
$y$	Output value	—
$k$	Conversion factor	—

Practical Example: Calculating Gravitational Force

The extracted text provides a concrete example of applying the universal law of gravitation. This section breaks down the calculation of the gravitational force (weight) acting on a person on Earth's surface.

Calculation Breakdown

We use the formula: $F = G \frac{m_1 m_2}{r^2}$

Where the values for this scenario are:

• $G$ (Universal Gravitation Constant): $6.668 \times 10^{-11} \, \text{N m}^2/\text{kg}^2$
• $m_1$ (Mass of Earth): $5.98 \times 10^{24} \, \text{kg}$
• $m_2$ (Mass of the person): $70 \, \text{kg}$
• $r$ (Distance from Earth's center to its surface): $6.37 \times 10^6 \, \text{m}$ (Earth's radius)

Plugging these into the formula yields: $F = (6.668 \times 10^{-11}) \frac{(5.98 \times 10^{24})(70)}{(6.37 \times 10^6)^2} \approx 688.1 \, \text{N}$

Summary of Example Parameters

Interactive Charts

References

• Original Source