Planet Mass Calculator

Formula

The formula to calculate the Planet Mass is:

\[ PM = \frac{a \cdot r^2}{G} \]

Where:

\(PM\) is the Planet Mass (kg)
\(a\) is the acceleration due to gravity (m/s²)
\(r\) is the radius between the planet and object (m)
\(G\) is the gravitational constant (\(6.67408 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2}\))

What is Planet Mass?

Planet Mass is the measure of the amount of matter contained in a planet. It is calculated using the acceleration due to gravity at the planet's surface, the radius of the planet, and the gravitational constant. This calculation is crucial for understanding the gravitational influence and various other physical characteristics of the planet.

Example Calculation 1

Let's assume the following values:

Acceleration Due to Gravity (a) = 9.8 m/s²
Radius between Planet and Object (r) = 6.371 \times 10⁶ m (Earth's average radius)

Using the formula:

\[ PM = \frac{9.8 \times (6.371 \times 10^6)^2}{6.67408 \times 10^{-11}} \approx 5.97 \times 10^{24} \, \text{kg} \]

The Planet Mass is approximately \(5.97 \times 10^{24}\) kg.

Example Calculation 2

Let's assume the following values:

Acceleration Due to Gravity (a) = 3.7 m/s² (Mars)
Radius between Planet and Object (r) = 3.389 \times 10⁶ m (Mars's average radius)

Using the formula:

\[ PM = \frac{3.7 \times (3.389 \times 10^6)^2}{6.67408 \times 10^{-11}} \approx 6.42 \times 10^{23} \, \text{kg} \]

The Planet Mass is approximately \(6.42 \times 10^{23}\) kg.