# Gravitational Force Calculator

### Mass of object 1 ($m_1$)

$\times 10 \text{ \^{} }$ $\text{ kilograms}$

### Mass of object 2 ($m_2$)

$\times 10 \text{ \^{} }$ $\text{ kilograms}$

### Distance between object centers ($d$)

$\times 10 \text{ \^{} }$ $\text{ meters}$

### Gravitational constant ($G$)

$\times 10 \text{ \^{} }$ $\text{ N}\,\text{m}^2/\text{kg}^2$

## Gravitational force formula

$$F = G \cdot \frac{m_1\,m_2}{d^2}$$ where $G$ is the gravitational constant in units of $\frac{\text{N}\,\text{m}^2}{\text{kg}^2}$. $$G = 6.67 \times 10^{-11}\ \frac{\text{ N m}^2}{\text{kg}^2}$$

## Derivations from gravitational force formula

### Acceleration due to gravity

$$a = G \cdot \frac{M}{r^2}$$

### Orbital velocity

$$v = \sqrt{ G \cdot \frac{ M }{ r } }$$
$M$ is the mass of the body being accelerated towards or orbited in the above two formulas. $r$ is the distance between the centers of the two bodies. For the orbital velocity formula, it is the average orbital radius.