Newton's Law of Gravitation

Universal Gravitation

Every mass attracts every other mass. Newton's law of universal gravitation:

$F = \frac{G m_1 m_2}{r^2}$

• $G = 6.674 \times 10^{-11}$ N·m²/kg² — the gravitational constant
• $m_1, m_2$ — masses in kg
• $r$ — distance between centres in metres
• $F$ — attractive force in Newtons

The Inverse-Square Law

Force falls off as $1/r^2$. Double the distance $\to$ one quarter the force. This is why the Moon orbits Earth rather than flying away — gravity weakens with distance, but never reaches zero.

Relation to $g = 9.81$ m/s²

At Earth's surface ($r = 6.371 \times 10^6$ m, $M_{\text{Earth}} = 5.972 \times 10^{24}$ kg):

$g = \frac{G M_{\text{Earth}}}{r^2} \approx 9.81 \ \text{m/s}^2$

The familiar constant $g$ is just Newton's law applied at Earth's surface.

Examples (using $m_1 = m_2 = 10^{10}$ kg)

Your Task

Implement gravForce(m1, m2, r) returning the gravitational force in Newtons.