Physics Demonstrations

Gravitational Force

Mass 1 (kg)
Mass 2 (kg)
Distance (m)

In this demonstration, we explore the gravitational interaction between two masses ( $m_{1}$ , $m_{2}$ ) separated by a distance ( $r$ ), and observe the angular velocity of $m_{1}$ orbiting $m_{2}$ . The gravitational force between the two masses is: $F = G \cdot \frac{m_{1} \cdot m_{2}}{r^{2}}$ For a circular orbit, this gravitational force acts as the centripetal force on $m_{1}$ : $G \cdot \frac{m_{1} \cdot m_{2}}{r^{2}} = m_{1} \cdot ω^{2} \cdot r$ Solving for the angular velocity $ω$ : $ω = \sqrt{\frac{G \cdot m_{2}}{r^{3}}}$ Where $G$ is the universal gravitational constant $G = 6.674 \times 10^{- 11}$ N·m²/kg². The orbital period is then: $T = \frac{2 π}{ω} = 2 π \sqrt{\frac{r^{3}}{G \cdot m_{2}}}$ Some questions to consider while viewing the demonstration: How does increasing the mass of $m_{2}$ affect the angular velocity of $m_{1}$ ? How does doubling the orbital radius $r$ affect the angular velocity? What power law does this illustrate? Notice that the angular velocity is independent of $m_{1}$ . Can you explain why physically? Identify a real-world example of this type of orbital motion in our solar system.