8.2.1 Circular Orbits

• What are the two main types of orbital motion?

  Circular and elliptical
• The gravitational force between two objects is given by $F =$$G \frac{m_{1} m_{2}}{r^{2}}$, where $r$ is the distance between their centers
• Orbital motion is primarily due to gravitational attraction.
• Match the type of orbit with its characteristic:

  Circular ↔️ Constant speed and distance

  Elliptical ↔️ Varying speed and distance
• In a circular orbit, the gravitational force provides the centripetal force needed to keep the object moving in a circle.
• In a circular orbit, the object's speed is constant.
• What is an example of an object in a circular orbit?

  Artificial satellites
• The equation $\frac{G m_{1} m_{2}}{r^{2}} =$$\frac{m v^{2}}{r}$ shows the balance between gravitational and centripetal forces in a circular orbit.
• In a circular orbit, the object's distance from the central object remains constant.
• What is an example of a circular orbit in our solar system?

  Artificial satellites around Earth
• The orbital speed $v$ in a circular orbit can be calculated using the equation $v =$$\sqrt{\frac{G m_{1}}{r}}$, where $r$ is the radius
• What equation shows the relationship between orbital speed and radius?

  $\frac{G m_{1} m_{2}}{r^{2}} =$$\frac{m v^{2}}{r}$
• The equation \frac{G m_{1} m_{2}}{r^{2}} = \frac{m v^{2}}{r}</latex> can be simplified to show the relationship between orbital speed and radius
• Rearranging the equation $\frac{G m_{1} m_{2}}{r^{2}} =$$\frac{m v^{2}}{r}$ for v results in $v =$$\sqrt{\frac{G m_{1}}{r}}$.
• What is the relationship between orbital speed and radius according to the equation $v =$$\sqrt{\frac{G m_{1}}{r}}$?


  Inversely proportional
• For satellites around Earth, as the orbital radius increases, their speed decreases
• What are the two main types of orbits?

  Circular and elliptical
• A circular orbit maintains a constant speed and distance from the central object.
• Orbital motion is caused by mutual gravitational attraction
• What law governs gravitational force?

  Universal Gravitation
• In a circular orbit, gravitational force and centripetal force are balanced.
• As the orbital radius increases, what happens to the orbital speed?

  Decreases
• In a circular orbit, gravitational force provides the necessary centripetal force.
• The balance between gravitational and centripetal forces in a circular orbit can be represented by the equation $G \frac{m_{1} m_{2}}{r^{2}} =$$\frac{mv^{2}}{r}$.
• What is the equation for centripetal force?

  $F_{c} =$$\frac{mv^{2}}{r}$
• In a circular orbit, gravitational force provides the necessary centripetal force.
• What is the equation for gravitational force?

  $F =$$G \frac{m_{1} m_{2}}{r^{2}}$
• The balance between gravitational force and centripetal force in a circular orbit is represented by the equation $\frac{G m_{1} m_{2}}{r^{2}}$
• What is the equation for the balance between gravitational force and centripetal force?

  $\frac{G m_{1} m_{2}}{r^{2}} =$$\frac{mv^{2}}{r}$
• A circular orbit is maintained by a balance between gravitational and centripetal forces.
• What is the gravitational constant denoted by?

  $G$
• What two forces maintain a circular orbit?

  Gravitational and centripetal
• A circular orbit requires a precise balance between gravitational and centripetal forces.
• The gravitational force is given by $F =$$G \frac{m_{1} m_{2}}{r^{2}}$, where $G$ is the gravitational constant
• What do $m_{1}$ and $m_{2}$ represent in the gravitational force equation?


  Masses of the objects
• What does $r$ represent in the gravitational force equation?


  Distance between centers
• The centripetal force is given by $F_{c} =$$\frac{mv^{2}}{r}$, where $m$ is the mass of the satellite
• What does $v$ represent in the centripetal force equation?


  Orbital speed
• What does $r$ represent in the centripetal force equation?


  Orbital radius
• For a circular orbit to be stable, the gravitational force must equal the centripetal force.