8.2.1 Circular Orbits

• A circular orbit is a path around a celestial body where an object maintains a constant speed and altitude
• In a circular orbit, the centripetal force is provided by the gravitational force between the satellite and the celestial body
• The gravitational force in a circular orbit pulls the satellite towards the center of the orbit.


  True
• Match the force with its description in a circular orbit:

  Gravitational Force ↔️ Pulls the satellite towards the celestial body

  Centripetal Force ↔️ Keeps the satellite moving in a circular path
• The strength of the gravitational force depends on the masses of the satellite and the celestial body.


  True
• What does the variable $G$ represent in the formula for gravitational force?


  Gravitational constant
• What is orbital velocity in a circular orbit defined as?

  Speed to maintain circular path
• What is the formula for centripetal force required to keep a satellite in a circular path?

  $F_{c} =$$\frac{mv^{2}}{r}$
• Steps to derive the formula for orbital velocity

  1️⃣ Express gravitational force

  2️⃣ Express centripetal force

  3️⃣ Equate gravitational and centripetal forces

  4️⃣ Rearrange and solve for $v$
• The orbital velocity of a satellite depends on the mass of the satellite itself.

  False
• What provides the centripetal force in a circular orbit?

  Gravity
• The gravitational force in a circular orbit pulls the satellite towards the planet's center.


  True
• Gravity in a circular orbit changes the satellite's speed.

  False
• What is orbital velocity of a satellite in a circular orbit determined by?

  Gravitational and centripetal forces
• The formula for orbital velocity is $v =$$\sqrt{\frac{Gm_{2}}{r}}$
• The gravitational constant $G$ is the same for all celestial bodies.


  True
• Steps to solve orbital velocity problems using the formula

  1️⃣ Identify the given information (mass of celestial body, orbit radius)

  2️⃣ Plug the values into the formula

  3️⃣ Calculate the orbital velocity
• Kepler's Third Law states that the square of the orbital period is proportional to the cube of the semi-major axis
• What does the semi-major axis represent in Kepler's Third Law?

  Average distance from the planet
• In a circular orbit, the object maintains constant speed and altitude.

  True
• The balance between gravitational and centripetal forces ensures constant speed and altitude in a circular orbit.

  True
• For a satellite to maintain a stable circular orbit, the gravitational force must equal the centripetal
• In a circular orbit, the gravitational force provides the necessary centripetal force.


  True
• The speed of an object in a circular orbit remains constant.


  True
• What two characteristics are constant in a circular orbit?

  Speed and altitude
• What would happen to a satellite in a circular orbit if there was no gravity?

  It would fly in a straight line
• The orbital velocity of a satellite in a circular orbit is determined by the balance between gravitational force and centripetal force.
• In a stable circular orbit, the gravitational force equals the centripetal force.


  True
• Orbital velocity is determined by the balance between gravitational force and centripetal force.


  True
• The gravitational force acting on the satellite is given by $F_{g} =$$\frac{Gm_{1}m_{2}}{r^{2}}$, where $m_{1}$ and $m_{2}$ are the masses of the satellite and the celestial body
• For a stable circular orbit, the gravitational force and centripetal force must be equal.

  True
• The formula for orbital velocity is $v =$$\sqrt{\frac{Gm_{2}}{r}}$, where $m_{2}$ is the mass of the celestial body
• Centripetal force acts towards the center of the circle.
• If the gravitational force were stronger in a circular orbit, the satellite would crash into the planet.
• Match the factor with its dependence on orbital velocity:

  Mass of celestial body ↔️ Directly proportional

  Orbit radius ↔️ Inversely proportional
• The gravitational constant $G$ is a fixed value in the orbital velocity formula.


  True
• For a stable orbit, the gravitational force equals the centripetal force.


  True
• How does the mass of the celestial body affect orbital velocity?

  Directly proportional
• In the orbital velocity formula, $v$ represents the orbital velocity
• What happens to orbital velocity if the orbit radius decreases?

  Increases