8.2.1 Circular Orbits

• Celestial bodies like planets can follow circular orbits.


  True
• Match Kepler's laws with their descriptions:

  Law of Ellipses ↔️ Planets move in elliptical orbits with the Sun at one focus

  Law of Equal Areas ↔️ Area swept by a planet's orbit in equal time intervals is constant

  Law of Periods ↔️ The square of the orbital period is proportional to the cube of the semi-major axis
• Celestial bodies such as planets, moons, and artificial satellites can follow circular orbits.


  True
• Which law states that planets move in elliptical orbits with the Sun at one focus?

  The Law of Ellipses
• The Law of Periods states that the square of the orbital period is proportional to the cube of the semi-major axis
• The gravitational force is inversely proportional to the square of the distance between objects.


  True
• What does the variable \(F\) represent in Newton's law of gravitation?

  Gravitational force
• Match the key concept with its description in Newton's law of gravitation:

  Gravitational force ↔️ Attracts all objects with mass

  Inverse square law ↔️ Force decreases with distance squared

  Newton's constant ↔️ Value: 6.674 × 10⁻¹¹ Nm²/kg²
• What is the defining characteristic of circular orbits?

  Constant radius
• In a circular orbit, the distance from the larger body remains constant
• The Law of Equal Areas states that the area swept by a planet's orbit in equal time intervals is constant.


  True
• What does Newton's law of gravitation describe?

  Universal gravitational force
• Newton's gravitational constant is approximately 6.674 × 10⁻¹¹ Nm²/kg²
• Match the Kepler's law with its description:

  Law of Ellipses ↔️ Planets move in elliptical orbits

  Law of Equal Areas ↔️ Constant area swept in equal time

  Law of Periods ↔️ T² ∝ a³
• Circular orbits maintain a constant radius
• In circular orbits, the gravitational force is balanced by the body's velocity
• The Law of Ellipses states that planets move in circular orbits.

  False
• Match Newton's concepts with their descriptions:

  Gravitational force ↔️ Attracts all objects with mass

  Directly proportional ↔️ Force increases with mass

  Inverse square law ↔️ Force decreases with distance squared

  Newton's constant ↔️ $6.674 \times 10^{ - 11} Nm^{2} / kg^{2}$
• Newton's gravitational constant is approximately $6.674 \times 10^{ - 11}$ Nm²/kg²
• In a circular orbit, gravitational force and centripetal force are equal.


  True
• Match the formula with its description:

  $F_{g} =$$G \frac{m_{1} m_{2}}{r^{2}}$ ↔️ Gravitational force

  $F_{c} =$$\frac{m_{2} v^{2}}{r}$ ↔️ Centripetal force

  $v =$$\sqrt{G \frac{m_{1}}{r}}$ ↔️ Orbital speed
• In circular orbits, the gravitational force and the body's velocity maintain a perfect balance.


  True
• In a circular orbit, there is a perfect balance between gravitational force and velocity
• What is the shape of a circular orbit?

  Perfect circle
• What do Kepler's laws describe?

  Planetary motion
• What does the Law of Equal Areas state?

  Constant area swept
• Kepler's Law of Periods states that the square of the orbital period is proportional to the cube of the semi-major axis
• The gravitational force is inversely proportional to the square of the distance between objects.


  True
• What is the value of Newton's gravitational constant?

  6.674 × 10^{-11} Nm²/kg²</latex>
• Match the key concept with its description:

  Gravitational Force ↔️ The force pulling the orbiting body towards the center

  Centripetal Force ↔️ The force required to maintain circular motion

  Orbital Speed ↔️ The speed at which the orbiting body moves
• The mass of the central body has a greater impact on orbital speed than the orbital radius.


  True
• Kepler's Law of Periods relates the orbital period to the semi-major axis
• Gravitational force is directly proportional to the product of masses.


  True
• Steps to derive the formula for orbital speed in circular orbits:

  1️⃣ Set gravitational force equal to centripetal force

  2️⃣ Substitute the formulas for gravitational and centripetal force

  3️⃣ Solve for orbital speed \(v\)
• The formula for orbital speed in a circular orbit is $v =$$\sqrt{G \frac{m_{1}}{r}}$, where \(m_1\) is the larger body's mass
• The orbital speed in a circular orbit depends on the larger body's mass and the orbit's radius
• What is the defining characteristic of a circular orbit?

  Constant radius
• The distance between an orbiting body and the larger body remains constant in a circular orbit.

  True
• In an elliptical orbit, the distance from the larger body varies
• Kepler's first law states that planets move in elliptical orbits with the Sun at one focus.

  True