9.2. Orbits of Planets and Satellites

• Newton's Law of Universal Gravitation states that the gravitational force between two objects is directly proportional to their masses
• The value of the gravitational constant G is 6.67 x 10^-11 N m^2/kg^2

  True
• Kepler's Three Laws of Planetary Motion

  1️⃣ Law of Ellipses: Planets move in elliptical orbits with the Sun at one focus

  2️⃣ Law of Areas: The radius vector from the Sun sweeps out equal areas in equal time

  3️⃣ Law of Periods: The square of the orbital period is proportional to the cube of the semi-major axis
• Kepler's Law of Periods states that the square of the orbital period is proportional to the cube of the semi-major axis
• Kepler's Laws are derived empirically, while Newton's Law of Universal Gravitation explains the underlying gravitational force

  True
• What is the mathematical relationship described in Kepler's Law of Periods?

  $T^{2} \propto r^{3}$
• Match the type of satellite orbit with its characteristics:

  Circular Orbit ↔️ Constant altitude, velocity, period

  Elliptical Orbit ↔️ Varies in altitude, velocity, period

  Geostationary Orbit ↔️ ~35,786 km altitude, 24-hour period
• Geostationary Orbit (GEO) satellites remain fixed above a point on the Earth's surface.
• What is the mathematical expression for Newton's Law of Universal Gravitation?

  $F =$$G \frac{m_{1} m_{2}}{r^{2}}$
• The gravitational force between two objects is inversely proportional to the square of the distance between them.
• What is the relationship between the orbital period and the semi-major axis in Kepler's Law of Periods?

  $T^{2} \propto r^{3}$
• What do Kepler's Laws of Planetary Motion describe?

  Planetary movement around the Sun
• What is the relationship between the orbital period and the semi-major axis in Kepler's Law of Periods?

  $T^{2} \propto r^{3}$
• Kepler's Laws are based on empirical observations, while Newton's Law explains the underlying gravitational force.
• A geostationary orbit has a period of 24 hours.
• What is a Low-Earth Orbit (LEO) commonly used for?

  Earth observation and communication
• Kepler's Laws and Newton's Law of Universal Gravitation are unrelated to each other.

  False
• The mathematical expression for Newton's Law of Universal Gravitation is F = G \frac{m_{1} m_{2}}{r^{2}}
• The gravitational force decreases linearly with the square of the distance between objects

  False
• Kepler's Law of Areas states that the speed of a planet is constant throughout its orbit

  False
• Kepler's Law of Ellipses states that planets move in elliptical orbits with the Sun at one focus
• A satellite in a circular orbit maintains a constant altitude
• What is the focus of Kepler's Laws compared to Newton's Law of Universal Gravitation?

  Empirically derived laws
• What is the altitude range of Low-Earth Orbit (LEO) satellites?

  160-2,000 km
• Arrange the key factors affecting satellite orbital characteristics in order of their effect on the satellite's velocity and period:

  1️⃣ Mass of central body

  2️⃣ Distance from central body

  3️⃣ Mass of satellite
• How does the mass of objects affect the gravitational force between them?

  Directly proportional
• What does Kepler's Law of Areas describe?

  Equal areas in equal time
• The radius vector from the Sun to a planet sweeps out equal areas during equal time intervals.

  True
• What does Kepler's Laws mathematically describe?

  T^{2} \propto r^{3}</latex>
• What is the altitude of a geostationary orbit (GEO)?

  ~35,786 km
• Geostationary satellites remain fixed above a point on the Earth's surface.


  True
• How does the distance from the central body affect the satellite's velocity?

  Inversely
• The effect of increasing the mass of an object on the gravitational force is that it becomes stronger
• Kepler's Law of Ellipses states that planets move in elliptical orbits.
• Match Kepler's Laws with their focus:

  Kepler's Laws ↔️ Describe planetary motion

  Newton's Law of Universal Gravitation ↔️ Describes gravitational force
• Match Kepler's Laws with their mathematical form:

  Kepler's Laws ↔️ $T^{2} \propto r^{3}$

  Newton's Law of Universal Gravitation ↔️ $F =$$G \frac{m_{1} m_{2}}{r^{2}}$
• Kepler's Laws describe planetary motion, while Newton's Law of Universal Gravitation describes the gravitational force. force
• Low-Earth Orbit (LEO) satellites are used for navigation systems like GPS.

  False
• Which factors determine the type of orbit a satellite will have?

  Altitude, velocity, period
• The gravitational constant (G) has a value of approximately 6.67 x 10^-11 N m^2/kg^2.


  True