Motion of Orbiting Satellites - AP Physics C Mechanics

1. What is the relationship between orbital radius and period?

   $T^2 \text{ is proportional to } r^3$. Kepler's third law relating orbital size to period.

2. Find the gravitational force on a satellite of mass $m$ orbiting Earth.

   $F = \frac{GMm}{r^2}$. Newton's law of gravitation with Earth's mass $M$ and distance $r$.

3. What is the formula for the angular momentum of a satellite in orbit?

   $L = mvr$. Product of mass, velocity, and orbital radius.

4. Identify the relation between gravitational potential and distance from Earth's center.

   $V = -\frac{G M}{r}$. Gravitational potential energy per unit mass.

5. State Kepler's Second Law.

   A line joining a planet and the Sun sweeps out equal areas in equal time intervals. Conservation of angular momentum causes variable orbital speeds.

6. State the formula for the centripetal force acting on a satellite in orbit.

   $F = \frac{mv^2}{r}$. Force directed toward center required for circular motion.

7. What is the formula for gravitational potential energy of a satellite?

   $U = -\frac{G M m}{r}$. Negative value indicates bound system with zero reference at infinity.

8. What happens to the period of orbit if the mass of the satellite increases?

   The period remains unchanged. Period depends only on orbital radius, not satellite mass.

9. What is the expression for kinetic energy of a satellite in orbit?

   $K = \frac{1}{2} \frac{GMm}{r}$. Half the gravitational potential energy magnitude.

10. What is the effect of increasing altitude on orbital speed?

    Orbital speed decreases. Higher orbits have slower speeds per $v = \sqrt{GM/r}$.

11. Identify the expression for the orbital speed of a satellite.

    $v = \frac{2 \pi r}{T}$. Circumference divided by period for uniform circular motion.

12. What is the gravitational field strength at distance $r$ from a planet?

    $g = \frac{GM}{r^2}$. Gravitational acceleration at any distance from planet center.

13. What happens to the orbital speed if the radius of orbit increases?

    Orbital speed decreases. Inverse relationship from $v = \sqrt{GM/r}$ formula.

14. Identify the expression for angular velocity of a satellite in orbit.

    $\text{Angular velocity} = \frac{2 \pi}{T}$. Rate of angular displacement for orbital revolution.

15. What is the semi-major axis for a circular orbit?

    It is equal to the orbital radius. Semi-major axis equals radius for circular orbital geometry.

16. What is the consequence of a satellite losing energy in orbit?

    It will spiral inward. Energy loss causes orbital decay toward the planet.

17. Identify the expression for total mechanical energy of a satellite in orbit.

    $E = -\frac{GMm}{2r}$. Sum of kinetic and gravitational potential energies.

18. Identify the condition for a stable orbit.

    Gravitational force equals centripetal force. Balance between gravitational attraction and centrifugal tendency.

19. Calculate the gravitational force on a satellite at height $h$ above Earth.

    $F = \frac{GMm}{(R + h)^2}$. Gravitational force decreases with square of distance.

20. What is the effect on orbital period if the mass of the planet increases?

    The period decreases. Larger planetary mass creates stronger gravitational field.

21. State Kepler's Third Law.

    $T^2 \text{ is proportional to } r^3$. Square of period proportional to cube of semi-major axis.

22. Calculate the gravitational potential energy at height $h$ above Earth.

    $U = -\frac{G M m}{R + h}$. Distance from Earth center becomes $R + h$.

23. What is the gravitational constant $G$?

    $6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2$. Universal gravitational constant in SI units.

24. Which force provides the centripetal force for an orbiting satellite?

    Gravitational force. Earth's gravity provides the centripetal force for circular orbits.

25. What is the specific energy of a satellite in orbit?

    $\text{Specific energy} = -\frac{GM}{2r}$. Total energy per unit mass for orbital motion.

26. What is the significance of a geostationary orbit?

    It has a period equal to Earth's rotation period. Satellite remains fixed above same Earth location.

27. What is the significance of a satellite's total mechanical energy being negative?

    The satellite is bound to the planet. Negative total energy indicates gravitationally bound system.

28. What is the formula for gravitational force between two masses?

    $F = G \frac{m_1 m_2}{r^2}$. Newton's law of universal gravitation between two point masses.

29. What is the condition for a geosynchronous orbit?

    Orbital period is 24 hours. Matches Earth's rotational period for stationary positioning.

30. State Kepler's First Law of planetary motion.

    Planets move in elliptical orbits with the Sun at one focus. Describes elliptical shape with Sun at focal point.

31. What is the formula for the centripetal acceleration of a satellite in orbit?

    $a_c = \frac{v^2}{r}$. Acceleration toward center for circular orbital motion.

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