Motion of Orbiting Satellites - AP Physics 1

1. What happens to a satellite's speed as it approaches perigee?

   Speed increases. Conservation of energy: closer orbit means higher speed.

2. State the formula for orbital speed of a satellite.

   $v = \frac{2\text{π}r}{T}$. Circumference divided by period gives orbital speed.

3. What is Kepler's first law of planetary motion?

   Planets orbit in ellipses with the Sun at one focus. Describes the elliptical shape of planetary orbits.

4. How does increasing a satellite's mass affect its orbital period?

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

5. What is the term for the velocity required to maintain a circular orbit?

   Orbital velocity. The speed needed to maintain circular orbital motion.

6. State the formula for centripetal force acting on an orbiting satellite.

   $F_c = \frac{mv^2}{r}$. Force needed to keep a satellite in circular motion.

7. What does the term 'semi-major axis' refer to in an elliptical orbit?

   Longest radius from center to edge of ellipse. Half the longest diameter of the elliptical orbit.

8. Which direction does centripetal force point for an orbiting satellite?

   Towards the center of the orbit. Centripetal force always points toward the center.

9. State the formula for gravitational potential energy of a satellite.

   $U = -\frac{GMm}{r}$. Negative because it's a bound system below zero reference.

10. What is Kepler's third law of planetary motion?

    $T^2 \text{ is proportional to } r^3$. Period squared varies with radius cubed.

11. Identify the unit of the gravitational constant $G$.

    N m²/kg². Derived from $F = G\frac{m_1 m_2}{r^2}$ dimensional analysis.

12. State the formula relating orbital period and radius for a satellite.

    $T^2 = \frac{4\text{π}^2r^3}{GM}$. Derived from setting gravitational and centripetal forces equal.

13. What happens to orbital speed if the orbital radius doubles?

    Orbital speed decreases. Larger radius requires smaller speed for stable orbit.

14. State Kepler's second law of planetary motion.

    A line from a planet to the Sun sweeps equal areas in equal times. Conservation of angular momentum causes varying speeds.

15. What is the term for the point in an orbit closest to Earth?

    Perigee. The closest approach point in an elliptical orbit.

16. What does $G$ represent in the gravitational force formula?

    Gravitational constant. The universal gravitational constant in Newton's law.

17. What is the typical shape of an orbit for artificial satellites?

    Elliptical. Most satellite orbits are elliptical, not perfectly circular.

18. What is the primary force acting on a satellite in orbit?

    Gravitational force. Gravity provides the centripetal acceleration for orbital motion.

19. What is required for a satellite to maintain a stable orbit?

    Balance of gravitational and centripetal forces. Gravitational force must equal required centripetal force.

20. Identify the main source of energy loss for satellites in low Earth orbit.

    Atmospheric drag. Air resistance gradually slows down low-altitude satellites.

21. What is the term for the path of a satellite around a celestial body?

    Orbit. The curved path a satellite follows around a body.

22. What is the key difference between geostationary and polar orbits?

    Geostationary remains fixed above a point; polar passes over poles. Different orbital planes and periods serve different purposes.

23. State the formula for gravitational force between two masses.

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

24. How does the eccentricity of an orbit affect its shape?

    Higher eccentricity means more elongated orbit. Eccentricity measures how much orbit deviates from circular.

25. What is the effect on orbital speed when satellite's altitude increases?

    Orbital speed decreases. Higher altitude means larger radius and slower speed.

26. Which quantity remains constant for a satellite in a circular orbit?

    Orbital speed. Constant radius and period give constant speed.

27. How does an increase in orbital radius affect gravitational force?

    Gravitational force decreases. Gravitational force decreases with distance squared.

28. What is the term for the point in an orbit farthest from Earth?

    Apogee. The farthest point in an elliptical orbit.

29. What is the relationship between gravitational force and centripetal force for satellites?

    They are equal: $F_g = F_c$. Gravitational force provides the centripetal force for orbit.

30. What is the effect on gravitational force if the distance $r$ is halved?

    Force increases by a factor of 4. Force varies as $1/r^2$, so halving $r$ quadruples force.

31. How does the gravitational force change if both masses in the formula double?

    Force increases by a factor of 4. Force is proportional to the product of both masses.

32. What is the effect on orbiting satellite's period if it's moved to a higher orbit?

    Period increases. Kepler's third law: larger orbits have longer periods.

33. Identify the unit of orbital period $T$.

    Seconds (s). Period is a time measurement.

34. What is meant by the term 'geosynchronous orbit'?

    Orbit with a period equal to Earth's rotation period. Satellite appears stationary relative to Earth's surface.

35. What factor is responsible for the curvature of satellite orbits?

    Gravitational force. Gravity provides the centripetal acceleration for curved motion.

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