Kepler's laws Knowledge-Based Download PDF

Questions

1. 1.

   An asteroid travels in an elliptical orbit around the Sun with the same semi-major axis as Earth's orbit. According to Kepler's third law, how does the orbital period of the asteroid compare to that of Earth?

   • A) It is equal to Earth's orbital period.
   • B) It is greater than Earth's orbital period.
   • C) It is less than Earth's orbital period.
   • D) It depends on the eccentricity of the asteroid's orbit.
2. 2.

   A planet moves in an elliptical orbit around the Sun with a perihelion distance of $2\text{ AU}$ and an aphelion distance of $6\text{ AU}$. What is the orbital period of this planet?

   • A) 4 years
   • B) 8 years
   • C) 16 years
   • D) 64 years
3. 3.

   A comet moves in an elliptical orbit around the Sun. If the line segment joining the comet to the Sun sweeps out an area $A$ during a 30-day interval near aphelion, what area does it sweep out during a 30-day interval near perihelion?

   • A) An area less than $A$, because the distance from the Sun is smaller near perihelion
   • B) An area equal to $A$, because the line segment sweeps out equal areas in equal intervals of time
   • C) An area greater than $A$, because the comet travels at a higher speed near perihelion
   • D) An area greater than $A$, because the gravitational force on the comet is stronger near perihelion
4. 4.

   A planet moves in an elliptical orbit around a star such that its distance from the star at aphelion is 3 times its distance at perihelion. According to Kepler's laws, what is the ratio of the planet's orbital speed at perihelion to its orbital speed at aphelion?

   • A) 3
   • B) 9
   • C) $\sqrt{3}$
   • D) $\frac{1}{3}$
5. 5.

   Two planets move in circular orbits of identical radius around two different stars, Star X and Star Y. If Star X has 4 times the mass of Star Y, what is the ratio of the orbital period of the planet orbiting Star X to that of the planet orbiting Star Y?

   • A) 1 : 2
   • B) 2 : 1
   • C) 1 : 4
   • D) 4 : 1
6. 6.

   Kepler's second law of planetary motion states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. Which physical conservation law directly accounts for this observation?

   • A) Conservation of linear momentum
   • B) Conservation of angular momentum
   • C) Conservation of kinetic energy
   • D) Conservation of mechanical energy
7. 7.

   According to Kepler's third law of planetary motion, how would the orbital period of a planet change if its mass were doubled while its orbital radius remained constant?

   • A) It would double.
   • B) It would increase by a factor of $\sqrt{2}$.
   • C) It would be halved.
   • D) It would remain unchanged.
8. 8.

   According to Kepler's first law of planetary motion, which statement correctly describes the shape of a planet's orbit and the location of the Sun?

   • A) The orbit is a circle with the Sun located at the center.
   • B) The orbit is an ellipse with the Sun located at the geometric center.
   • C) The orbit is an ellipse with the Sun alternating between the two foci.
   • D) The orbit is an ellipse with the Sun located at one of the two foci.
9. 9.

   A planet moves in an elliptical orbit around the Sun. According to Kepler's second law of planetary motion, which statement correctly describes the planet's speed as it travels from aphelion (the point farthest from the Sun) to perihelion (the point closest to the Sun)?

   • A) The planet's speed remains constant because the total mechanical energy of the orbit is conserved.
   • B) The planet's speed continuously decreases because the gravitational attraction from the Sun strengthens.
   • C) The planet's speed decreases until reaching perihelion, where its orbital speed attains a minimum value.
   • D) The planet's speed continuously increases because the position vector from the Sun must sweep out equal areas in equal time intervals.
10. 10.

    A satellite moves in a circular orbit of radius $r$ around a planet with an orbital period $T$. According to Kepler's third law, what is the orbital period of a satellite orbiting the same planet at an orbital radius of $4r$?

    • A) $2T$
    • B) $8T$
    • C) $16T$
    • D) $64T$