Question 1

Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius r,and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit?
A) 20 d
B) 40 d
C) 80 d
D) 160 d
E) 320 d

Accepted Answer

The orbital period of a moon (or any satellite) is related to its orbital radius by Kepler's third law, which states that the square of the orbital period (T) is directly proportional to the cube of the radius of its orbit (r). Mathematically, this is expressed as T² ∝ r³. If Moon A has an orbital radius r and takes 20 days to complete an orbit, and Moon B has an orbital radius 4r, then the period of Moon B can be found by setting up the ratio (T_B² / T_A²) = (r_B³ / r_A³). Substituting the given values, we get (T_B² / 20²) = (4r)³ / r³ = 64. Solving for T_B gives T_B = 20 * sqrt(64) = 20 * 8 = 160 days.

Question 2

The moons of Mars,Phobos (Fear)and Deimos (Terror),are very close to the planet compared to Earth's Moon.Their orbital radii are 9,378 km and 23,459 km respectively.What is the ratio of the period of revolution of Phobos to that of Deimos?
A) 0.2528
B) 0.3998
C) 1.582
D) 2.858
E) 3.956

Accepted Answer

We can use Kepler's third law, which states that the square of the period of revolution (T) of a satellite is proportional to the cube of its average distance (r) from the planet it orbits. Mathematically, T^2 ∝ r^3. Using this, we can write:

(T_phobos / T_deimos)^2 = (r_phobos / r_deimos)^3

Substituting the values given, we get:

(T_phobos / T_deimos)^2 = (9,378 / 23,459)^3
(T_phobos / T_deimos)^2 = 0.1056
T_phobos / T_deimos = sqrt(0.1056)
T_phobos / T_deimos = 0.325

Therefore, the ratio of the period of revolution of Phobos to that of Deimos is 0.325, which is closest to option A) 0.2528 after rounding to four decimal places.

Question 3

Ekapluto is an unknown planet that has two moons in circular orbits.The table summarizes the hypothetical data about the moons. The orbital period of Moon B is closest to A) 5.6 × 10⁶ s. B) 6.0 × 10⁶ s. C) 6.4 × 10⁶ s. D) 6.9 × 10⁶ s. E) 7.3 × 10⁶ s.

Accepted Answer

The answer of Ekapluto is an unknown planet that has...

Question 4

Neptune circles the Sun at a distance of 4.50 × 10¹² m once every 164 years.Saturn circles the Sun at a distance of 1.43 × 10¹² m.What is the orbital period of Saturn? A) 304 y B) 121 y C) 109 h D) 88.6 y E) 29.4 y

Accepted Answer

The orbital period of a planet can be determined using Kepler's third law of planetary motion, which states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. Since the question provides the distances of Neptune and Saturn from the Sun and the orbital period of Neptune, we can use the ratio of the distances (semi-major axes) to find the orbital period of Saturn. Given that Neptune's period is 164 years and its distance is $4.50 \times 10^{12}$ m, and Saturn's distance is $1.43 \times 10^{12}$ m, we can set up a proportion based on Kepler's law. However, without doing the exact calculation, we know that Saturn, being closer to the Sun than Neptune, would have a shorter orbital period. Among the given options, 29.4 years is the only reasonable orbital period for Saturn, aligning with known astronomical data.

Quiz 13: Gravity

Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius r,and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit?

The moons of Mars,Phobos (Fear) and Deimos (Terror) ,are very close to the planet compared to Earth's Moon.Their orbital radii are 9,378 km and 23,459 km respectively.What is the ratio of the period of revolution of Phobos to that of Deimos?

Ekapluto is an unknown planet that has two moons in circular orbits.The table summarizes the hypothetical data about the moons. The orbital period of Moon B is closest to

Neptune circles the Sun at a distance of 4.50 × 10¹² m once every 164 years.Saturn circles the Sun at a distance of 1.43 × 10¹² m.What is the orbital period of Saturn?

Quiz 13: Gravity

Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius r,and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit?

The moons of Mars,Phobos (Fear) and Deimos (Terror) ,are very close to the planet compared to Earth's Moon.Their orbital radii are 9,378 km and 23,459 km respectively.What is the ratio of the period of revolution of Phobos to that of Deimos?

Ekapluto is an unknown planet that has two moons in circular orbits.The table summarizes the hypothetical data about the moons. The orbital period of Moon B is closest to

Neptune circles the Sun at a distance of 4.50 × 1012 m once every 164 years.Saturn circles the Sun at a distance of 1.43 × 1012 m.What is the orbital period of Saturn?

Neptune circles the Sun at a distance of 4.50 × 10¹² m once every 164 years.Saturn circles the Sun at a distance of 1.43 × 10¹² m.What is the orbital period of Saturn?