Question 1

Kepler's laws: A planet has two small satellites in circular orbits around the planet. The first satellite has a period 18.0 hours and an orbital radius 2.00 × 10⁷ m. The second planet has an orbital radius 3.00 × 10⁷ m. What is the period of the second satellite?

Accepted Answer

The answer of Kepler's laws: A planet has two small...

Question 2

Kepler's laws: 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?

Accepted Answer

According to Kepler's third law, the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. If moon B has an orbital radius 4 times that of moon A, then the period of moon B is (4^1.5) times that of moon A. Therefore, the period of moon B is 8 times 20 days, which is 160 days.

Question 3

Kepler's laws: A planet has two small satellites in circular orbits around the planet. The first satellite has a period 12.0 hours and an orbital radius 6.00 × 10⁷ m. The second planet has a period 16.0 hours. What is the orbital radius of the second satellite?

Accepted Answer

According to Kepler's third law, the square of the orbital period is proportional to the cube of the orbital radius. Using the formula (T1/T2)^2 = (R1/R2)^3, we can solve for R2. Substituting the given values, we find R2 ≈ 7.27 × 10^7 m.

Question 4

Kepler's laws: 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?

Accepted Answer

Kepler's third law of planetary motion 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. This law can be expressed as $T^2 \propto r^3$, where $T$ is the orbital period and $r$ is the average distance from the Sun. Given the orbital period of Neptune and its distance, we can use the ratio of the squares of the orbital periods of Neptune and Saturn to the cubes of their respective distances to find Saturn's orbital period. The correct answer, after applying Kepler's third law and solving for Saturn's orbital period, is 29.4 years, which corresponds to choice E.

Question 5

Satellites: Ekapluto is an unknown planet that has two moons in circular orbits. The table summarizes the hypothetical data about the moons. (G = 6.67 × 10^-11 N ∙ m²/kg²) The mass of Ekapluto is closest to

Accepted Answer

According to Newton's law of gravitation, F = G(m1m2)/(r^2). We know the radius and period of orbit of both moons. Using the equation v = 2πr/T, we can find their velocities, and from there we can find the centripetal force needed for them to stay in orbit, which is also equal to the gravitational force between the moon and Ekapluto. Solving for the mass of Ekapluto using the gravitational constant G, we get a value of approximately 3.0 × 10^23 kg, which is closest to choice D.

Question 6

Kepler's laws: 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?

Accepted Answer

According to Kepler's third law, the square of the orbital period is proportional to the cube of the semi-major axis of its orbit. Therefore, the ratio of the periods is the square root of the ratio of the cubes of their orbital radii: (9378/23459)^(3/2) ≈ 0.2528.

Question 7

Satellites: Suppose we want a satellite to revolve around the earth 5 times a day. What should be the radius of its orbit? (The mass of the earth is 5.97 × 10²⁴ kg, G = 6.67 × 10^-11 N ∙ m²/kg², and you can neglect the presence of the moon.)

Accepted Answer

To find the radius of the orbit, we can use the formula for the orbital period $T = 2\pi\sqrt{\frac{r^3}{GM}}$, where $T$ is the orbital period, $r$ is the radius of the orbit, $G$ is the gravitational constant, and $M$ is the mass of the Earth. Given that the satellite revolves around the Earth 5 times a day, we need to convert this into seconds to find $T$ (1 day = 86400 seconds, so $T = \frac{86400}{5}$ seconds). Rearranging the formula to solve for $r$ and substituting the given values for $G$ and $M$, we can calculate the radius $r$. The correct calculation leads to the radius in the order of magnitude of $10^{7}$ meters, which matches option A.

Question 8

Kepler's laws: 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

Accepted Answer

The answer of Kepler's laws: Ekapluto is an unknown planet...

Question 9

Satellites: A man-made satellite of mass 6105 kg is in orbit around the earth, making one revolution in 430 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth? (The mass of the earth is 6.0 × 10²⁴ kg and G = 6.67 × 10^-11 N ∙ m²/kg²)

Accepted Answer

The answer of Satellites: A man-made satellite of mass 6105...

Quiz 10: Dynamics of Rotational Motion

Kepler's laws: A planet has two small satellites in circular orbits around the planet. The first satellite has a period 18.0 hours and an orbital radius 2.00 × 10⁷ m. The second planet has an orbital radius 3.00 × 10⁷ m. What is the period of the second satellite?

Kepler's laws: 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?

Kepler's laws: A planet has two small satellites in circular orbits around the planet. The first satellite has a period 12.0 hours and an orbital radius 6.00 × 10⁷ m. The second planet has a period 16.0 hours. What is the orbital radius of the second satellite?

Kepler's laws: 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?

Satellites: Ekapluto is an unknown planet that has two moons in circular orbits. The table summarizes the hypothetical data about the moons. (G = 6.67 × 10^-11 N ∙ m²/kg²) The mass of Ekapluto is closest to

Kepler's laws: 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?

Satellites: Suppose we want a satellite to revolve around the earth 5 times a day. What should be the radius of its orbit? (The mass of the earth is 5.97 × 10²⁴ kg, G = 6.67 × 10^-11 N ∙ m²/kg², and you can neglect the presence of the moon.)

Kepler's laws: 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

Satellites: A man-made satellite of mass 6105 kg is in orbit around the earth, making one revolution in 430 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth? (The mass of the earth is 6.0 × 10²⁴ kg and G = 6.67 × 10^-11 N ∙ m²/kg²)

Quiz 10: Dynamics of Rotational Motion

Kepler's laws: A planet has two small satellites in circular orbits around the planet. The first satellite has a period 18.0 hours and an orbital radius 2.00 × 107 m. The second planet has an orbital radius 3.00 × 107 m. What is the period of the second satellite?

Kepler's laws: 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?

Kepler's laws: A planet has two small satellites in circular orbits around the planet. The first satellite has a period 12.0 hours and an orbital radius 6.00 × 107 m. The second planet has a period 16.0 hours. What is the orbital radius of the second satellite?

Kepler's laws: 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?

Satellites: Ekapluto is an unknown planet that has two moons in circular orbits. The table summarizes the hypothetical data about the moons. (G = 6.67 × 10-11 N ∙ m2/kg2) The mass of Ekapluto is closest to

Kepler's laws: 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?

Satellites: Suppose we want a satellite to revolve around the earth 5 times a day. What should be the radius of its orbit? (The mass of the earth is 5.97 × 1024 kg, G = 6.67 × 10-11 N ∙ m2/kg2, and you can neglect the presence of the moon.)

Kepler's laws: 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

Satellites: A man-made satellite of mass 6105 kg is in orbit around the earth, making one revolution in 430 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth? (The mass of the earth is 6.0 × 1024 kg and G = 6.67 × 10-11 N ∙ m2/kg2)

Kepler's laws: A planet has two small satellites in circular orbits around the planet. The first satellite has a period 18.0 hours and an orbital radius 2.00 × 10⁷ m. The second planet has an orbital radius 3.00 × 10⁷ m. What is the period of the second satellite?

Kepler's laws: A planet has two small satellites in circular orbits around the planet. The first satellite has a period 12.0 hours and an orbital radius 6.00 × 10⁷ m. The second planet has a period 16.0 hours. What is the orbital radius of the second satellite?

Kepler's laws: 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?

Satellites: Ekapluto is an unknown planet that has two moons in circular orbits. The table summarizes the hypothetical data about the moons. (G = 6.67 × 10^-11 N ∙ m²/kg²) The mass of Ekapluto is closest to

Satellites: Suppose we want a satellite to revolve around the earth 5 times a day. What should be the radius of its orbit? (The mass of the earth is 5.97 × 10²⁴ kg, G = 6.67 × 10^-11 N ∙ m²/kg², and you can neglect the presence of the moon.)

Satellites: A man-made satellite of mass 6105 kg is in orbit around the earth, making one revolution in 430 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth? (The mass of the earth is 6.0 × 10²⁴ kg and G = 6.67 × 10^-11 N ∙ m²/kg²)