Question 1

An Earth satellite in an elliptical orbit "speeds down" (that is, as it comes closer to the Earth, its speed increases). This is consistent with the fact that the gravitational potential energy U of the satellite-Earth system at points closer to the Earth is

Accepted Answer

As the satellite comes closer to Earth, its gravitational potential energy decreases because potential energy is inversely related to the distance from the Earth. This decrease in potential energy is converted into kinetic energy, causing the satellite to speed up.

Question 2

For a large spherical mass and a small test mass, the force between them is at a maximum when the test mass is located

Accepted Answer

The gravitational force between two masses is given by Newton's law of gravitation, which states that the force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. When the test mass is on the surface of the spherical mass, it is as close as possible to the mass without being inside it, thus experiencing the maximum gravitational force. Moving the test mass either closer to the center or farther away would decrease the force due to the inverse-square nature of the gravitational force law.

Question 3

For a large spherical mass and a small test mass, the gravitational potential energy between them is at a minimum when the test mass is located

Accepted Answer

Gravitational potential energy is at a minimum when the test mass is at the center of the spherical mass, as it is inversely proportional to the distance from the center.

Question 4

Consider the tidal forces on body A as it orbits body B in a particular configuration and state of motion. Each of the following independent changes would increase these forces except if

Accepted Answer

Tidal forces depend on the gravitational gradient, which increases as the distance between the two bodies decreases (A) or as the size of the body experiencing the forces increases (B). Increasing the radius of body B without changing its mass (C) does not increase the gravitational pull on A, thus not increasing the tidal forces experienced by A.

Question 5

If frictional drag due to the atmosphere acts on an Earth satellite in a low orbit, the net effect on its orbital speed will be

Accepted Answer

The answer of If frictional drag due to the atmosphere...

Question 6

Two objects with masses M₁ and M₂ are originally separated by a distance r. The distance between the two masses is increased to 3r. The force between the two objects will

Accepted Answer

The gravitational force between two objects is inversely proportional to the square of the distance between them (Newton's law of universal gravitation). Therefore, if the distance is increased to 3 times the original distance, the force will decrease by a factor of $3^2 = 9$.

Question 7

Two masses, M₁ = 10²² kg and M₂ = 10³⁰ kg, are separated by a distance of 10¹¹ m. The magnitude of the gravitational force between the two masses is

Accepted Answer

The answer of Two masses, M₁ = 10²² kg and...

Question 8

Atomic oxygen is one of the major constituents of the upper atmosphere in the region of low Earth orbit (LEO). LEO is approximately 150 miles $( 240 \mathrm {~km} )$ above the surface of the Earth. The radius and mass of the Earth are $6.4 \times 10 ^ { 6 } \mathrm {~m}$ and $5.98 \times 10 ^ { 24 } \mathrm {~kg}$. The mass of atomic oxygen is $16 \times \left( 1.67 \times 10 ^ { - 27 } \mathrm {~kg} \right)$. The kinetic energy at which the atomic oxygen strikes the surface of the space shuttle is

Accepted Answer

The answer of Atomic oxygen is one of the major...

Question 9

The Earth's radius is 6.4 $\times$ 10⁶m. The acceleration due to gravity (in g's) that is experienced by an object at a distance of 150 miles (240 km) above the Earth's surface is

Accepted Answer

The acceleration due to gravity decreases with the square of the distance from the center of the Earth. At 240 km above the Earth's surface, the distance from the Earth's center is $6.4 \times 10^6 m + 240 \times 10^3 m$. Using the formula for gravitational force, $F = G\frac{m_1m_2}{r^2}$, where $r$ is the distance from the center of the Earth, the acceleration due to gravity is less than 1 g but does not drop to zero or half. It remains significant, hence the closest estimate given the options is 0.92 g, indicating a slight decrease from 1 g due to the increased distance from the Earth's center.

Question 10

The mass of Mars is 6.42 $\times$ 10²³kg, and the radius of the planet is 3.40 $\times$ 10⁶ m. The acceleration due to gravity on the surface of Mars is

Accepted Answer

The acceleration due to gravity is calculated using the formula $ g = \frac{G \cdot M}{R^2} $. Substituting the given values and converting to cm/s², the result is approximately 370 cm/s².

Question 11

Two planets have masses M and M/2 respectively. The distance between the two planets is r. The relative distance from the first planet where the gravitational force on a third body due to the two planets would be zero is

Accepted Answer

The answer of Two planets have masses M and M/2...

Question 12

Low Earth orbit (LEO) is approximately 150 miles (240 km) above the surface of the Earth. The radius and mass of the Earth are 6.40 $\times$ 10⁶ m and 5.98 $\times$ 10²⁴ kg. The time it takes a space shuttle in LEO to travel around one orbit

Accepted Answer

The time it takes for a space shuttle in LEO to complete one orbit around the Earth is approximately 90 minutes. This is a well-established fact based on the physics of orbital mechanics, which does not require the mass of the shuttle to calculate the orbital period.

Question 13

Low Earth orbit (LEO) is approximately 150 miles (240 km) above the surface of the Earth. The radius and mass of the Earth are 6.4 $\times$ 10⁶ m and 5.98 $\times$ 10²⁴ kg. The velocity of the space shuttle in LEO

Accepted Answer

The answer of Low Earth orbit (LEO) is approximately 150...

Question 14

The orbit of Io, a moon of Jupiter, is found to have a period of 1.769 days, and its average distance from the center of Jupiter is 420,000 km. The mass of Jupiter

Accepted Answer

The mass of Jupiter can be determined using Kepler's third law of planetary motion, which relates the orbital period of a satellite to the mass of the central body (in this case, Jupiter) and the average distance of the satellite from the central body. The given information about Io's orbital period and average distance from Jupiter is sufficient to calculate Jupiter's mass, without needing to know the mass of Io. The correct calculation leads to the mass of Jupiter being approximately 1.9 $\times$ 10^27 kg.

Question 15

The period of a planetary orbit about a star is one Earth year, whereas the average distance between the planet and the star is 1.5 AU (astronomical units). A second planet is orbiting the star at a distance of 6.0 AU. The period of the second planet orbiting the same star is

Accepted Answer

According to Kepler's Third Law, the square of the orbital period (T) is proportional to the cube of the semi-major axis (a) of its orbit. For the first planet, T^2 = a^3, so (1 year)^2 = (1.5 AU)^3. For the second planet, T^2 = (6.0 AU)^3. Solving gives T ≈ 8 years.

Question 16

The period of a planetary orbit about a star is 1.5 Earth years, whereas the average distance between the planet and the star is 2.0 AU (astronomical units). A second planet is orbiting the star with a period of 12 Earth years. The orbital radius of the second planet is

Accepted Answer

The answer of The period of a planetary orbit about...

Question 17

A planet in another solar system is found to have twice the radius of the Earth and a mass that is double that of the Earth. The acceleration due to gravity on this other planet is

Accepted Answer

The acceleration due to gravity is given by the formula g' = G * (M'/R'^2), where M' is the mass and R' is the radius of the planet. If the planet has twice the radius (R' = 2R) and double the mass (M' = 2M) of Earth, then g' = G * (2M/(2R)^2) = G * (2M/4R^2) = (1/2) * (G * M/R^2) = 0.5g.

Question 18

A planetary orbit follows an ellipse in which the star is located at one of the foci. At the location of the second focus is

Accepted Answer

In the elliptical orbit model of planets, the second focus of the ellipse does not contain any physical object; it is simply a geometric point necessary to define the shape of the orbit.

Question 19

A comet is found to move in an elliptical orbit. When the comet's aphelion distance is 2.5 AU, it has a velocity of 100 m/s. The point of closest approach is 0.5 AU from the Sun. The velocity of the comet at the point of closest approach is

Accepted Answer

The conservation of angular momentum and energy in the orbit of a comet allows us to determine its velocity at different points in its orbit. When a comet moves closer to the Sun, its velocity increases due to the conservation of angular momentum. The specific orbital energy (the sum of kinetic and potential energy) is constant throughout the orbit. Using these principles, we can calculate the velocity at perihelion (closest approach) if we know the velocity at aphelion (farthest point). The significant increase in velocity from 100 m/s at aphelion to a much higher value at perihelion is consistent with these conservation laws, making option C (5.0 × 10^2 m/s) the correct answer.

Question 20

The orbital angular momentum of Io was calculated to be approximately 1.55 $\times$ 10²⁷ kg·m²/s at perihelion. The angular momentum at the aphelion

Accepted Answer

The orbital angular momentum of a body in orbit around another body remains constant (is conserved) throughout its orbit, assuming no external torques act on the system.

Quiz 9: Gravitation

An Earth satellite in an elliptical orbit "speeds down" (that is, as it comes closer to the Earth, its speed increases) . This is consistent with the fact that the gravitational potential energy U of the satellite-Earth system at points closer to the Earth is

For a large spherical mass and a small test mass, the force between them is at a maximum when the test mass is located

For a large spherical mass and a small test mass, the gravitational potential energy between them is at a minimum when the test mass is located

Consider the tidal forces on body A as it orbits body B in a particular configuration and state of motion. Each of the following independent changes would increase these forces except if

If frictional drag due to the atmosphere acts on an Earth satellite in a low orbit, the net effect on its orbital speed will be

Two objects with masses M₁ and M₂ are originally separated by a distance r. The distance between the two masses is increased to 3r. The force between the two objects will

Two masses, M₁ = 10²² kg and M₂ = 10³⁰ kg, are separated by a distance of 10¹¹ m. The magnitude of the gravitational force between the two masses is

The Earth's radius is 6.4 $\times$ 10⁶m. The acceleration due to gravity (in g's) that is experienced by an object at a distance of 150 miles (240 km) above the Earth's surface is

The mass of Mars is 6.42 $\times$ 10²³kg, and the radius of the planet is 3.40 $\times$ 10⁶ m. The acceleration due to gravity on the surface of Mars is

Two planets have masses M and M/2 respectively. The distance between the two planets is r. The relative distance from the first planet where the gravitational force on a third body due to the two planets would be zero is

Low Earth orbit (LEO) is approximately 150 miles (240 km) above the surface of the Earth. The radius and mass of the Earth are 6.40 $\times$ 10⁶ m and 5.98 $\times$ 10²⁴ kg. The time it takes a space shuttle in LEO to travel around one orbit

Low Earth orbit (LEO) is approximately 150 miles (240 km) above the surface of the Earth. The radius and mass of the Earth are 6.4 $\times$ 10⁶ m and 5.98 $\times$ 10²⁴ kg. The velocity of the space shuttle in LEO

The orbit of Io, a moon of Jupiter, is found to have a period of 1.769 days, and its average distance from the center of Jupiter is 420,000 km. The mass of Jupiter

The period of a planetary orbit about a star is one Earth year, whereas the average distance between the planet and the star is 1.5 AU (astronomical units) . A second planet is orbiting the star at a distance of 6.0 AU. The period of the second planet orbiting the same star is

The period of a planetary orbit about a star is 1.5 Earth years, whereas the average distance between the planet and the star is 2.0 AU (astronomical units) . A second planet is orbiting the star with a period of 12 Earth years. The orbital radius of the second planet is

A planet in another solar system is found to have twice the radius of the Earth and a mass that is double that of the Earth. The acceleration due to gravity on this other planet is

A planetary orbit follows an ellipse in which the star is located at one of the foci. At the location of the second focus is

A comet is found to move in an elliptical orbit. When the comet's aphelion distance is 2.5 AU, it has a velocity of 100 m/s. The point of closest approach is 0.5 AU from the Sun. The velocity of the comet at the point of closest approach is

The orbital angular momentum of Io was calculated to be approximately 1.55 $\times$ 10²⁷ kg·m²/s at perihelion. The angular momentum at the aphelion

Quiz 9: Gravitation

An Earth satellite in an elliptical orbit "speeds down" (that is, as it comes closer to the Earth, its speed increases) . This is consistent with the fact that the gravitational potential energy U of the satellite-Earth system at points closer to the Earth is

For a large spherical mass and a small test mass, the force between them is at a maximum when the test mass is located

For a large spherical mass and a small test mass, the gravitational potential energy between them is at a minimum when the test mass is located

Consider the tidal forces on body A as it orbits body B in a particular configuration and state of motion. Each of the following independent changes would increase these forces except if

If frictional drag due to the atmosphere acts on an Earth satellite in a low orbit, the net effect on its orbital speed will be

Two objects with masses M1 and M2 are originally separated by a distance r. The distance between the two masses is increased to 3r. The force between the two objects will

Two masses, M1 = 1022 kg and M2 = 1030 kg, are separated by a distance of 1011 m. The magnitude of the gravitational force between the two masses is

The Earth's radius is 6.4 ×\times× 106 m. The acceleration due to gravity (in g's) that is experienced by an object at a distance of 150 miles (240 km) above the Earth's surface is

The mass of Mars is 6.42 ×\times× 1023 kg, and the radius of the planet is 3.40 ×\times× 106 m. The acceleration due to gravity on the surface of Mars is

Two planets have masses M and M/2 respectively. The distance between the two planets is r. The relative distance from the first planet where the gravitational force on a third body due to the two planets would be zero is

Low Earth orbit (LEO) is approximately 150 miles (240 km) above the surface of the Earth. The radius and mass of the Earth are 6.40 ×\times× 106 m and 5.98 ×\times× 1024 kg. The time it takes a space shuttle in LEO to travel around one orbit

Low Earth orbit (LEO) is approximately 150 miles (240 km) above the surface of the Earth. The radius and mass of the Earth are 6.4 ×\times× 106 m and 5.98 ×\times× 1024 kg. The velocity of the space shuttle in LEO

The orbit of Io, a moon of Jupiter, is found to have a period of 1.769 days, and its average distance from the center of Jupiter is 420,000 km. The mass of Jupiter

The period of a planetary orbit about a star is one Earth year, whereas the average distance between the planet and the star is 1.5 AU (astronomical units) . A second planet is orbiting the star at a distance of 6.0 AU. The period of the second planet orbiting the same star is

The period of a planetary orbit about a star is 1.5 Earth years, whereas the average distance between the planet and the star is 2.0 AU (astronomical units) . A second planet is orbiting the star with a period of 12 Earth years. The orbital radius of the second planet is

A planet in another solar system is found to have twice the radius of the Earth and a mass that is double that of the Earth. The acceleration due to gravity on this other planet is

A planetary orbit follows an ellipse in which the star is located at one of the foci. At the location of the second focus is

A comet is found to move in an elliptical orbit. When the comet's aphelion distance is 2.5 AU, it has a velocity of 100 m/s. The point of closest approach is 0.5 AU from the Sun. The velocity of the comet at the point of closest approach is

The orbital angular momentum of Io was calculated to be approximately 1.55 ×\times× 1027 kg·m2/s at perihelion. The angular momentum at the aphelion

Two objects with masses M₁ and M₂ are originally separated by a distance r. The distance between the two masses is increased to 3r. The force between the two objects will

Two masses, M₁ = 10²² kg and M₂ = 10³⁰ kg, are separated by a distance of 10¹¹ m. The magnitude of the gravitational force between the two masses is

The Earth's radius is 6.4 $\times$ 10⁶m. The acceleration due to gravity (in g's) that is experienced by an object at a distance of 150 miles (240 km) above the Earth's surface is

The mass of Mars is 6.42 $\times$ 10²³kg, and the radius of the planet is 3.40 $\times$ 10⁶ m. The acceleration due to gravity on the surface of Mars is

Low Earth orbit (LEO) is approximately 150 miles (240 km) above the surface of the Earth. The radius and mass of the Earth are 6.40 $\times$ 10⁶ m and 5.98 $\times$ 10²⁴ kg. The time it takes a space shuttle in LEO to travel around one orbit

Low Earth orbit (LEO) is approximately 150 miles (240 km) above the surface of the Earth. The radius and mass of the Earth are 6.4 $\times$ 10⁶ m and 5.98 $\times$ 10²⁴ kg. The velocity of the space shuttle in LEO

The orbital angular momentum of Io was calculated to be approximately 1.55 $\times$ 10²⁷ kg·m²/s at perihelion. The angular momentum at the aphelion