Question 1

The elliptical orbit of a planet around the Sun is shown on the diagram.Which of the following statements is true?

Accepted Answer

The orbit is elongated and not circular, so the eccentricity is greater than 0 but less than 1. The Sun is located at one of the two foci of the ellipse, and since point B is one of the foci, the Sun could be located at point B. The Sun cannot be at points C or D because those are not foci of the ellipse.

Question 2

Two planets are orbiting a star in a distant galaxy.The first has a semimajor axis of 150 *10⁶ km, an eccentricity of 0.20, and a period of 1.0 Earth years.The second has a semimajor axis of 250 * 10⁶ km, an eccentricity of 0.30, and a period of:

Accepted Answer

The answer of Two planets are orbiting a star in...

Question 3

Consider the statement: "Earth moves in a stable orbit around the Sun and is therefore in equilibrium".The statement is:

Accepted Answer

The statement is false because the Earth indeed has a considerable acceleration as it orbits the Sun. This acceleration is centripetal, directed towards the Sun, allowing Earth to maintain its orbit rather than moving in a straight line.

Question 4

Assume that Earth is in circular orbit around the Sun with kinetic energy K and potential energy U, taken to be zero for infinite separation.Then, the relationship between K and U:

Accepted Answer

In a circular orbit, the kinetic energy (K) is equal to half the magnitude of the potential energy (U), but with a positive sign, making the relationship K = -U/2. This is a result of the conservation of energy and the specifics of gravitational force, where the total energy (which is the sum of kinetic and potential energy) is negative, indicating a bound system.

Question 5

Einstein's principle of equivalence states:

Accepted Answer

Einstein's principle of equivalence, a cornerstone of general relativity, posits that gravitational mass (how much an object is pulled by gravity) and inertial mass (how much an object resists acceleration) are equivalent. This principle suggests that the effects of gravity can locally be indistinguishable from the effects of acceleration.

Question 6

A planet travels in an elliptical orbit about a star X as shown.The magnitude of the acceleration of the planet is:

Accepted Answer

The answer of A planet travels in an elliptical orbit...

Question 7

Neglecting air resistance, the escape speed from a certain planet for an empty space vehicle is 1.12 *10⁴ m/s.What is the corresponding escape speed for the fully loaded vehicle which has triple the mass of the empty one?

Accepted Answer

The escape speed from a planet is independent of the mass of the escaping object. It only depends on the mass of the planet and the distance from its center.

Question 8

Given the perihelion distance, aphelion distance, and speed at perihelion of a planet, which of the following CANNOT be calculated?

Accepted Answer

The mass of the planet cannot be calculated directly from the given information (perihelion distance, aphelion distance, and speed at perihelion) because these parameters are primarily influenced by the mass of the star around which the planet orbits, not the mass of the planet itself. The gravitational force (and thus the orbital characteristics) that a planet experiences is predominantly due to the star's mass according to Kepler's laws and Newton's law of universal gravitation.

Question 9

A small satellite is in elliptical orbit around Earth as shown.If L denotes the magnitude of its angular momentum and K denotes kinetic energy:

Accepted Answer

The answer of A small satellite is in elliptical orbit...

Question 10

A planet is in circular orbit around the Sun.Its distance from the Sun is four times the average distance of Earth from the Sun.The period of this planet is:

Accepted Answer

The period of a planet's orbit is given by Kepler's third law:

T² = (4π²/G) × (r³/m)

where:
T = period of orbit
G = gravitational constant
r = distance from the center of the Sun to the center of the planet's orbit
m = mass of the Sun

Since the planet's distance from the Sun is four times the average distance of Earth from the Sun, we have:

r = 4 × 1 AU = 4 AU

where 1 AU is the average distance of Earth from the Sun.

Substituting this into Kepler's third law, we get:

T² = (4π²/G) × (4³/m)

T²/T²(earth) = (4³/1) / (1/(GM))

where T²(earth) and GM are the period and gravitational parameter of Earth, respectively.

Simplifying this expression, we get:

T²/T²(earth) = 64

Taking the square root of both sides, we get:

T/T(earth) = 8

Therefore, the period of the planet's orbit is 8 Earth years.

Question 11

The orbit of a certain a satellite has a semimajor axis of 1.5 * 10⁷ m and an eccentricity of 0.20.Its perigee (minimum distance)and apogee (maximum distance)are respectively:

Accepted Answer

The perigee and apogee distances can be calculated using the semi-major axis (a) and the eccentricity (e) with the formulas: perigee = a(1 - e) and apogee = a(1 + e). Substituting the given values, a = 1.5 x 10^7 m and e = 0.20, we get perigee = 1.5 x 10^7 x (1 - 0.20) = 1.2 x 10^7 m and apogee = 1.5 x 10^7 x (1 + 0.20) = 1.8 x 10^7 m.

Question 12

The speed of a comet in an elliptical orbit about the sun:

Accepted Answer

According to Kepler's laws of planetary motion, a comet moves faster when it is closer to the sun and slower when it is farther away, so its speed decreases as it recedes from the sun.

Question 13

A planet in another solar system orbits a star with a mass of 4.0 x 10³⁰ kg.At one point in its orbit it is 250 x 10⁶ km from the star and is moving at 35 km/s.Take the universal gravitational constant to be 6.67 x 10^-11 m²/s² .kg and calculate the semimajor axis of the planet's orbit.The result is:

Accepted Answer

We can use Kepler's third law to solve for the semimajor axis:

T^2 = (4π^2/ GM) a^3

where T is the period of the planet's orbit, G is the gravitational constant, M is the mass of the star, and a is the semimajor axis.

We can first solve for the period of the orbit:
r = 250 x 10^6 m = 250 x 10^3 km

v = 35 km/s

From conservation of energy we can write:

(1/2)mv^2 - GMm/r = (1/2)mv2' - GMm/r'

where r' is the distance from the star at another point in the orbit, and v' is the velocity at that point.

We can set r' equal to the semimajor axis a, and v'=0 at the furthest point in the orbit:

(1/2)(35 km/s)^2 - (6.67x10^-11 N(m^2/kg^2))(4x10^30 kg)/250x10^9 m = -(6.67x10^-11 N(m^2/kg^2))(4x10^30 kg)/a

Solving for a, we get:

a = 290 x 10^6 m = 290 x 10^3 km

Therefore, the answer is C) 290 x 10^3 km.

Question 14

For a planet in orbit around a star the perihelion distance is r_p and its speed at perihelion is v_p.The aphelion distance is r_a and its speed at aphelion is v_a.Which of following is true?

Accepted Answer

The correct answer is based on the conservation of angular momentum in an elliptical orbit, where the product of the speed and the radial distance at any two points (such as perihelion and aphelion) remains constant. This is expressed as $v_{\text{a}} r_{\text{a}} = v_{\text{p}} r_{\text{p}}$, where $v_{\text{a}}$ and $v_{\text{p}}$ are the speeds at aphelion and perihelion, respectively, and $r_{\text{a}}$ and $r_{\text{p}}$ are the corresponding radial distances.

Question 15

Planet 1 and planet 2 are both in circular orbits around the same central star.The orbit of planet 2 has a radius that is much larger than the radius of the orbit of planet 1.This means that:

Accepted Answer

According to Kepler's third law of planetary motion, the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. This means that a planet with a larger orbital radius (like planet 2) will have a longer period than a planet with a smaller orbital radius (like planet 1). Additionally, in circular orbits, the orbital speed is inversely proportional to the square root of the orbital radius, meaning that planet 1, with its smaller orbit, moves faster than planet 2.

Question 16

In planetary motion the line from the star to the planet sweeps out equal areas in equal times.This is a direct consequence of:

Accepted Answer

The conservation of angular momentum is responsible for the law that states that the line from the star to the planet sweeps out equal areas in equal times. Angular momentum is conserved because there are no external forces acting on the system.

Question 17

An artificial Earth satellite is moved from a circular orbit with radius R to a circular orbit with radius 2R.During this move:

Accepted Answer

When moving to a higher orbit, gravitational force does negative work as it opposes the motion. The kinetic energy decreases because the satellite moves slower in a higher orbit. The potential energy increases as the satellite is further from Earth.

Question 18

An artificial satellite of Earth nears the end of its life due to air resistance.While still in orbit:

Accepted Answer

As an artificial satellite's orbit lowers due to air resistance, it moves faster due to conservation of angular momentum and the gravitational pull becoming stronger as it gets closer to Earth.

Question 19

A spaceship is returning to Earth with its engine turned off.Consider only the gravitational field of Earth.Let M be the mass of Earth, m be the mass of the spaceship, and R be the distance from the center of Earth.In moving from position 1 to position 2 the kinetic energy of the spaceship increases by:

Accepted Answer

The answer of A spaceship is returning to Earth with...

Question 20

A planet travels in an elliptical orbit about a star as shown.At what pair of points is the speed of the planet the same?

Accepted Answer

The answer of A planet travels in an elliptical orbit...

Quiz 13: Gravitation

The elliptical orbit of a planet around the Sun is shown on the diagram.Which of the following statements is true?

Two planets are orbiting a star in a distant galaxy.The first has a semimajor axis of 150 10⁶ km, an eccentricity of 0.20, and a period of 1.0 Earth years.The second has a semimajor axis of 250 10⁶ km, an eccentricity of 0.30, and a period of:

Consider the statement: "Earth moves in a stable orbit around the Sun and is therefore in equilibrium".The statement is:

Assume that Earth is in circular orbit around the Sun with kinetic energy K and potential energy U, taken to be zero for infinite separation.Then, the relationship between K and U:

Einstein's principle of equivalence states:

A planet travels in an elliptical orbit about a star X as shown.The magnitude of the acceleration of the planet is:

Neglecting air resistance, the escape speed from a certain planet for an empty space vehicle is 1.12 *10⁴ m/s.What is the corresponding escape speed for the fully loaded vehicle which has triple the mass of the empty one?

Given the perihelion distance, aphelion distance, and speed at perihelion of a planet, which of the following CANNOT be calculated?

A small satellite is in elliptical orbit around Earth as shown.If L denotes the magnitude of its angular momentum and K denotes kinetic energy:

A planet is in circular orbit around the Sun.Its distance from the Sun is four times the average distance of Earth from the Sun.The period of this planet is:

The orbit of a certain a satellite has a semimajor axis of 1.5 * 10⁷ m and an eccentricity of 0.20.Its perigee (minimum distance) and apogee (maximum distance) are respectively:

The speed of a comet in an elliptical orbit about the sun:

For a planet in orbit around a star the perihelion distance is r_p and its speed at perihelion is v_p.The aphelion distance is r_a and its speed at aphelion is v_a.Which of following is true?

Planet 1 and planet 2 are both in circular orbits around the same central star.The orbit of planet 2 has a radius that is much larger than the radius of the orbit of planet 1.This means that:

In planetary motion the line from the star to the planet sweeps out equal areas in equal times.This is a direct consequence of:

An artificial Earth satellite is moved from a circular orbit with radius R to a circular orbit with radius 2R.During this move:

An artificial satellite of Earth nears the end of its life due to air resistance.While still in orbit:

A planet travels in an elliptical orbit about a star as shown.At what pair of points is the speed of the planet the same?

Quiz 13: Gravitation

The elliptical orbit of a planet around the Sun is shown on the diagram.Which of the following statements is true?

Two planets are orbiting a star in a distant galaxy.The first has a semimajor axis of 150 *106 km, an eccentricity of 0.20, and a period of 1.0 Earth years.The second has a semimajor axis of 250 * 106 km, an eccentricity of 0.30, and a period of:

Consider the statement: "Earth moves in a stable orbit around the Sun and is therefore in equilibrium".The statement is:

Assume that Earth is in circular orbit around the Sun with kinetic energy K and potential energy U, taken to be zero for infinite separation.Then, the relationship between K and U:

Einstein's principle of equivalence states:

A planet travels in an elliptical orbit about a star X as shown.The magnitude of the acceleration of the planet is:

Neglecting air resistance, the escape speed from a certain planet for an empty space vehicle is 1.12 *104 m/s.What is the corresponding escape speed for the fully loaded vehicle which has triple the mass of the empty one?

Given the perihelion distance, aphelion distance, and speed at perihelion of a planet, which of the following CANNOT be calculated?

A small satellite is in elliptical orbit around Earth as shown.If L denotes the magnitude of its angular momentum and K denotes kinetic energy:

A planet is in circular orbit around the Sun.Its distance from the Sun is four times the average distance of Earth from the Sun.The period of this planet is:

The orbit of a certain a satellite has a semimajor axis of 1.5 * 107 m and an eccentricity of 0.20.Its perigee (minimum distance) and apogee (maximum distance) are respectively:

The speed of a comet in an elliptical orbit about the sun:

For a planet in orbit around a star the perihelion distance is rp and its speed at perihelion is vp.The aphelion distance is ra and its speed at aphelion is va.Which of following is true?

Planet 1 and planet 2 are both in circular orbits around the same central star.The orbit of planet 2 has a radius that is much larger than the radius of the orbit of planet 1.This means that:

In planetary motion the line from the star to the planet sweeps out equal areas in equal times.This is a direct consequence of:

An artificial Earth satellite is moved from a circular orbit with radius R to a circular orbit with radius 2R.During this move:

An artificial satellite of Earth nears the end of its life due to air resistance.While still in orbit:

A planet travels in an elliptical orbit about a star as shown.At what pair of points is the speed of the planet the same?

Two planets are orbiting a star in a distant galaxy.The first has a semimajor axis of 150 10⁶ km, an eccentricity of 0.20, and a period of 1.0 Earth years.The second has a semimajor axis of 250 10⁶ km, an eccentricity of 0.30, and a period of:

Neglecting air resistance, the escape speed from a certain planet for an empty space vehicle is 1.12 *10⁴ m/s.What is the corresponding escape speed for the fully loaded vehicle which has triple the mass of the empty one?

The orbit of a certain a satellite has a semimajor axis of 1.5 * 10⁷ m and an eccentricity of 0.20.Its perigee (minimum distance) and apogee (maximum distance) are respectively:

For a planet in orbit around a star the perihelion distance is r_p and its speed at perihelion is v_p.The aphelion distance is r_a and its speed at aphelion is v_a.Which of following is true?