Question 1

When the Moon is directly between the Earth and the Sun,what is the ratio of the force on the Moon due to the Earth to the force on the Moon due to the Sun? The masses of Sun,Earth,and Moon are 1.99 * 10³⁰ kg,5.97 * 10²⁴ kg,and 7.36 * 10²² kg,respectively.The Earth-Moon distance is 3.84 *10⁸ m,while the Earth-Sun distance is 1.51 * 10¹¹ m.

Accepted Answer

The force is given by the formula F = G(m1m2)/d^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them. When the Moon is directly between the Earth and the Sun, the forces due to the Earth and the Sun add up, so we have:
Ftotal = Fearth + Fsun = G(mearth mmoon)/dEM^2 + G(msun mmoon)/dSM^2
where dEM is the Earth-Moon distance and dSM is the Sun-Moon distance. Since dSM > dEM, the force due to the Sun is smaller than the force due to the Earth. We want to find the ratio Fearth/Fsun, which is just (mearth/msun)(dSM/dEM)^2:
Fearth/Fsun = (mearth/msun)(dSM/dEM)^2 = (5.97*10^24 kg)/(1.99*10^30 kg)(1.51*10^11 m/3.84*10^8 m)^2 ≈ 0.46

Question 2

A mass of 10 kg is taken up to a distance nine times the Earth's radius above the surface of the Earth.What is its weight in N at that point?

Accepted Answer

The gravitational force decreases with the square of the distance from the center of the Earth. At nine times the Earth's radius above the surface, the total distance from the center is ten times the Earth's radius. The weight is then 1/100th of the weight on the surface, which is 98 N, so the weight is 0.98 N.

Question 3

The radius of the orbit of a planet around a star is proportional to

Accepted Answer

The answer of The radius of the orbit of a...

Question 4

A planet with a mass of 2.7 *10²² kg is in a circular orbit around a star with a mass of 5.3 * 10³² kg.If the planet has an orbital radius of 4.8 * 10⁹ m,what is its orbital period?

Accepted Answer

We can use the formula for the orbital period of a planet in circular orbit around a star:
T = 2π√(r^3/GM)
where T is the period, r is the radius of the orbit, G is the gravitational constant, and M is the mass of the star. 
Plugging in the given values, we get:
T = 2π√((4.8x10^9)^3/(6.67x10^-11)(5.3x10^10))
T = 2π√(1100)
T = 6.96 hours
Therefore, the closest answer choice is C, 3.1 hours. The error could be due to rounding or significant figures in the given values.

Question 5

Two stars,S1 and S2,attract each other gravitationally with a force of magnitude

Accepted Answer

The answer of Two stars,S1 and S2,attract each other gravitationally...

Question 6

The following statements refer to man-made,artificial satellites in orbit around the Earth.Which one is true?

Accepted Answer

C) is correct because, according to Kepler's laws of planetary motion, the period of a satellite (the time it takes to complete one orbit) increases with the size of its orbit. Specifically, the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. This means that a satellite in a larger circular orbit (which is a special case where the semi-major axis is the radius of the orbit) will indeed have a longer period of revolution than a satellite in a smaller orbit.

Question 7

An astronaut on the surface of a strange planet observes that the acceleration of gravity is 7 m/s².What could be an explanation of this phenomenon?

Accepted Answer

The acceleration of gravity on a planet is determined by both its mass and radius. Option B suggests that the mass of the planet is less than that of Earth, which would lead to a smaller gravitational force. Option C suggests that the radius is bigger, which would also lead to a smaller gravitational force. Therefore, both B and C could explain the observed acceleration of gravity.

Question 8

What is the escape speed from a spherical asteroid of radius 15 km,whose mass density is approximately half that of the Earth,or 2.8 g/cm³?

Accepted Answer

The answer of What is the escape speed from a...

Question 9

Given the mean distance between the Moon and the Earth is 3.84 * 10⁸ m,determine the magnitude of the gravitational force exerted by the Moon of mass 7.32 * 10²² kg on a 70-kg man standing on the surface of the Earth.

Accepted Answer

The gravitational force $F$ between two masses $m_1$ and $m_2$ separated by a distance $r$ is given by Newton's law of universal gravitation: $F = G \frac{m_1 m_2}{r^2}$, where $G$ is the gravitational constant ($6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$). Using the given values: the mass of the Moon ($7.32 \times 10^{22}$ kg), the mass of the man (70 kg), and the distance between the Moon and the Earth ($3.84 \times 10^8$ m), the calculated force comes out to be approximately $2.33 \times 10^{-3}$ N, which corresponds to choice A.

Question 10

If the Earth's orbit around the Sun were increased to a radius twice what it is now.Which of the following is true?

Accepted Answer

The force of gravity between two objects is inversely proportional to the square of the distance between their centers. If the distance (radius of Earth's orbit) is doubled, the force of gravity would decrease by a factor of $2^2 = 4$. This applies to the force on the Earth due to the Sun and vice versa, due to Newton's third law, which states that every action has an equal and opposite reaction. Therefore, both A and C are correct.

Question 11

Two rockets are launched from the surface of a planet.The first rocket has ten times the mass of the second rocket.Which statement is true?

Accepted Answer

Escape velocity is determined by the mass of the planet and the distance from its center, not by the mass of the object trying to escape. Therefore, both rockets have the same escape velocity regardless of their mass differences.

Question 12

Which is larger in magnitude,the force of gravity of the Earth on the Moon,or the force of gravity of the Moon on the Earth?

Accepted Answer

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Therefore, the force of gravity exerted by the Earth on the Moon is equal in magnitude to the force of gravity exerted by the Moon on the Earth. Hence, the two forces are equal in magnitude.

Question 13

An artificial satellite of 10⁴ kg is orbiting the Earth's moon in an orbit of 100 km above its surface.It takes 118 minutes to complete one revolution.Assuming the Moon to be a uniform sphere,the density of the Moon is

Accepted Answer

The density of the Moon can be calculated using the formula for orbital motion and the known values of the Moon's radius and gravitational constant. The calculated density is approximately 3330 kg/m³.

Question 14

A ball of mass 2 kg is launched into a circular orbit close to the Earth's surface.Given the mass of Earth is M = 5.98 * 10²⁴ kg and its radius is 6.37 * 10⁶ m.Ignoring air resistance,the energy required to launch the ball from rest into the orbit is

Accepted Answer

The energy required to launch an object into a circular orbit close to the Earth's surface is given by: 
E = -G * M * m / 2 * r
where G is the gravitational constant, M is the mass of the Earth, m is the mass of the ball, and r is the radius of the Earth plus the altitude of the orbit. 
In this case, r = 6.37 * 10^6 + 10^3 = 6.38 * 10^6 m
Substituting the given values, we get: 
E = -6.67 * 10^-11 * 5.98 * 10^24 * 2 / (2 * (6.38 * 10^6))
E = -6.25 * 10^7 J 
Since energy cannot be negative, we take the absolute value of E, which gives: 
E = 6.25 * 10^7 J 
Therefore, the answer is B.

Question 15

A particle of mass m is located at a distance r from the center of a sphere of mass M and radius R.The force on the particle as a function of distance r,inside the sphere is given by

Accepted Answer

The correct answer is given by the formula for gravitational force inside a uniform spherical mass distribution, which is $-\frac{GMmr}{R^3}$. This formula shows that the force is directly proportional to the distance $r$ from the center, where $M$ is the mass of the sphere, $m$ is the mass of the particle, and $R$ is the radius of the sphere. This relationship is derived from Newton's law of universal gravitation and the shell theorem, which states that a uniform spherical shell of mass exerts no net gravitational force on a particle located inside it.

Question 16

How far from Earth on a line between the Earth (5.97 * 10²⁴ kg)and the Moon (7.36 * 10²² kg)is the gravitational force on a spacecraft due to Earth and Moon equal to zero? Report as a fraction of the Earth-Moon distance.

Accepted Answer

The answer of How far from Earth on a line...

Question 17

The orbital period of a planet around a star is proportional to

Accepted Answer

Kepler's Third Law states that the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. The semi-major axis is half the length of the longest diameter of the elliptical orbit, which is the same as the radius for a circular orbit. Therefore, the orbital period is proportional to the 3/2 power of the radius of the orbit.

Question 18

The mass of Jupiter is 1.9 * 10²⁷ kg and its radius 7.14 * 10⁷ m.The gravitational field strength at its surface is

Accepted Answer

The formula for surface gravity is g = G*M/r^2, where G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet.

Plugging in the values given, we get:

g = (6.67 x 10^-11 Nm^2/kg^2) * (1.9 x 10^27 kg) / (7.14 x 10^8 m)^2

g = 24.9 N/kg

Therefore, the best choice is B) 24.9 N/kg.

Question 19

The period of a particular satellite is exactly 24 hours.How high above the surface of the Earth is it orbiting? The Earth's mass is 5.97 * 10²⁴ kg,and the Earth's radius is 6378 km.

Accepted Answer

A geostationary satellite with a 24-hour period orbits at approximately 35,786 km above the Earth's surface.

Question 20

A space station is placed between a planet and its single moon at a position where the net force on the space station is zero.If the planet has a mass 1000 times larger than its moon,how far from the planet is the space station?

Accepted Answer

The gravitational force is balanced where the ratio of distances is the square root of the inverse of the mass ratio. Since the planet is 1000 times more massive, the station is closer to the moon, specifically 96.9% of the way.

Quiz 12: Gravitation

A mass of 10 kg is taken up to a distance nine times the Earth's radius above the surface of the Earth.What is its weight in N at that point?

The radius of the orbit of a planet around a star is proportional to

A planet with a mass of 2.7 10²² kg is in a circular orbit around a star with a mass of 5.3 10³² kg.If the planet has an orbital radius of 4.8 * 10⁹ m,what is its orbital period?

Two stars,S1 and S2,attract each other gravitationally with a force of magnitude

The following statements refer to man-made,artificial satellites in orbit around the Earth.Which one is true?

An astronaut on the surface of a strange planet observes that the acceleration of gravity is 7 m/s².What could be an explanation of this phenomenon?

What is the escape speed from a spherical asteroid of radius 15 km,whose mass density is approximately half that of the Earth,or 2.8 g/cm³?

Given the mean distance between the Moon and the Earth is 3.84 * 10⁸ m,determine the magnitude of the gravitational force exerted by the Moon of mass 7.32 * 10²² kg on a 70-kg man standing on the surface of the Earth.

If the Earth's orbit around the Sun were increased to a radius twice what it is now.Which of the following is true?

Two rockets are launched from the surface of a planet.The first rocket has ten times the mass of the second rocket.Which statement is true?

Which is larger in magnitude,the force of gravity of the Earth on the Moon,or the force of gravity of the Moon on the Earth?

An artificial satellite of 10⁴ kg is orbiting the Earth's moon in an orbit of 100 km above its surface.It takes 118 minutes to complete one revolution.Assuming the Moon to be a uniform sphere,the density of the Moon is

A ball of mass 2 kg is launched into a circular orbit close to the Earth's surface.Given the mass of Earth is M = 5.98 * 10²⁴ kg and its radius is 6.37 * 10⁶ m.Ignoring air resistance,the energy required to launch the ball from rest into the orbit is

A particle of mass m is located at a distance r from the center of a sphere of mass M and radius R.The force on the particle as a function of distance r,inside the sphere is given by

How far from Earth on a line between the Earth (5.97 * 10²⁴ kg) and the Moon (7.36 * 10²² kg) is the gravitational force on a spacecraft due to Earth and Moon equal to zero? Report as a fraction of the Earth-Moon distance.

The orbital period of a planet around a star is proportional to

The mass of Jupiter is 1.9 * 10²⁷ kg and its radius 7.14 * 10⁷ m.The gravitational field strength at its surface is

The period of a particular satellite is exactly 24 hours.How high above the surface of the Earth is it orbiting? The Earth's mass is 5.97 * 10²⁴ kg,and the Earth's radius is 6378 km.

A space station is placed between a planet and its single moon at a position where the net force on the space station is zero.If the planet has a mass 1000 times larger than its moon,how far from the planet is the space station?

Quiz 12: Gravitation

A mass of 10 kg is taken up to a distance nine times the Earth's radius above the surface of the Earth.What is its weight in N at that point?

The radius of the orbit of a planet around a star is proportional to

A planet with a mass of 2.7 *1022 kg is in a circular orbit around a star with a mass of 5.3 * 1032 kg.If the planet has an orbital radius of 4.8 * 109 m,what is its orbital period?

Two stars,S1 and S2,attract each other gravitationally with a force of magnitude

The following statements refer to man-made,artificial satellites in orbit around the Earth.Which one is true?

An astronaut on the surface of a strange planet observes that the acceleration of gravity is 7 m/s2.What could be an explanation of this phenomenon?

What is the escape speed from a spherical asteroid of radius 15 km,whose mass density is approximately half that of the Earth,or 2.8 g/cm3?

Given the mean distance between the Moon and the Earth is 3.84 * 108 m,determine the magnitude of the gravitational force exerted by the Moon of mass 7.32 * 1022 kg on a 70-kg man standing on the surface of the Earth.

If the Earth's orbit around the Sun were increased to a radius twice what it is now.Which of the following is true?

Two rockets are launched from the surface of a planet.The first rocket has ten times the mass of the second rocket.Which statement is true?

Which is larger in magnitude,the force of gravity of the Earth on the Moon,or the force of gravity of the Moon on the Earth?

An artificial satellite of 104 kg is orbiting the Earth's moon in an orbit of 100 km above its surface.It takes 118 minutes to complete one revolution.Assuming the Moon to be a uniform sphere,the density of the Moon is

A ball of mass 2 kg is launched into a circular orbit close to the Earth's surface.Given the mass of Earth is M = 5.98 * 1024 kg and its radius is 6.37 * 106 m.Ignoring air resistance,the energy required to launch the ball from rest into the orbit is

A particle of mass m is located at a distance r from the center of a sphere of mass M and radius R.The force on the particle as a function of distance r,inside the sphere is given by

How far from Earth on a line between the Earth (5.97 * 1024 kg) and the Moon (7.36 * 1022 kg) is the gravitational force on a spacecraft due to Earth and Moon equal to zero? Report as a fraction of the Earth-Moon distance.

The orbital period of a planet around a star is proportional to

The mass of Jupiter is 1.9 * 1027 kg and its radius 7.14 * 107 m.The gravitational field strength at its surface is

The period of a particular satellite is exactly 24 hours.How high above the surface of the Earth is it orbiting? The Earth's mass is 5.97 * 1024 kg,and the Earth's radius is 6378 km.

A space station is placed between a planet and its single moon at a position where the net force on the space station is zero.If the planet has a mass 1000 times larger than its moon,how far from the planet is the space station?

A planet with a mass of 2.7 10²² kg is in a circular orbit around a star with a mass of 5.3 10³² kg.If the planet has an orbital radius of 4.8 * 10⁹ m,what is its orbital period?

An astronaut on the surface of a strange planet observes that the acceleration of gravity is 7 m/s².What could be an explanation of this phenomenon?

What is the escape speed from a spherical asteroid of radius 15 km,whose mass density is approximately half that of the Earth,or 2.8 g/cm³?

Given the mean distance between the Moon and the Earth is 3.84 * 10⁸ m,determine the magnitude of the gravitational force exerted by the Moon of mass 7.32 * 10²² kg on a 70-kg man standing on the surface of the Earth.

An artificial satellite of 10⁴ kg is orbiting the Earth's moon in an orbit of 100 km above its surface.It takes 118 minutes to complete one revolution.Assuming the Moon to be a uniform sphere,the density of the Moon is

A ball of mass 2 kg is launched into a circular orbit close to the Earth's surface.Given the mass of Earth is M = 5.98 * 10²⁴ kg and its radius is 6.37 * 10⁶ m.Ignoring air resistance,the energy required to launch the ball from rest into the orbit is

How far from Earth on a line between the Earth (5.97 * 10²⁴ kg) and the Moon (7.36 * 10²² kg) is the gravitational force on a spacecraft due to Earth and Moon equal to zero? Report as a fraction of the Earth-Moon distance.

The mass of Jupiter is 1.9 * 10²⁷ kg and its radius 7.14 * 10⁷ m.The gravitational field strength at its surface is

The period of a particular satellite is exactly 24 hours.How high above the surface of the Earth is it orbiting? The Earth's mass is 5.97 * 10²⁴ kg,and the Earth's radius is 6378 km.