What is escape velocity?
The minimum velocity required to project a mass to infinity from the surface of a planet.
p.11
Gravitational Potential
What is the formula for the gravitational potential at point P due to objects A and B?
Φ_P = Φ_A + Φ_B = -GM_A/r_A - GM_B/r_B
p.4
Gravitational Field Strength
What is the condition for the 1.0 kg object in the given scenario?
It experiences zero resultant force.
p.9
Gravitational Potential
How is gravitational potential defined?
As the work done per unit mass in bringing a small test mass from infinity to that point.
What is the escape velocity from the Earth's surface?
Approximately 11,200 m/s.
p.5
Gravitational Field Strength
How is gravitational field strength defined?
As the gravitational force per unit mass acting at a point.
How is escape velocity mathematically expressed in terms of gravitational field strength?
v_esc = √(gR), where g is the gravitational field strength at the Earth's surface.
p.15
Energy of Satellite in Orbit
How is the kinetic energy (KE) of an orbiting satellite derived?
By applying Newton’s second law: F = ma, leading to KE = (1/2)mv^2 = (GMm)/(2r).
p.4
Gravitational Field Strength
What is the formula used to calculate the distance x between the 1.0 kg and 1000 kg objects?
5000 = 1000 * 10 * (x^2) / (x^2).
p.16
Energy of Satellite in Orbit
What is the change in kinetic energy for the satellite?
Approximately 8.48 × 10^8 J.
p.6
Gravitational Field Strength
What is the radius ratio of the Earth to the Moon?
The Earth's radius is approximately 3.7 times that of the Moon.
p.18
Gravitational Potential
What is the definition of gravitational potential at a point?
The work done per unit mass in bringing a small test mass from infinity to that point.
What happens if the launch of a satellite is not from the Earth's surface?
The gravitational field strength g = 9.81 N/kg cannot be used.
p.3
Newton's Law of Gravitation
What is the significance of the 1.0 kg object experiencing no resultant force?
It indicates a balance of gravitational forces from the two larger masses.
p.17
Gravitational Field Strength
How is electric field strength defined?
Electric field strength E at a point is defined as the electrostatic force per unit positive charge q placed at that point.
What is the relationship between kinetic energy and gravitational potential energy for escape velocity?
The minimum kinetic energy required is equivalent to the gain in gravitational potential energy.
p.15
Energy of Satellite in Orbit
What happens to the total energy (TE) when a satellite is boosted to a higher orbit?
TE decreases as the gravitational potential energy becomes less negative.
p.3
Newton's Law of Gravitation
What does the negative sign in the gravitational force equation indicate?
The attractive nature of the force.
p.6
Gravitational Field Strength
What is the mass ratio of the Earth to the Moon?
The mass of the Earth is approximately 80 times that of the Moon.
What does the term 'geostationary' imply about a satellite?
It is fixed above a position on the Earth.
p.16
Gravitational Potential Energy
What is the change in gravitational potential energy for the satellite?
Approximately 2.95 × 10^8 J.
p.8
Gravitational Field Strength
What is the approximate value of gravitational field strength near the Earth's surface?
9.81 N kg⁻¹ (or 9.81 m s⁻²).
p.8
Gravitational Field Strength
How does gravitational field strength vary from the surface of the Earth upwards?
It follows an inverse square law (g ∝ 1/r²).
What keeps a satellite in orbit around a celestial body?
The gravitational attraction of the body it is orbiting.
p.11
Gravitational Potential Energy
What is the gravitational potential energy (G.P.E.) change formula when moving a satellite?
Energy required = G.P.E. change = GMm(1/R - 1/(R+h))
p.11
Gravitational Potential Energy
How do you calculate the energy required to move a satellite to a height of 200 km?
Use the formula: Energy required = GMm(1/R - 1/(R+h)) with given values.
What provides the centripetal force for a satellite orbiting the Earth?
The Earth's gravitational attraction.
p.5
Gravitational Field Strength
What does the gravitational field strength depend on?
The distance r from the object causing the gravitational field.
p.4
Gravitational Field Strength
What is a gravitational field?
A region of space where a mass experiences a force due to another mass.
p.17
Comparison Between Gravitational Field and Electric Field
What is the nature of the force in an electric field?
The force can be attractive or repulsive; unlike charges attract, like charges repel.
In which direction does a geostationary satellite revolve?
From West to East, in the same direction as the Earth's rotation.
p.7
Gravitational Field Strength
In which direction does the resultant gravitational field strength at point P act?
Towards the midpoint of AB.
What is the relationship between gravitational force and centripetal acceleration in circular orbits?
Gravitational force is equal to the centripetal force required to keep the satellite in orbit.
How do you calculate the height of a geostationary satellite above the Earth's surface?
Height = radius of orbit - radius of Earth.
What must an object overcome to escape from the Earth's surface?
The gravitational pull of the Earth.
p.8
Gravitational Field Strength
What happens to gravitational field strength as one moves towards the center of the Earth?
It decreases uniformly and becomes zero at the center.
p.8
Gravitational Field Strength
What factors can cause variations in the value of gravitational field strength on Earth?
The Earth's shape and its rotation.
p.17
Comparison Between Gravitational Field and Electric Field
What is the nature of the force in a gravitational field?
The force is attractive in nature; all masses attract each other.
How does the escape velocity compare to the speed of sound?
It is equivalent to traveling at about 34 times the speed of sound.
p.6
Gravitational Field Strength
How does the gravitational field strength at the Earth's surface compare to that on the Moon's surface?
The gravitational field strength on the Moon's surface is approximately 1.7 N kg⁻¹.
p.8
Gravitational Field Strength
What is the relationship between gravitational field strength and the radius of the Earth?
Gravitational field strength decreases with radius (g ∝ r).
p.6
Gravitational Field Strength
If the gravitational field strength at the Earth's surface is 10 N kg⁻¹, what is the formula used to estimate it on the Moon's surface?
g_M = g_E * (M_E / M_M) * (r_M / r_E)².
p.7
Gravitational Field Strength
What is the gravitational field strength due to object A at point P?
Approximately 1.33 × 10^-5 N kg^-1.
p.9
Gravitational Potential
What does the negative sign in the gravitational potential formula indicate?
That the gravitational force is an attractive force.
p.3
Newton's Law of Gravitation
What are the masses of the two stationary objects in Example 2?
5.0 × 10^3 kg and 1.0 × 10^3 kg.
p.5
Gravitational Field Strength
What type of quantity is gravitational field strength?
It is a vector quantity, having both direction and magnitude.
p.2
Newton's Law of Gravitation
What did Newton's law of gravitation state?
The force of attraction between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
p.5
Gravitational Field Strength
Is the gravitational field strength at a point dependent on the mass of the object experiencing the force?
No, it is independent of mass m.
p.4
Gravitational Field Strength
How can a gravitational field be represented?
By field lines directed towards the center of the mass.
What is the formula for the speed of a satellite in orbit around the Earth?
v = √(GM_E / r), where G is the gravitational constant and M_E is the mass of the Earth.
What is the period of a geostationary satellite?
24 hours, the same as the Earth's rotation.
p.16
Energy of Satellite in Orbit
What is the total change in energy for the satellite?
Approximately 1.47 × 10^8 J.
p.17
Newton's Law of Gravitation
What does Newton's law of gravitation state?
The gravitational force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their distance apart.
What is the plane of revolution for a geostationary satellite?
In the plane of the Equator.
How does the expression for orbital speed differ from escape speed?
The expression for orbital speed is different from the expression for escape speed.
What assumption is made about kinetic energy at infinity when calculating escape velocity?
Kinetic energy at infinity is assumed to be zero.
p.16
Energy of Satellite in Orbit
Is the change in total energy an increase or decrease?
The total energy has increased.
What is an equipotential surface?
A surface where all points have the same gravitational potential.
p.18
Comparison Between Gravitational Field and Electric Field
What does the relationship dr/dΦ = -g represent?
The relationship between gravitational field strength and gravitational potential.
p.9
Gravitational Potential
What type of quantity is gravitational potential (φ)?
It is a scalar and a property of a point in the field.
p.2
Newton's Law of Gravitation
What is meant by the term 'inverse square law' in gravitation?
The magnitude of the gravitational force varies with the inverse square of the separation of the particles.
p.7
Gravitational Field Strength
What is the resultant gravitational field strength at point P?
Approximately 2.09 × 10^-5 N kg^-1.
p.2
Newton's Law of Gravitation
Who published 'Philosophiæ Naturalis Principia Mathematica' and in what year?
Isaac Newton published it in 1687.
What relationship exists between gravitational force and centripetal acceleration in circular orbits?
Gravitational force is related to the centripetal acceleration it causes.
p.2
Newton's Law of Gravitation
How does Newton's third law relate to gravitational forces?
Gravitational forces of attraction between two bodies form an action-reaction pair.
What is the approximate height of a geostationary satellite above the Earth's surface?
Approximately 6.3 x 10^7 m.
p.18
Gravitational Potential
How is electric potential defined at a point?
The work done per unit positive charge in bringing a small test charge from infinity to that point.
p.8
Gravitational Field Strength
What is the significance of the height 'h' in relation to gravitational field strength?
If 'h' is small compared to the Earth's radius, g remains approximately constant.
p.17
Newton's Law of Gravitation
What does Coulomb's law state?
The electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of their distance apart.
What is true about gravitational field lines in relation to equipotential surfaces?
Gravitational field lines are always normal to equipotential surfaces.
What is a geostationary orbit?
An orbit where a satellite remains in a fixed position relative to the Earth's surface.
p.17
Gravitational Field Strength
How is gravitational field strength defined?
Gravitational field strength g at a point is defined as the gravitational force per unit mass m placed at that point.
p.18
Comparison Between Gravitational Field and Electric Field
What does the relationship dr/dV = -E represent?
The relationship between electric field strength and electric potential.
p.17
Gravitational Potential Energy
How is electric potential energy defined?
Electric potential energy U of a charge q at a point is defined as the work done in bringing it from infinity to that point.
What can be said about points at the same distance from the center of the Earth?
They have the same gravitational potential.
p.1
Gravitational Field Strength
What is the definition of gravitational field strength at a point?
The gravitational force exerted per unit mass placed at that point.
What is the approximate radius of a geostationary satellite's orbit?
Approximately 7.4 x 10^7 m.
p.2
Newton's Law of Gravitation
How is the distance r measured for spherical masses in gravitation?
It is measured between their respective centers of mass.
p.2
Newton's Law of Gravitation
What sparked Newton's studies in gravitation?
Observing an apple falling to the ground.
What is the formula used to determine the radius of a geostationary satellite's orbit?
r = (GM_E * T^2 / (4π^2))^(1/3).
p.18
Comparison Between Gravitational Field and Electric Field
What does dr/dU = -F represent in terms of force and potential energy?
The relationship between force and potential energy for gravitational and electric fields.
p.17
Gravitational Potential Energy
How is gravitational potential energy defined?
Gravitational potential energy U of a mass m at a point is defined as the work done in bringing it from infinity to that point.
p.1
Gravitational Field Strength
What is the approximate value of gravitational field strength near the Earth's surface?
It is approximately constant and equal to the acceleration of free fall.
p.1
Gravitational Potential
How is gravitational potential defined at a point?
As the work done per unit mass in bringing a small test mass from infinity to that point.
p.1
Gravitational Field Strength
How is the gravitational field strength of a point mass derived?
From Newton's law of gravitation and the definition of gravitational field strength, g = GM/r^2.
