What is Newton's law of gravitation ?

Newton's law of gravitation states that the gravitational force between two point masses is directly proportional to the product of the masses and inversely proportional to the square of their separation.

True or False? The gravitational force between two masses can be attractive or repulsive.

False. The gravitational force between two masses is always attractive.

What assumptions are made about planets in Newton's law of gravitation?

The assumptions made about planets in Newton's law of gravitation are: they are perfectly spherical they are point masses (all the mass acts at their centres) their separations are much greater than their radii

Define gravitational field strength at a point.

The gravitational field strength at a point is the force per unit mass experienced by a test mass at that point.

What are the two equivalent units of gravitational field strength?

The two equivalent units of gravitational field strength are N kg -1 and m s -2 .

What is the significance of a test mass ?

Test masses are used to define the strength of a field at a point and the direction a mass will move in the field. This is because gravitational field strength is a vector quantity.

True or False? An object's mass changes depending on the strength of the gravitational field.

False. An object's mass remains the same at all points in space, but the force it experiences changes depending on the strength of the gravitational field.

Which two quantities does the strength of a gravitational field at the surface of a planet depend on?

The strength of a gravitational field at the surface of a planet depends on: the radius of the planet the mass of the planet

True or False? The variation of gravitational field strength around a planet and a point mass are identical.

False. The variation of gravitational field strength around the outside of a planet and a point mass are identical. Inside the planet, the gravitational field strength decreases linearly from a maximum value (at the surface) to zero at the centre.

How is the resultant gravitational field due to multiple masses determined?

The resultant gravitational field due to multiple masses is determined by vector addition . This could be using simple addition (if the point lies on a line joining the masses) using Pythagoras (if the point makes a right-angled triangle with the masses)

What do gravitational field lines represent?

Gravitational field lines represent the strength of the gravitational field the direction of the gravitational field

What is a uniform gravitational field?

A uniform gravitational field is one where the field strength is the same at all points.

True or False? Radial gravitational field lines always point towards the centre of mass of a body.

True. Radial gravitational field lines always point towards the centre of mass of a body.

True or False? Radial fields are considered uniform fields.

False. Radial fields are considered non-uniform fields.

What is the difference between radial and uniform gravitational fields?

The difference between radial and uniform gravitational fields is: in a uniform gravitational field, field strength is the same at all points in a radial gravitational field, field strength varies with distance from the centre

What is the relationship between gravitational field strength and line density ?

The density of field lines represents the strength of a gravitational field the closer together the field lines, the stronger the field the further apart the field lines, the weaker the field

State Kepler's first law .

Kepler's first law states that the orbit of a planet is an ellipse , with the Sun at one of the two foci .

State Kepler's second law .

Kepler's second law states that a line segment joining the Sun to a planet sweeps out equal areas in equal time intervals.

At what point in a comet's orbit does it travel fastest ?

Comets travel fastest when they are at the closest point to the Sun in their elliptical orbit.

At what point in a comet's orbit does it travel slowest ?

Comets travel slowest when they are at the furthest point from the Sun in their elliptical orbit.

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Gravitational Fields (DP IB Physics)

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FrontNewton's Law of Gravitation
What is Newton's law of gravitation?
FrontNewton's Law of Gravitation
What is the gravitational force between two identical masses separated by a distance, $r$ ?
BackNewton's Law of Gravitation
The gravitational force between the two identical masses is: $F = \frac{G M^{2}}{r^{2}}$
Where:
$G$ = gravitational constant (6.67 × 10^-11 N m² kg^–2)
$M$ = magnitude of each mass, measured in kilograms (kg)
$r$ = separation of the masses, measured in metres (m)

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What is Newton's law of gravitation?
Newton's law of gravitation states that the gravitational force between two point masses is directly proportional to the product of the masses and inversely proportional to the square of their separation.
What is the gravitational force between two identical masses separated by a distance, $r$ ?
The gravitational force between the two identical masses is: $F = \frac{G M^{2}}{r^{2}}$
Where:
- $G$ = gravitational constant (6.67 × 10^-11 N m² kg^–2)
- $M$ = magnitude of each mass, measured in kilograms (kg)
- $r$ = separation of the masses, measured in metres (m)
True or False?
The value of, $G$ , (gravitational constant) is the same in all of space.
True.
The value of, $G$ , (gravitational constant) is the same in all of space.
True or False?
The gravitational force between two masses can be attractive or repulsive.
False.
The gravitational force between two masses is always attractive.
What is the relationship between gravitational force and distance?
The relationship between gravitational force and distance is an inverse square law.
This means that when the distance between two point masses doubles, the gravitational force between them falls by $\frac{1}{4}$ .
What assumptions are made about planets in Newton's law of gravitation?
The assumptions made about planets in Newton's law of gravitation are:
- they are perfectly spherical
- they are point masses (all the mass acts at their centres)
- their separations are much greater than their radii
Draw arrows to show the gravitational force between the Earth and the Moon.
The gravitational force between the Earth and the Moon:
- is attractive (arrows point towards each other)
- has the same magnitude on each object (arrows are the same size)
- treats the objects as point masses (arrows begin from the centres)
Define gravitational field strength at a point.
The gravitational field strength at a point is the force per unit mass experienced by a test mass at that point.
What are the two equivalent units of gravitational field strength?
The two equivalent units of gravitational field strength are N kg^-1 and m s^-2.
What is the significance of a test mass?
Test masses are used to define the strength of a field at a point and the direction a mass will move in the field.
This is because gravitational field strength is a vector quantity.
True or False?
An object's mass changes depending on the strength of the gravitational field.
False.
An object's mass remains the same at all points in space, but the force it experiences changes depending on the strength of the gravitational field.
Which two quantities does the strength of a gravitational field at the surface of a planet depend on?
The strength of a gravitational field at the surface of a planet depends on:
- the radius of the planet
- the mass of the planet
What is the gravitational field strength due to a point mass of magnitude, $M$ , at a distance, $r$ ?
The gravitational field strength due to a point mass is: $g = \frac{G M}{r^{2}}$
Where:
- $G$ = gravitational constant (6.67 × 10^-11 N m² kg^–2)
- $M$ = magnitude of the point mass, measured in kilograms (kg)
- $r$ = distance from the mass to the point, measured in metres (m)
True or False?
The variation of gravitational field strength around a planet and a point mass are identical.
False.
The variation of gravitational field strength around the outside of a planet and a point mass are identical.
Inside the planet, the gravitational field strength decreases linearly from a maximum value (at the surface) to zero at the centre.
How is the resultant gravitational field due to multiple masses determined?
The resultant gravitational field due to multiple masses is determined by vector addition. This could be
- using simple addition (if the point lies on a line joining the masses)
- using Pythagoras (if the point makes a right-angled triangle with the masses)
Sketch the variation of gravitational field strength with distance from the centre of Earth.
The variation of gravitational field strength with distance from the centre of Earth is:
What do gravitational field lines represent?
Gravitational field lines represent
- the strength of the gravitational field
- the direction of the gravitational field
What is a uniform gravitational field?
A uniform gravitational field is one where the field strength is the same at all points.
True or False?
Radial gravitational field lines always point towards the centre of mass of a body.
True.
Radial gravitational field lines always point towards the centre of mass of a body.
True or False?
Radial fields are considered uniform fields.
False.
Radial fields are considered non-uniform fields.
Draw the gravitational field lines around a planet.
The gravitational field lines around a planet are radial:
Draw the gravitational field lines close to the Earth's surface.
The gravitational field lines close to the Earth's surface are uniform:
What is the difference between radial and uniform gravitational fields?
The difference between radial and uniform gravitational fields is:
- in a uniform gravitational field, field strength is the same at all points
- in a radial gravitational field, field strength varies with distance from the centre
Draw the gravitational field lines between larger mass P and smaller mass Q. Indicate the neutral point with an X.
The gravitational field lines between P and Q are:
What is the relationship between gravitational field strength and line density?
The density of field lines represents the strength of a gravitational field
- the closer together the field lines, the stronger the field
- the further apart the field lines, the weaker the field
State Kepler's first law.
Kepler's first law states that the orbit of a planet is an ellipse, with the Sun at one of the two foci.
State Kepler's second law.
Kepler's second law states that a line segment joining the Sun to a planet sweeps out equal areas in equal time intervals.
State Kepler's third law.
Kepler's third law states that for planets or satellites in a circular orbit about the same central body, the square of the time period is proportional to the cube of the orbital radius.
- $T^{2} \propto R^{3}$ or $\frac{R^{3}}{T^{2}} = constant$
How is Kepler's third law derived?
Kepler's third law is derived by equating the centripetal force and the gravitational force on an orbiting mass and substituting the expression for the speed of an object in circular motion:
- $F = \frac{m v^{2}}{r} = \frac{G M m}{r^{2}}$
- $v^{2} = \frac{G M}{r} = {(\frac{2 π r}{T})}^{2}$
- $T^{2} = \frac{4 π r^{3}}{G M}$
On the diagram, label the Sun, a planet and a comet.
The Sun is at the centre of the near-circular orbit of a planet and one of the two foci of the elliptical orbit of a comet.
At what point in a comet's orbit does it travel fastest?
Comets travel fastest when they are at the closest point to the Sun in their elliptical orbit.
At what point in a comet's orbit does it travel slowest?
Comets travel slowest when they are at the furthest point from the Sun in their elliptical orbit.
True or False?
A graph of $\log T$ against $\log r$ for the planets in the Solar System is a straight line.
True.
A graph of $\log T$ against $\log r$ for the planets in the Solar System is a straight line.
Sketch the graph of $\log T$ against $\log r$ and label the position of Earth.
The graph of $\log T$ against $\log r$ is a straight line. Earth is at (1, 1) as the orbital period is in years and the orbital radius is in astronomical units (AU)

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