AQA Physics Gravitational Fields

What is a gravitational field?

A region in which an object that has mass experiences a force.

What is the strength of a gravitational field?

the force per unit mass on a small test mass placed in the field.

Why does the test mass need to be small?

otherwise it might pull on the other object so much that it changes its position and alters the field strength

If an object is only acted on by a gravitational force, what is its acceleration?

g

When is an object in free fall?

when the only force acting on an object is gravity (it is unsupported)

What is the unit for gravitational field strength?

Nkg^-1

What is a radial field?

A field in which the field lines are all directed towards a single point.

What is a uniform field?

where the gravitational field strength is the same magnitude and direction throughout the field and field lines are parallel to one another and equally spaced

When does g decrease in a radial field?

as it gets further away from the massive body

What is gravitational potential energy?

the energy of an object due to its position in a gravitational field

What is the position for zero gravitational potential energy?

infinity

What is gravitational potential?

the gpe per unit mass or the work done per unit mass to move a small object from infinity to that point

What is the equation for work needed to be don for object to escape completely?

V=W/m where V= gravitational potential (values are always negative)

What is the unit for V?

Jkg^-1

What is the value of g at the earth's surface?

9.81 Nkg^-1

What are equipotentials?

surfaces of a constant potential

What are equipotential lines?

lines on which an object at any point would have the same gravitational potential

What are equipotential lines perpendicular to?

the lines of force (field lines).

What is a potential gradient?

the rate of change of potential with distance

What is the equation for the potential gradient for a change of potential v?

change in v/ change in r

What is Kepler's first law?

the orbits of the planets are ellipses with the sun at one focus of the ellipse

What is Kepler's second law?

the line joining a planet and the sun sweeps out equal areas in equal intervals of time as the planet travels around the ellipse

What is Kepler's third law?

the ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semimajor axes

What is a constant for all the planets?

r^3/t^2

What does Newton's law of gravitation assume about the gravitational force between 2 point objects?

it's always attractive, it's proportional to the products of the masses, and it's inversely proportional to the square of seperation

What is G?

the universal Gravitational constant 6.67 x 10^-11

How does g vary with R?

g decreases in inverse proportion to r^2

For an object of small mass in a circular orbit around the earth, what is the centripetal force supplied by?

the gravitational force

What is escape velocity?

the minimum velocity an object must be given to escape from a planet when projected vertically from the surface

What is the equation for an object's escape velocity?

V = root(2MG/R)

What is a Schwarzschild radius?

the radius of a sphere such that if all the mass of an object were to be compressed within that sphere the escape velocity from the surface of the sphere would equal the speed of light

What does the area under curve of g against r show?

the work done needed to move 1kg from R to infinity

What is the equation for gravitational potential energy?

-GMm/R

What is a satellite?

any object in orbit around a planet

What is a geostationary satellite?

stays in the same spot of earth

What is a polar satellite?

low orbit, quick orbit time and stronger pull of gravity so its going quicker

How do you find geosynchronous orbit?

r^3/T^2 = GM/4pi^2

What is the equation for energy of an orbiting satellite?

E = -GMm/2r

What are the uses of polar orbits?

spy satellites, imagery, weather monitoring satellites

What are the uses of geostationary orbits?

communications and satellite television

How much work is done on a test mass that moves along an equipotential?

None. No work is done as Gravitational/Electrical potential along the equipotential is equal, so there is no Gravitational/Electrical potential difference.

State Newton's law of gravitation

The gravitational attraction between two objects is proportional to the product of their masses and inversely proportional to the sqaure of the distance between their centres of mass.

What is the difference between centre of mass and gravity

Centre of mass is the point where mass is equally distributed and does not depend on a gravitational field.
Centre of gravity is where the distribution of weight is equal in all directions and does depend on gravitational field.

Over a small horizontal region on the surface of the earth, state why at a point the lines begin to curve.

The gravitational field strength at that point is greater due to the floor of that area having a greater density.

A ball moving at uniform speed passes a position with equal field lines and meets a point with a higher gravitational field strength then goes past it. Describe the affect on the object's velocity as it approaches the point with higher Gravitational field.

Speed is constant as there is no resultant force in the horizontal, but as it reaches the point of greater then it would accelerate towards K due to experiencing a Resultant Force towards the earth.

The area under a Force and Seperation graph represents?

The work done.

What is Kepler's third law?

Kepler's third law states that a planet's orbital period, p, is related to its average (semimajor axis) orbital distance, a, according to the mathematical relationship Time period squared=distance cubed.

What is a test mass attracted to?

A gravitating body.

How do you find the total gravitational force acting on an object between 2 bodies?

Force(1)-Force(2)= The force of gravity on the intermediatory object from 1 body - the force of gravity on the intermediate object from the other body. (You take them away because the forces are acting in seperate directions.)

What is constant in a uniform field?

Gravitational field strength

How do you find the total gravitational field strength acting on an object between 2 bodies?

g(1)-g(2)= The gravitational field strength on the intermediatory object from 1 body - the gravitational field strength on the intermediate object from the other body. (You take them away because the fields are acting in seperate directions.)

Define a test mass and gravitating body?

A gravitating body is any object/mass which creates a gravitational field.

A test mass is an object that experiences a gravitational force towards the gravitational body.

what can you tell me about the relationship of force and gravitational field strength vs separation?

Both of these have the same relationship with separation, being directly proportional to 1/r².

What experiment could you use to determine the gravitational field strength close to the surface of the earth?

The gravitational field strength ggg can be calculated using a simple pendulum.

Apparatus:

• String (non-elastic)

• Small mass (bob)

• Meter stick

• Stopwatch

• Stand and clamp

Procedure:

1. Attach a small mass (the pendulum bob) to a string of known length LLL.

2. Displace the pendulum by a small angle (less than 15° to approximate simple harmonic motion).

3. Measure the time TTT it takes for the pendulum to complete multiple oscillations (e.g., 10 oscillations).

4. Calculate the period TTT by dividing the total time by the number of oscillations.

5. Use the formula for the period of a pendulum:

T=2πLgT = 2\pi \sqrt{\frac{L}{g}}T=2πgL​​

6. Rearrange the formula to solve for the gravitational field strength ggg:

g=4π2LT2g = \frac{4\pi^2 L}{T^2}g=T24π2L​

7. Repeat the experiment several times and take the average value of g.