IB PHYSICS GRAVITATIONAL FIELDS

FIRST KEPLER LAW

Describes the motion of planets in their orbits around the sun, stating that planets move in elliptical paths with the sun at one focus, and the line connecting a planet to the sun sweeps out equal areas in equal times.

SECOND KEPLER LAW

States that a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time, indicating that a planet's speed varies depending on its distance from the sun. This law implies that planets move faster when they are closer to the sun and slower when they are farther away.

THIRD KEPLER LAW

Relates the square of the orbital period of a planet to the cube of the semi-major axis of its orbit, showing that the ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun.

GRAVITATION LAW

A fundamental principle that describes the attraction between two masses, stating that every point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

GRAVITATIONAL FIELD

A region around a mass where another mass experiences a force of attraction, defined by the gravitational force per unit mass. g = F/m

DENSITY

The mass per unit volume of a substance, often expressed in kilograms per cubic meter (kg/m³). It indicates how much matter is packed into a given space. D=MASS/VOLUME

GRAVITATIONAL FIELDS REPRESENTATION

. GRAVITATIONAL FIELDS ARE ALWAYS ATTRACTIVE

. LINES POINTING TO THE OBJECT

. HIGHER NUMBER OF LINES SHOWS HIGHER ELECTRICAL FIELD strength. The density of the lines indicates the strength of the gravitational field, with closer lines representing stronger fields.

GRAVITATIONAL POTENTIAL

. The work done per unit mass to move an object from a reference point to a point in the gravitational field, usually measured in joules per kilogram (J/kg). It represents the potential energy per unit mass at a point in the field.

Gravitational potential is always negative because

. it is defined relative to a point at infinity where the potential is zero.

. since gravitational interactions are attractive, work must be done against the gravitational force to move an object away from a mass.

Gravitational potential becomes less negative (increases) when

we move away from a mass . Work has to be done against the gravitational force to move the mass away from the planet

Gravitational potential equation

• The equation for gravitational potential V is defined by the mass M and distance r:

Vg = -GM/r

Work done on a Mass

∆W = m∆Vg Work done on a Mass is the change on potential energy

GPE Equation

Ep = - GMm / r

Gravitational force vs distance graph

Area under the force-distance graph of a gravitationa field is the work done or Energy transferred. Area= Work done = m ∆V

Gravitational field and potential relationship

TThe gravitational field at a particular point is equal to the negative gradient of a potential-distance graph at that point

g = -∆Vg / ∆r. or g = -dV/dr

Gravitational potential lines are

. Perpendicular to the gravitational field lines

An object travelling around an equipotential line

doesn’t loose or lose energy. Work done is zero

Escape Speed

The minimum speed that will allow an object to escape a gravitational field with no further energy input

Escape Speed

It is the same for all masses i the same gravitational field (in example, without friction, escape speed of a rocket and a tennis ball ins the same)

Escape speed is

• the speed at which all its kinetic energy has been transferred to gravitational potential energy

• This is calculated by equating the equations:

Escape speed is calculating as

Orbital Motion

ENERGY OF AND ORBITING SATELLITE

it has both kinetic energy (E_k) and gravitational potential energy (E_p) and its total energy is always constant

Total energy = Kinetic energy + Gravitational potential energy

EFFECTS OF DRAG ON ORBITAL MOTION

satellites travelling through these thin layers of air will experience a small dissipation of kinetic energy into thermal energy

• This heating is due to the friction between the air particles and the surface of the satellite

• the satellite's total energy is reduced

  • When a satellite loses energy, its orbital radius decreases

  • However, as the satellite's orbit becomes lower, some of its potential energy is transferred to kinetic energy