5.4 Gravitational Fields Flashcards
what is a gravitational field?
a gravitational field is the region around a body in which other bodies will feel a force due to the mass of the body
what do gravitational field lines show?
the shape and direction of the field line at a point is the direction in which a small mass would move when placed at that point
what is gravitational field strength defined as?
the gravitational field strength at any point in a gravitational field is the force acting per unit mass at that point, g = F / m (units are NKg^-1)
how do gravitational field lines act around a spherical mass?
they act radially inwards, towards the centre because spherical objects can be modelled as a point mass at its centre
what are gravitational field caused by?
they occur because objects have mass, the more mass that body has, the more that it will attract the smaller masses around it
what happens to the field lines of Earth as you get closer and closer to the surface of the Earth?
the gravitational field lines become uniform and straight, the lines converge to become almost parallel, the radial field becomes apparent the further we move away from the Earth and observe it from space
state Newton’s law of gravitation?
Newton’s law of gravitation states that the gravitational force of attraction between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation
what is the equation for Newton’s law of gravitation?
F = - GMm / r^2
where M and m are the masses of the two bodies and r is the separation of their centres
(the minus shows it is an attractive force)
what is G?
the universal gravitational constant, 6.67 x 10^-11
what law does Newton’s law of gravitation follow in terms of force? (think of intensity)
follows an inverse square law, forces gets smaller with distance because the strength changes
a spherical mass is often assumed to be what?
a point mass with all its mass concentrated at the centre
what is the other equation for gravitational field strength for a point mass and how can you get to it?
first g = F / m
F = - GMm / r^2, equate Fs
leading to g = - GMm / mr^2, cancel little m
leading to g = - GM / r^2
what is gravitational field strength equal to on earth?
g = 9.81 ms^-2 (acceleration due to freefall)
what are Kepler’s free laws of planetary motion?
- planets travel around the sun in elliptical orbits
- a line joining the Sun to a planet will sweep out equal areas in equal times
- the time period of the orbit squared is proportional to the mean radius of the orbit cubed, or T^2 ∝ r^3
what is Kepler’s third law?
kepler’s third law states that the square of the period of a planet orbiting the Sun is proportional to the mean radius of its orbit cubed (his law also applies to other planetary stems, to the orbits of moons around planets and to binary stars)
what is a geostationary orbit?
a geostationary orbit is an orbit of the Earth made by a satellite that has the same time period and orbital direction as the rotation of the Earth (i.e 24 hours) and is in the equatorial plane
what are geostationary satellites used for?
- broadcasting TV signals and relating mobile telephone signals
- monitoring the weather and changes in the environment
- monitoring air traffic
what is the equation that relates time period to mean radius (kepler’s third law)?
T^2 = (4π^2 / GM ) x r^3
how do you derive the equation or get to T^2 = (4π^2 / GM ) x r^3 ?
F = - GMm / r^2 equate the gravitational force to centripetal force mrω^2/ r = GMm / r^ substituting ω = 2π / T gets you to... T^2 = (4π^2 / GM ) x r^3
what is gravitational potential?
gravitational potential at a point in a gravitational field is defined a the work done in moving unit mass from infinity (where the gravitational potential is zero) to that point
what is gravitational potential energy?
the gravitational potential energy, E, of a body in a gravitational field is the work/energy required to move a body of mass, m, from infinity to that point in the field
what is the equation for gravitational potential?
Vg = - GM / r
at a distance r from a point mass M
what is the equation for gravitational potential energy?
E = mVg (bit like V = E / Q but for mass) E = - GMm / r
what does a force-distance graph for a point or spherical mass look like? (for moving a mass in a radial gravitational field, force varies with position)
curve exponential from negative y axis going up to x axis (x axis is asymptote), the area underneath is equal to the work done to move a mass
what is escape velocity?
the minimum velocity required of an object to escape Earth’s gravitational field and not return to the ground
how can you calculate escape velocity?
equate the initial kinetic energy of the object with the change in gravitational potential energy as it is thrown up,
0.5mv^2 ≥ GMm / r
rearranging vies us v ≥ (2GM / r)^0.5
