Gravitational Fields Flashcards
What is a gravitational field?
A gravitational field is a region of space where an object with mass experiences a force
Define gravitational field strength
At any point in a gravitational field the gravitational field strength is equal to the force per unit mass exerted on a particle at that point in the field
g = F/m
What does a line of force show?
The path taken by a mass released in the field
What does an equipotential do?
Joins up regions of the same potential
Where can you find uniform gravitational fields?
A uniform field may exist in a small region of space, close to a large mass, where the field lines may be considered to be uniform, parallel and equidistant
Where can you find a radial gravitational field?
In the region around an isolated mass the field lines are considered radial. The field lines would be drawn radially, with arrows pointing in towards the centre of mass
State Newton’s law of universal gravitation
“Every particle of matter in the universe attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of their distances apart”
State the equation for Newton’s law of universal gravitation
F = -GMm/r²
where G is a universal constant
What is the value of G?
6.67x10^-11
What does the minus sign in Newton’s law of universal gravitation show?
The minus sign shows that the force is attractive
What is the equation for gravitational field strength for a point mass?
g = -GM/r²
State the characteristics of g close to Earth
gravitational field strength is uniform close to the surface of the Earth and numerically equal to the acceleration of free fall
How is a satellite kept in orbit around a planet?
Gravity provides a centripetal force
Derive an equation for the speed of a satellite in orbit
F = GMm/r²
and F = mv²/r
So GMm/r² = mv²/r
GM/r² = v²/r
GM/r = v²
v = √(GM/r)
What provides the centripetal force on a planet?
The centripetal force on a planet is provided by the gravitational force between it and the Sun
State Kepler’s first law
Each planet moves in an elliptical orbit with the Sun at one focus
State Kepler’s second law
A line drawn from the Sun to a planet sweeps out equal areas in equal times
State Kepler’s third law
The square of the period, T, of a planet is directly proportional to the cube of its average distance, r, from the Sun
T² ∝ r³
Derive an equation for period squared (T²)
v² = GM/r
and v = circumference of sphere/period
v = 2πr/T
So GM/r = (2πr)²/T²
GM/r = 4π²r²/T²
GMT²/r = 4π²r²
T² = 4π²r³/GM
Define a geostationary orbit
A geostationary orbit is one such that the period of rotation is the same as that of the Earth. The satellite will therefore always stay in the same place over the Earth provided it orbits in the plane of the equator and rotates in the same direction as the Earth’s rotation.
How can geostationary satellites be used?
- Sky TV
- communications
- providing information about the Earth
Define gravitational potential in a radial field
Gravitational potential at a point is the work done in bringing unit mass from infinity to that point; a mass at infinity is defined as having zero potential
State the equation for gravitational potential
Vg = -GM/r
where r is measured from the centre of the planet
Define gravitational potential energy
Gravitational potential energy is the work done in bringing a mass from infinity to the point concerned; a mass at infinity is defined as having zero potential energy
State the equation for gravitational potential energy
Ep = mVg and Vg = -GM/r
Therefore Ep = -GMm/r
where r is the distance between the two masses
What is the area under a force/distance graph for a point or spherical mass equal to?
Work done
Define escape velocity of a planet
The escape velocity of a planet is the velocity which a projectile must be given at the surface of the planet so that it will completely escape from the planet’s gravitational field due to its kinetic energy alone
Derive the equation for escape velocity
Ek = 1/2mv²
Ep = -GMm/r
1/2mv² = GMm/r
v = √(2GM/r)
State the two equations for escape velocity
v = √(2GM/r)
v = √(2gr)
