21 Gravitational Fields Flashcards
what is the strength of a gravitational field, g?
the force per unit mass on a small test mass placed in the field
what is the formula for g?
g = F/m
what else is g?
the acceleration of a freely falling object
what is a radial field?
a field in which the field lines are straight and converge or diverge as if from a single point
what is a uniform field?
a region where the field strength is the same in magnitude and direction at every point in the field
what is the gravitational potential energy?
the energy of an object due to its position
what is gravitational potential, V?
the work done per unit mass to move a small object from infinity to that point
what is the formula for V?
V = W/m
what is an equipotential?
a surface with a constant gravitational potential
what is a potential gradient?
the change in the potential per metre at a point
what is the formula for change of potential(potential gradient)?
potential gradient = ΔV/Δr (Δr = small distance
what is gravitational field strength equal to?
negative of the potential gradient
g = -ΔV/Δr
what is Kepler’s 3rd law?
r³ ∝ T²
r = average radius of orbit
T = time period for orbit
what is Newton’s law of gravitation?
the gravitational force F between two point masses m₁ and m₂ at a distance r apart is given by:
F = Gm₁m₂ / r²
what is G?
the universal constant of gravitation
what is a formula for g using Newton’s law of gravitation?
g = GM / r²
how does g vary with distance from the centre of a spherical planet?
follows the inverse square law
what is escape velocity?
the minimum velocity an object must be given to escape from the planet when projected vertically from the surface
how do you derive the escape velocity formula?
- substitute V = -GM/r into W = mV
- equate Eₖ = 1/2(mv²) to W = mV
- Rearrange to make v the subject
what is a formula for gravitational potential?
V = - GM/r
How can you prove Kepler’s third law by using Newton’s law of gravitation?
- g = GM/r² and g = v²/r (centripetal acceleration)
- equate these and v² = GM/r
- v = 2𝜋r / T
- so, (2𝜋r)² / T² = GM / r
- rearrange, r³/T² = GM/4𝜋²
what are geostationary satellites?
orbits the earth directly above the equator and has a time period of exactly 24 hours.
This means it remains in a fixed position above the equator
what is the total energy of a satellite?
E = gravitational potential energy + kinetic energy
