Gravitational Fields Flashcards
What is a Gravitational Field?
A region in which a mass, experiences an attractive non-contact force.
What is gravitational Potential?
The amount of work done per unit mass, to move an object from infinitely far away to that point (r).
What is Newton’s law of Gravitation?
The force of gravity is proportional to the product of the masses involved and inversely proportional to the square of the separation of the masses.
What is Gravitational Field strength defined as?
g = F/m, where F is the gravitational force and m is the mass of the object.
What equation is used to find the acceleration due to gravity?
g=GM/r², where G is the gravitational constant, M is the mass of a planet and r is the radius of the planet.
What is the equation for the force of gravity in Newton’s law of Gravitation?
F = GMm/r², where ‘M’ is the mass of the planet and ‘m’ is the mass of the object.
Derive ρ
ρ = M/V (V = 4/3πr³)
ρ = 3M/4πr³
M = ρ4πr³/3 (g = GM/r²)
g = Gρ4πr³/3r²
g = Gρ4πr/3
g = Kr (K is some constant)
∴ g ∝ r
What is the equation for gravitational potential at a distance ‘r’ from a planet or mass?
V = -GM/r
What is the equation for gravitational potential in a radial field?
Ep = GMm/r
What does the gradient for a ‘V’ (J/kg) over ‘r’ (m) graph give?
g, where g = -Gm/r²
What is an equipotential?
A surface of constant gravitational potential, that is perpendicular to the radial field lines.
What is a satellite?
Any smaller mass in the orbit of a bigger one.
What are the three laws of planetary motion?
- The orbit of every planet is an ellipse (meaning circular motion laws still apply)
- A planet sweeps out of the same area between equal time intervals
3.T² ∝ r³
Derive orbital velocity ‘V’
Fc = Fg (Centripetal force = Gravitational force)
MV² /r = GMm/r²
V² = GMm/Mr
V² = Gm/r
V = √Gm/r
