Topic D.1 Gravitational Fields

Kepler’s 1st Law

Each planet orbits the sun along an elliptical path. The sun is located at one of the foci of the elliptical path.

Kepler’s 2nd Law

For a given time, the area swept out by the line representing distance between a planet orbiting the sun and the sun (the “radius”) is constant. Equal areas in equal times.

Kepler’s 3rd Law

(T_1/T_2)² alpha (r_1/r_2)³. The square of a point mass’s orbital period (T) is directly proportional to the cube of the average distance between the point mass and the point mass it is orbiting, which is represented as r.

Gravitational Field

A region in space where mass experiences a gravitational force.

Newton’s General Law of Gravitation

The attraction between ant two point masses is directly proportionate to the product of their masses and inversely proportional to the square of the distance between them (R). Represented as F_g= (GMm)/r², where G is a constant.

Gravitational potential

The work done to bring a unit mass from infinity to the point concerned. V_g= -G(M/r). GP can never be positive because the gravitational force is always attractive. It is the E_p per mass.

Gravitational potential units

J kg^-1

Gradient/derivative of potential vs. distance graph (V vs. r)

gravitational field strength, g.

Integral of F_g from infinity to r

Gravitational potential energy (E_p). E_p=-G(Mm/r), which divided by m gives us V_g= -G(M/r).

Equipotential surface/line

A line/surface that connects places which have the same potential. It takes 0 work to move along the same equipotential line, but it takes work to move across them. Equipotential lines are always perpendicular to field lines.

Gravitational field lines

Perpendicular to equipotential lines. They point from a higher potential to a lower potential (g).

Escape velocity

The minimum speed required by a mass to escape the gravitational field of a planet. When KE+PE=0, or when E_P_i + KE_i = E_p_f + KE_f. v_(esc) = sqrt((2GM)/r).

Gravitational potential energy

Work done to bring together the components of a system from infinite separation.

Gravitational field strength

“g.” Gravitational potential (V_g) gradient/derivative as given by g= -(ΔV_g)/(Δr). Force per unit point mass.

Work done in moving a mass in a gravitational field

W= m ΔV , aka E_p = -G (Mm)/r