Gravitational

A student was asked to find the resultant gravitational field at a point some distance from two objects. How should they go about doing this?

1. Calculate the gravitational field strength due to each object at the point.

2. Draw both field strength vectors pointing towards their respective masses.

3. Find the resultant by adding the vectors, taking their directions into account.

Give the similarities between gravitational and electric fields

Both can be represented with field lines

Both have equipotential surfaces

Both have potentials as a concept

Both have inverse-square laws

Give the major difference between electric and gravitational fields

Electric fields can attract and repel

Gravitational fields only attract

Uniform fields actually exist for electric fields, but are an assumption near the surface of a radial field only in gravitational fields

Why is potential negative?

Potential is defined as zero at infinity.

Positive work must be done against gravity to move an object from a finite distance to infinity.

Therefore, an object at a finite distance has less gravitational potential energy than it would have at infinity.

Thus, its gravitational potential is negative.

Sketch the graph of g against r

Sketch the graph of V against r

How can you use graphs to determine g?

Plot V against r

The gradient = -g

negate the gradient for g

Derive Kepler’s third law

F_c = F_g

mv²/r = Gm₁m₂ / r²

cancel m

write v as 2 pi r / T

rearrange for : T² = k r³

where k = 4 pi squared / GM

Derive E_k , E_p , and E_T for an orbiting satellite.

Why is the total energy negative?

E_k = ½ m v²

GMm / r² = mv² / r

v² = GM/r

E_k = GMm / 2r

W = m delta V

E_p = -GMm / r

E_T = E_k + E_p

E_T = -GMm / 2r

The magnitude of kinetic energy is half the magnitude of gravitational potential energy, GPE is negative, Hence total energy must be negative

Define escape velocity

The minimum speed needed to escape the gravitational field of a body without further propulsion

Derive escape velocity

KE and GPE = 0 at infinity because escape velocity is a minimum and potential is 0 at infinity

Thus total energy (Which is constant due to conservation of energy) is 0

Hence ½ m v_e² = GMm / r

v_e = sqr 2GM / r

Define Synchronous orbit

The orbital period = rotational period of the body its orbiting

Define Geostationary orbit and give the requirements

A special case of a synchronous orbit in which the satellite appears stationary above the same point on Earth’s surface.

Orbit in the plane of Earth’s equator

Travel in the same direction as Earth’s rotation

Have an orbital period equal to Earth’s rotational period

Be in circular orbit

How could you find the geostationary radius?

Set F_g = m omega² r

rearrange for r

Give some uses of low orbit and geostationary satellites and pros of each

low Earth orbit: ISS , Imaging + observation

cheaper to launch, clearer images

Geostationary: satellite tv, communications, weather monitoring of the same location

monitor same region + a larger region

Derive orbital velocity

F_c = F_g

mv²/r = Gm₁m₂ / r²

cancel m

multiply through by r

v = sqr GM/r

A ball is moving from point J to point K. The field lines are denser at point K.

What happens to the ball’s acceleration and why?

Increases

Denser field lines = stronger field = more negative potential

More negative potential means GPE decreases so KE increases