TOPIC 7: GRAVITATIONAL FIELD Flashcards
[Definition] Gravitational Field
A region of space where a mass experiences a gravitational force.
[Definition] Line of force
A line of force in a gravitational field is the direction of the gravitational force acting on a small test mass.
What does the tangent at a point on a gravitational field line represents?
It represents the direction of gravitational force acting on a small test mass placed at that point.
Why is the acceleration of free fall near the Earth’s surface approximately constant?
The lines of force are radial and appear to converge at the centre of Earth
The heights near and above the surface of Earth is so small relative to the Earth’s large radius, so the lines are approximately parallel
The parallel field lines indicate uniform field strength, hence constant acceleration of free fall
[Definition] Newton’s Law of Gravitation
Newton’s law of gravitation states that the gravitational force of attraction between two point masses is directly proportional to the product of the masses and inversely proportional to the square of separation between the masses.
[Formula] Gravitational Force
F = G(m₁m₂/r²)
G = 6.67 x 10⁻¹¹ Nm²kg⁻²
Derivation of useful formula (T² ∝ r³)
Gravitational force by Earth provides centripetal force
Gmₑm₂/r² = m₂rω²
Gmₑ/r² = rω²
Gmₑ/r² = r(2π/T)²
Gmₑ/r² = r(4π/T²)
T² = (4π/Gmₑ) r³
T² ∝ r³
4 Features of a Geostationary Satellite
- Orbit directly above Equator
- Be in circular orbit at a particular radius
- Have a period of 24h
- Rotate from west to east along same axis as Earth’s rotation
[Definition] Gravitational Field Strength
The gravitational field strength at a point in the gravitational field is the gravitational force of attraction per unit mass acting on a small test mass placed at that point in the field.
[Formula] Gravitational Field Strength
g = GM / r²
unit of g = Nkg⁻¹ / ms⁻²
[Definition] Gravitational Potential
The gravitational potential at a point in the gravitational field is the work done per unit mass in bringing a small test mass from inifinity to that point in the field.
[Formula] Gravitational Potential
Ø = - GM/r
Unit: J kg⁻¹ / ms⁻²
Relation between gravitational potential and gravitational field strength
dØ/dr = d/dr(-GM/r) = GM/r² (gravitational field strength)
dØ/dr & g are numerically equal
g is the negative of the potential gradient at that point
[Formula] Gravitational Potential Energy
Eₚ = mØ
When to use the 2 GPE formulas?
Eₚ = mØ & Eₚ = mgh
If object is close to surface of Earth, use mgh
If object is far from Earth e.g. in space, use mØ
