7: Gravitational Field Flashcards
Newton’s Law of Gravitation
The force of attraction between any two point masses is directly proportional to the product of their masses and inversely proportional to the square of their distance apart.
Gravitational force, F formula
F = Gm₁m₂ / r²
Kepler’s Third Law
The square of the orbital period of a planet is directly proportional to the cube of its average distance from the Sun.
Kepler’s Third Law equation
T² ∝ r³
Binary stars
- have same _____ but may not have same ________.
A system consisting of 2 stars orbiting around their common centre of mass (may be empty).
- have same angular velocity (ω), but may not have same orbital radius (r)
Geostationary satellites
- 4 points
Satellites that appear to be fixed over one spot above the equator.
- There’s only ONE such orbit around the Earth.
- Orbital period = 24 hours
- Both satellite and Earth must be rotating in SAME DIRECTION
- It is ABOVE the equator
Gravitational field strength, g
Gravitational field strength at a point is defined as the gravitational force per unit mass acting on a small mass placed at that point.
Gravitational field strength, g formula
2 types
- g = F / m
* g = Gm₁ / r²
Gravitational potential energy, U
The gravitational potential energy of a mass at a point is defined as the work done by an external agent in bringing the mass from infinity to that point.
Gravitational potential energy, U formula
U = - Gm₁m₂ / r
Gravitational potential, φ
Gravitational potential at a point is defined as the work done per unit mass by an external agent in bringing a mass from infinity to that point.
Gravitational potential, φ formula
φ = - U / m
R/s between gravitational potential (φ) and gravitational field (g)
g = gφ / dr
R/s between gravitational potential (φ) and gravitational potential energy (U)
▵U = m ▵φ
R/s between gravitational potential (φ) and gravitational potential energy (U)
▵U = m ▵φ
