C18 Gravitational Field Flashcards
Poop
Define gravitational field strength g at a point within a gravitational field
The gravitational force exerted per unit mass on a small object placed at that point within the field.
Formula for gravitational field strength using mass and force
g = F / m
F = gravitational force
m = mass of object in the field
Uniform gravitational field
Field lines will be parallel and equidistant, perpendicular to the surface and the field strength does not change.
Newton’s Law Of Gravitation
The force between two point masses is:
- Directly proportional to the product of the masses, F ∝ Mm.
- Inversely proportional to the square of their separation, F ∝ 1/r^2.
Equation for Newton’s law of gravitation, calculating force of attraction
F = - [ GMm / r^2 ]
Universal Gravitational Constant, G
6.67 x 10^-11
Relationship between the attractive force, F and distance between objects, r
F ∝ 1/r^2
If r x2, force x1/4.
Mass of the Sun
1.99 x 10^30 kg
Mass of the Earth
5.97 x 10^24 kg
Formula for calculating the gravitational field strength, g
g = - [ GM / r^2 ]
Kepler’s First Law
The orbit of a planet is an ellipse with the Sun at one of the two foci.
What is the ‘eccentricity’ of an orbit?
- A measure of how elongated the circle is.
- So an orbit with a low eccentricity is almost a circle.
Kepler’s Second Law
A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
Kepler’s Third Law
The square of the orbital period T of a planet is directly proportional to the cube of its average distance r from the sun. T^2 ∝ r^3
Relationship for Kepler’s Third Law including a constant
T^2 / r^3 = K
They are directly proportional, K is a constant.
Astronomical Unit
Defined as the mean distance between the Earth and the Sun.
Formula relating centripetal force on planet and gravitational force acting on a planet
mv^2 / r = GMm / r^2
How to calculate the orbital speed of a planet in orbit
Dividing the circumference of its orbit by its orbital period, 2πr / T
Mathematical version of Kepler’s third law
T^2 = (4π^2 / GM) r^3
What is the gradient of a graph of T^2 against R^3?
4π^2 / GM
Deriving Kepler’s Third Law
start with:
mv^2 / r = GMm / r^2
substitute v = 2πr / T
rest you can do in the exam:
4π^2r^2 / T^2 = GM / r
T^2 = (4π^2 / GM) r^3
Formula for orbital speed v, given M and r (not given)
v = √ (GM / r)
Different industries modern satellites are used in
Communications, military uses, scientific research, weather and climate, global positioning.
Requirements for a satellite to be geostationary
- Be in orbit above the Earth’s equator.
- Rotate in the same direction as the Earth’s rotation.
- Have an orbital period of 24 hours.
Why are polar satellites useful for mapping/reconnaissance?
The Earth rotates beneath their path, so after a number of orbits they can map all parts of the globe.
Define Natural Satellite
Celestial bodies that orbit around a planet or another larger body.
Define Artificial Satellite
Human-made objects that are intentionally placed into orbit around Earth or other celestial bodies.
Define Gravitational Potential
The work done per unit mass to move an object to that point from infinity.
Formula for gravitational potential, Vg
Vg = - [ GM / r ]
Graph of Vg against 1/r
A straight line through the origin, with gradient, -GM
How do changes in gravitational potential work
- Moving toward a point mass will decrease it, e.g. from -40 MJ kg to -70MJ kg
- Moving away from a point mass will increase it, e.g. from -30 MJ kg to -20MJ kg
Define gravitational potential energy
The work done to move a mass from infinity to a point in a gravitational field.
Formulas for GPE related to Vg, M, r
E = mVg
E = - [ GMm / r ]
Define escape velocity
The lowest velocity which a body must have in order to escape the gravitational attraction of a particular planet or other object.
Formula for escape velocity
v^2 = 2GM / r
NEW CARDS FROM HERE ONWARD XDDDDDDDDDDDDDDD
What are the units used in Kepler’s Third Law?
T² / R^3 = K
T = time period in years
R = distance in AU
How do you derive the formula for escape velocity?
GPE must equal KE.
