5.4 Gravitational Flashcards
What causes gravitational fields
Objects having mass
How a spherical mass can be modelled
As a point mass
How do gravitational field lines work
They point in the direction that a mass would move and the closer together they are the stronger the field
Gravitational field strength
The force in newtons per unit mass
Equation for gravitational field strength in terms of forces (g=)
g=F/m
How are gravitational fields related to electric fields
They are both a form of a field giving rise to a force
What is the force between two masses proportional to
The product of the masses
The inverse square of the separation
Equation for gravitational field strength in terms of distance
g = -GM/r^2
Why do we not have to consider changing gravitational field strength when considering problems on earths surface
The change in distance is so small that the field can be considered uniform at the surface (this also applies to direction since we can consider the surface flat)
Relation between acceleration of free fall and gravitational field strength
They have the same numerical value (9.81) but are different things with different units
Keplers first law
Planets move around the Sun in an ellipse, with the Sun at one focus of the ellipse
Keplers second law
A line joining the Sun to a planet will sweep out equal areas in equal times
Keplers third law
T^2 ∝ r^3
where T is the period and r is the mean distance
How centripetal force relates to gravity
The centripetal force on a planet is provided by the gravitational force between it and the Sun
How to derive the constant for keplers third law
Equation centripetal force to the gravitational force
Geostationary Orbit
An orbit directly over the equator with the same angular speed as the Earths rotation, causing it to always be in the same place in the sky relative to the Earth
Period of a geostationary orbit
1 day
Uses of geostationary orbits
Telecommunications. A satellite dish can be pointed at a geostationary satellite and can remain stationary because the satellite is stationary relative to the Earth
How to calculate the orbital radius of a geostationary satellite
Keplers third law with the constant
Gravitational potential at a point
The work done to bring a unit mass from infinity to that point
Gravitational potential at infinity
0
How to calculate the energy required to move an object over a gravitational potential difference
W=mΔV
where V is the gravitational potential
What a force-distance graph for gravitational force from a sphere mass looks like
1/x
x > r where r is the radius of the sphere
Area under a force-distance graph
Work done to move the object between the two points
What is gravitational potential energy (over large distances) proportional to
Product of the masses
inverse of the distance
Escape velocity
Minimum velocity required to escape a gravitational field i.e. the kinetic energy of the object is equal to the magnitude of its gravitational potential energy
How to calculate escape velocity
KE=GPE
How gravity relates to atmospheric thickness
The more massive a planet is the more kinetic energy will be needed to overcome its gravitational energy and therefore a higher escape velocity will be required, making it less likely that a particle will reach this velocity and escape. Therefore more massive planets have thicker atmospheres.
