12. Gravitational fields Flashcards
What is a gravitational field?
A region where any object with mass experiences a uniform/ radical gravitational force
What are the units of gravity, g?
As F=ma
W=mg
so g=ms^-2
or g=Nkg^-1
What’s Newton’s Law of universal gravitation?
The gravitational force, F(G) between 2 masses of any size
The further the masses are, the weaker the force by area
- so F(G) is inversely proportional to r^2
The higher the masses, the greater the force
- directly proportional to m(1) and m(2)
F(G)=(Gm(1)m(2))/r^2
Where G is a constant
G = 6.67x10^-11 Nm^2kg^-2
What’s the value and units for Newton’s gravitational constant, G?
G = 6.67x10^-11 Nm^2kg^-2
As you re-arrange the units of Newton’s Law of universal gravitation
What is gravitational potential, V?
The amount of gravitational potential energy possessed per unit mass at that point/ distance from planet
V=Jkg^-1
Why is the value of gravitational potential, V negative?
The value of gravitational potential,
V is negative because gravitational potential energy is defined as zero at an infinite distance from a mass (where no gravitational force acts). As an object moves closer to the mass, it loses potential energy, and this energy becomes increasingly negative. This reflects the fact that work must be done to move an object out of a gravitational field and escape the pull of the mass.
What’s the equation for gravitational potential, V?
V = -GM/r
What is the gravitational field due to a point mass, g?
g refers from the centre of big mass, M, which is the point mass
It doesn’t need to know m, as this is just the field strength, not the force, F
It’s the region where another object experiences a force due to the gravitational attraction of the mass.
g=GM/r^2
What is orbital motion?
When planets orbit the sun, or satellites orbit Earth, the gravitational force, F(G) provides a centripetal force to keep them in orbit.
F(G) = F(centripetal)
GMm/r^2 = GM/r
v^2 = GM/r
So it doesn’t matter on the weight of the object orbiting the planet, they will orbit at the same speed
Why do the orbiting objects have centripetal acceleration?
Centripetal force changes the direction of the object’s velocity, causing it to move in a circular or elliptical path rather than a straight line.
a(c) = v^2/r
What is the orbital time period,
T?
The orbital time period,
T, is the time taken for an object to complete one full orbit/ the circumference, 2πr
What’s the linear speed of the objects in orbit?
As v=s/t
v=2πr/T
How can we link the time period, T to r within orbital motion?
v^2=(2πr/T)^2
so…
(2πr/T)^2=GM/r
so…
T^2=(4π^2r^3)/GM
Therefore
T^2 ∝ r^3
What are the similarities between electric fields and gravitational fields?
Both fields follow an inverse square law for point sources
Objects in both fields have potential energy due to their position in the field
Both are force fields that influence objects within their range
Both have equipotential surfaces
What are the differences between electric fields and gravitational fields?
Gravitational always attracts, but electric can be attractive or repulsive
Gravitational is created by mass, electric is created by charge
Gravitational is much weaker, Electric is much stronger for fundamental particles
What is an equipotential surface?
Where every point has the same gravitational/ electric potential
These are displayed by equipotential lines
No work is required to move a charge anywhere on this surface because the potential difference is zero between any two points.
