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
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
