Gravitational Field (DONE) Flashcards
Gravitational field equation
g=f/m
Gravitational field units
Nkg^-1
What is a field
A region where an object experiences a force
What other units can a gravitational field have?
Ms^-2 (acceleration due to gravity)
What kind of quantity is a gravitational field?
- vector quantity
How to draw radial gravitational field diagram
- straight lines towards centre of mass
- with arrows (towards centre of mass)
Types of gravitational field
- radial (drawn from centre point, the field is stronger nearer the centre of mass)
- uniform (field lines are parallel, even field strength throughout field)
Where are gravitational fields found
- around any object with a mass
How do gravitational fields of different objects interact in space
- attractive forces would eventually pull objects together
What is the relationship between the size of attractive force and mass
Force is directly proportional to mass
What does Newton’s third law show when talking about the attractive forces of 2 objects
- the attractive force of object A on object B, is equal to the force of object B on object A.
What is the relationship between attractive force and distance between 2 centre of masses?
F is directly proportional to 1/(r^2)
- meaning if r (distance between centre of masses) doubles the force will quarter.
By bringing all 3 gravitational field equations together, what is newtons law of gravitation?
F is directly proportional to Mm/(r^2)
Therefore:
F = -GMm/(r^2)
What s the value of constant G?
6.67 x 10^-11
What are the units of the constant G?
Nm^2kg^-2
Why is the force of a gravitational field negative?
- because the force is attractive towards centre of mass
What is newtons law of gravitation
F=-GMm/(r^2)
Summarise newtons law of gravitation
- the force between 2 objects is proportional to the product of the masses and inversely proportional to their separation squared.
What is the equation for gravitational field strength
g=-GM/(r^2)
How do you derive the equation for gravitational field strength
1. Sub F=-GMm/(r^2) into g=f/m Therefore: g=-GMm/(r^2)m 2. Cancel terms So: g= -Gm/(r^2)
gravitational field strengths relationship with mass is…
Directly proportional to mass
What is gravitational field strengths relationship with radius
g is inversely proportional to r
G is proportional to 1/(r^2)
How can gravitational field strength and radius be represented on a graph
r on x axis
g on y axis
- from r0 1/(r^2) relationship, line never touches x axis but gets closer and closer
- linear relationship from surface of mass towards centre of mass, gravitational field strength is zero at centre of mass
What is the gravitational field strength at the centre of mass
Zero
Summary of escape velocity
- the speed needed to escape the gravitational pull of a mass
When talking about the escape velocity, what is the equation for the potential energy
Ep= GMm/r
How do you derive the equation for escape velocity
*provided the kinetic energy exceeds potential energy
Ek (kinetic energy) = Ep (potential energy)
(1/2)mv^2 = GMm/r
1. Cancel m’s from equation
2. V= root(2GM/r)
What is keplers first law
- the orbit of a planet is an ellipse with the sun at one of two foci
What is a foci
- the 2 centre points that form an ellipse
When talking about keplers first law what does the distance from 2 foci to the same point on an ellipse equal?
The distance from a to point x and b to point x equals a constant for any point on an ellipse
a + b = constant
What is keplers 2nd law?
- a line segment joining a planet and the sun sweeps out an equal area during equal time intervals.
What is keplers 3rd law?
- the square of the orbital period T, is directly proportional to the cube of the average distance from the sun r.
Therefore:
T^2 proportional to r^3
What is the force causing a planet to move in a circular path?
- centripetal force
What is the equation for the centripetal force?
F=mv^2/r
Prove that T squared is proportional to r cubed
- Use equations F=-GMm/(r^2) and F=mv^2/r
- Substitute
- Simplify to GM/r = v^2
- Use S=D/T to find v=2(pie)r/T for a planet
- Substitute v into equation (3)
- Rearrange to find T^2= [4(pie^2)/GM]r^3
- Therefore T squared is proportional to r cubed
How is the centripetal force provided
- centripetal force is provided by the gravitational pull
What does it mean when a satellite has a low earth orbit?
- the value of r is very small (close to earths surface)
- some rotate at 90 degrees to earths rotation (from north to south poles)
- used for:
Communications
Military
Weather
Gps
What effect does a low value of r have on a satellite?
- low value of r leads to high value of v
v=root(GM/r)
What is a geostationary satellite?
- satellites which orbit above equator with a time period of 24 hours equal to the speed of the earths rotation
- occupy fixed portion of land
- good for communications
