Gravititational Fields Flashcards
Define Newton’s law of gravitation:
The force between two point masses is directly proportional to the product of the masses and inversely proportional to the square of the distance between their centres.
Label F = -GMm/r^2
F = Force of attraction from mass M on mass m (N)
G = Universal gravitational constant
M = Mass of the large body (kg)
m = Mass of small body (kg)
r = Distance from the centres of the large mass to the centre of the small mass (m)
Define gravitational field strength:
Force per unit mass at a point in a gravitational field
Equation for gravitational field strength:
g = F/m
g= Gravitational field strength (Nkg^-1)
F = Force (N)
m = Mass (kg)
How do you determine the gravitational field strength for a radial field?
g = -GM/r^2
g = gravitational field strength (Nkg^-1)
G = Universal gravitational constant
M = Mass of the large body (kg)
r = Distance from the centres of the large mass to the centre of the small mass (m)
What’s Kepler’s 1st Law?
The orbit of a planet is an ellipse with the Sun at one of the two focii
What is Kepler’s 2nd Law?
A line segment connecting the planet and the Sun sweeps out equal areas in equal time intervals
What is Kepler’s 3rd Law?
The square of the orbital period of a planet T is directly proportional to the cube of its average distance r from the Sun
Show Kepler’s 3rd Law
1) Assuming the orbits are circular we can equate the equation for circular motion to the equation for the force on a body due to gravity:
mv^2/r = GMm/r^2
2) Simplify v^2 = GM/r
3) Since v = 2pir/T :
(2pir/T)^2 = GM/r
4) T^2 = 2pi/GM r^3
This equation shows that T^2 is directly proportional to r^3
What makes a geostationary orbit?
What’s its use?
- Satellite orbits round the equator
- Satellite has the same period of Earth (24 hours)
USE: In communications as the satellite can be in direct line of sight with a transmitter/receiver on the Earth’s surface
Name the two types of binary star system orbits and describe the conditions for the orbit:
1) Equal massed stars orbiting a common centre of mass
(The time period of each star and the radius of orbit is the same. The two stars are diametrically opposite as the centripetal force is produced by the gravitational force. This force acts along a line joining the two stars which must pass through the centre of mass of the system)
2) Unequal mass stars orbiting a common centre of mass ( The time period of each star is the same but the radius of orbit is different. The larger massed star will have a smaller orbital radius. The ratio for the two stars: M1/M2 = R2/R1
Name the two types of binary star system orbits and describe the conditions for the orbit:
1) Equal massed stars orbiting a common centre of mass
(The time period of each star and the radius of orbit is the same. The two stars are diametrically opposite as the centripetal force is produced by the gravitational force. This force acts along a line joining the two stars which must pass through the centre of mass of the system)
2) Unequal mass stars orbiting a common centre of mass ( The time period of each star is the same but the radius of orbit is different. The larger massed star will have a smaller orbital radius. The ratio for the two stars: M1/M2 = R2/R1
Define escape velocity and give the equation for it:
If an object is shot away from the centre of the Earth with a certain amount of kinetic energy it could feasibly have enough kinetic energy to escape the planet’s gravitational field and therefore reach infinity.
Equation:
Initial kinetic energy=Decrease in gravitational potential energy to zero
1/2mv^2=GMm/r
v=squroot2GM/r
Define gravitational potential:
The energy required per mass to bring an object from a point in infinity to a point in a space
