7.2 Gravitational Fields Flashcards
Define a gravitational field
a region in which an object that has mass experiences a force
Define an equipotential
lines that are drawn to indicate points of equal potential and cross the field lines at 90 degrees
What are field lines
arrows that indicate in which a small test would experience a force of attraction. The closer the field lines are together, the stronger the gravitational field
What does the density of the field lines (how close the lines are) indicate
the strength of the field.
The closer the lines are, the stronger the field
as the weaker field exerts a smaller force on a mass
what are the separations like in a radial field or a uniform field
radial field : variable separation
uniform field : constant separation
- so if an object is far away from the earth, the force acting on it will be small as the field lines have a larger seperation
When are the lines of radial fields approximately parallel
Over small distances
for a uniform field if two objects are dropped at different heights, which one would hurt more
the one from a greater height because object from greater height will have GPE.
What is Newtons law of gravitation
the attractive force between two-point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation
Define gravitational field strength
the force acting on a body per unit of mass
A body is placed between the moon and the earth where it feels equal attraction to both bodies. How far is it from the Earth?
mass of earth = 6.0 x 10^24 kg
moons orbital radius around the earth = 3.8 x 10^8
mass of the moon = 7.4 x 10^22 kg
GM / r^2 (of earth) = GM / r^2 (of moon)
square root of m1 / m2
= r1 / r2
r1 / r2 = 8.98
total distance = 3.8 x 10^8 = r1 +r2
use both equations to get [r1 / (3.8 x 10^8) - r1] = 8.98
Define potential energy and give the equation for potential energy in a radial field
definition : work done in moving an object with mass from infinity to that point in the field
Ep = -GM1M2 / r
Define the absolute gravitational potential at a point
the work done per unit mass in moving a body from infinity to that point in the gravitational field
What is the equation for Keplers 3rd law
T^2 = (4 pi^2) / GM x r^3
equation for escape velocity
and equation for orbital velocity
v = Square root of (2GM / r)
v = Square root of (GM / r)
What happens as an orbit increases
its potential energy increases
kinetic energy decreases
total energy increases
satellite has to do work (by burning fuel) to increase total energy
State the three types of orbits and their time periods
Low earth orbit : less than 128 minutes
medium earth orbit : between 2 hours and 24 hours
high earth orbit : greater than 24 hours
What are the three types of orbits used for
Low earth orbit :
good for spying and weather
medium earth orbit :
used for GPS in high latitude
regions close to north and south pole
high earth orbit :
most of earths surface
What is a geosynchronous orbit
a satellite that orbits with a period of 24 hours
orbits in same direction as earth’s rotation (anticlockwise)
what is a geostationary orbit
a satellite that orbits with a period of 24 hours
orbits in the same direction as the earths rotation
orbits in the equatorial plane
advantages of a geostationary orbit
remains in a fixed relative position
satellite dishes only need to be aligned once
what are geostationary satellites used for
communications
GPS, satellite television and mobile phone communications
what problems do worlds space agencies face as more satellites are put into orbit
satellites orbit in closer proximity
greater risk of collisions between satellites and with space debris
what is a polar orbit
what uses do satellites in these orbits have
satellites pass over the polar regions (north and south)
used for communication
for espionage (spying on countries)
for meteorology
The distance between the Sun and the Earth is 1.5 × 10^11 m
What is the gravitational force exerted on the Sun by the Earth?
mass of earth = 5.97 x 10^24
mass of sun = 1.99 x 10^30
F = Gm1m2 / r^2
= (6.67 x 10^-11) (both masses) / 1.5 x 10^11
The distance between the Sun and Mars varies from 2.1 × 10^11 m to 2.5 × 10^11 m.
When Mars is closest to the Sun, the force of gravitational attraction between them is F.
What is the force of gravitational attraction between them when they are furthest apart?
Force is proportional to 1 / r^2
F1r1 = F2r2 (with both radius squared)
F2 = 0.7056F
B
As the field lines are closest together
T^2 is proportional to r^3
Log T^2 is proportional to Log r^3
2 Log T is proportional to 3 Log r
Log T is proportional to Log r
Hence C is the correct answer
C
As line need to be perpendicular to field line, in direction where potential gets more negative
An object moves freely at 90° to the direction of a gravitational field.
The acceleration of the object is
A zero.
B opposite to the direction of the gravitational field.
C in the direction of the gravitational field.
D at 90° to the direction of the gravitational field.
C
What is the equation for potential energy in gravitational fields
Ep = - GMm / r
A different satellite is in a higher circular orbit.
Explain how the linear speed of this satellite compares with the linear speed of the satellite in a closer orbit
speed of higher circular orbit is lower as distance is higher as
v is inversely proportional to radius
The potential difference between the lines is constant but the distances are not
The equipotential surfaces are not straight / not parallel as they are curved. A uniform field would have straight parallel lines
what is the earths orbital period for a year
1 year
The total mass of the Rosetta spacecraft was 3050 kg. This included the robotic probe of mass 108 kg and 1720 kg of propellant. The propellant was used for changing velocity while travelling in deep space where the gravitational field strength is negligible.
As it approached the comet, the speed of the Rosetta spacecraft was reduced to match that of the comet. This was done in stages using four ‘thrusters’. These were fired simultaneously in the same direction.
Explain how the propellant produces the thrust.
there is an equal and opposite change of momentum in the spacecraft
as there is a change in momentum of gases escaping
gas is expelled / gone through the nozzle
fuel / gasses produced at a high pressure
Zero
Which one of the following statements about gravitational fields is incorrect?
A Moving a mass in the direction of the field lines reduces its potential energy.
B A stronger field is represented by a greater density of field lines.
C Moving a mass perpendicularly across the field lines does not alter its potential
energy.
D At a distance r from a mass the field strength is inversely proportional to r.
D
The gravitational potential difference between the surface of a planet and a point P,
10 m above the surface, is 8.0 J kg–1. Assuming a uniform field, what is the value of the
gravitational field strength in the region between the planet’s surface and P?
use of equation g = V / r
8 / 10 = 0.8
A projectile moves in a gravitational field. Which one of the following is a correct
statement for the gravitational force acting on the projectile?
A The force is in the direction of the field.
B The force is in the opposite direction to that of the field.
C The force is at right angles to the field.
D The force is at an angle between 0° and 90° to the field.
A
D
C
B
A
Sketch two graphs to show how gravitational potential V, varies with distance r. For a radial field and a uniform field
