Chapter 18 Gravitational Fields Flashcards
What is required for a gravitational field to be produced?
Mass
What is the range of gravity?
Infinite
What is the equation to find the gravitational field strength?
g = F / m g = gravitational field strength F = Force m = Mass
What is the unit of gravitational field strength?
N Kg^-1
What is the equation to find the force experienced by a force with a mass?
F = mg
What direction does gravity act?
It is always attractive
How are gravitational field lines mapped?
They always point to the centre of mass
They do not cross
What do the field lines for a spherical object look like?
They are radial
What does the field lines for a spherical mass and point mass look like? What does this mean?
They are very similar so this means that spherical objects like planets or stars can be modelled as point masses
What does it mean if the gravitational field lines are parallel and equidistant?
This means that the field is said to be a uniform gravitational field and the gravitational field strength does not change
What is the gravitational field strength across a planets surface?
It is approximately uniform
What does newtons law of gravitation state?
- The force between two point masses is proportional to the product of the masses F ∝ Mm
- The force between two point masses is inversely proportional to their separation F ∝ 1/r^2
What is the equation for newtons law of gravitation?
F = - GMm / r^2 F = Force G = gravitational constant M = Mass 1 m = Mass 2 r = distance between the two point masses
Explain why F = - GMm / r^2 has G and a - ?
It is negative because it is always attractive
G is the gravitational field constant
What is the value of the gravitational field constant? What are its units?
6.67x10^-11 Nm^2kg^-1
What happens to the force if you double the distance between two point masses?
The force decreases by a factor of 4
a.k.a 1/4 the force
How can the resultant force be calculated for 3 objects in a line? e.g. object A,B,C with B in the middle
Object A gets attracted by B and C both in the same direction so the forces combine
Object B gets attracted by A and C in opposite directions
Object C gets attracted by A and b both in the same direction so the forces combine
How can the resultant force bet calculated for 3 objects in 2D space?
Using Pythagorus theorem
What is the equation for gravitational field strength at r distance from a point mass? How is the equation derived?
g = -GM / r^2
Derived using F = -GMm / r^2 and using g = F / m and then cancelling out the m’s in: g = -GMm / mr^2
Using the equation g = -GM / r^2 what is g proportional to?
g is proportional to Mass
and
g is inversely proportional to the distance from the centre of the object
What does the graph of gravitational field strength against distance between objects look like?
It starts steep and the gradient decreases and reaches 0 at infinity
What does the graph of gravitation field strength against 1/distance^2 for 2 objects look like?
It is a straight line with the gradient being -Gm
What happens to the gravitational field strength for uniform fields?
the strength does not change with distance
What is Kepler’s first law?
The orbit of a planet is an ellipse with the sun at one of the two foci
What is an ellipse?
It is a squashed or elongated circle with two foci
What is eccentricity a measure of?
This is a measure of how elongated the circle is.
A low eccentricity means that it is nearer a circle
What is aphelion?
This it the furthest distance from the sun for an object orbiting in an ellipse
What is perihelion?
This is the closest distance from the sun for an object orbiting in a ellipse
What is Kepler’s second law?
A line segment joining a planet and the sun sweeps out equal areas during equal intervals of time
What does Kepler’s law describe?
As a planet orbits an object in an ellipse. The area that is made between the planet and the object as it orbits for an interval of time is the same for the same interval of time between any two points as it orbits.
What does Kepler’s law say about the speed of an object passing either foci of an elliptical orbital
As it passes the foci it is moving the fastest and is the slowest moving between the foci
What is Kepler’s third law?
The square of the orbital period T is directly proportional to the cube of its average distance from the sun
T^2 ∝ r^3
What equations is associated with Kepler’s 3rd law?
T^2 / r^3 = k
T = time period
r = average distance from the sun
k = a constant for objects orbiting the sun
What is the distance from the earth to the sun called?
It is called an astronomical unit
How can the orbits of planets be modelled?
As a circle
For an object (e.g. a planet) orbiting a larger object what is the centripetal force equal to?
Centripetal force = gravitational force
What equation can be made because the centripetal force on a planet is equal to the gravitational force?
v^2 = GM / r
derived from
mv^2 / r = GMm / r^2
How can the speed or an orbiting planet be calculated?
The circumference of the orbit per time
v = 2πr / T
What is the equation for Keplar’s 3rd law? How is it derived?
T^2 = (4π^2 / GM)r^3
v^2 = GM / r
sub in v = 2πr / T
(2πr / T)^2 = GM / r
which rearranges to the equation
Using the equation T^2 = (4π^2 / GM)r^3 what is the ratio of T^2 / r^3 equal to?
T^2 / r^3 = 4π^2 / GM
What is the gradient of a graph of T^2 against r^3 equal to?
4π^2 / GM
Does Kepler’s laws only apply to planets?
No It applies to any small object orbiting a larger one
What is required for a satellite to stay in orbit?
It must have the right speed and altitude
What are some uses of satellites?
Communication Military Scientific Weather and climate GPS
What is a polar orbit?
It orbits the poles of the earth
What is a low earth orbit? How fast do LEO satellites orbit?
It orbits close to the earth and they travel very fast so have a short orbiting time
What is a geostationary satellite?
It is a specific orbit where the orbiting period is 24 hours and it orbits the earth at the equator so that the satellite remains above the same point over the earth as it rotates
What are the 3 requirements for a geostationary orbit?
Orbit above the equator
Rotate in the same direction as the earth
Have an orbital period of 24 hours
All values of gravitational potential energy are…
Negative
If the gravitation potential of a planet of mass M is -30MJkg^-1 at point X. What does this mean?
This means that to bring an object weighting 1kg from point X to infinity would require 30MJ of energy.
If the object weighs 2kg then 60MJ is required
What two factors affect the gravitational potential at any point in a radial field around a point mass?
The distance r
The mass of the point mass
What is the equation for gravitational potential?
Vg = - GM / r Vg = Gravitational potential G = Gravitational constant M = Point mass r = Distance from point mass
What happens to the gravitational potential of an object if it is infinitely far away?
Vg = 0
What does the graph of Vg against r show?
It shows how the potential energy changes as distance increases.
What is the equation of the line produced for the graph of Vg against r?
The equation is: Vg = -GM / r
What happens to Vg as the radius is doubled?
Vg is halved
How does gravitational potential energy change as you move away / towards a point mass?
Moving away: Vg gets less negative
Moving towards: Vg gets more negative
How does gravitational potential change as you fly from the earth to the moon?
As you move away from earth Vg decreases and as you approach the moon Vg increases
How is gravitational potential energy defined?
It is the work done to move a mass (m) from infinity to a point in a gravitational field. It is always negative
What are the units for gravitational potential energy?
Jkg^-1
What is the equation for work done on a mass moving through a radial gravitational field?
E = m x Vg
How does gravitational potential change when moving along a uniform field?
There is no change in Vg as it moves ALONG a uniform field. Only when it moves further away from the surface does Vg change
How does the magnitude of gravitational force change with distance from the centre of a point mass?
The further you are away the smaller the force. It looks like and exponential decay curve.
What is the area under a gravitational force - distance graph equal to?
It is equal to work done on the object
What is required to escape the gravitational force of the earth?
Enough energy needs to be supplied to at least equal the gain in the gravitational potential energy of the object moving away from the earth
What is the equation for escape velocity?
1/2mv^2 = GMm / r
rearranged to
v = √2GM / r
The escape velocity on a given planet is…
What is the equation?
The same regardless of mass
v = √2GM / r
