Topic 9.2
1.4.1 Gravity Again
Gravitational Field Lines
The gravitational field surrounding an object with mass can be
represented by field lines (just like electric field lines around a
negative charge) The closer the field lines are together the
stronger the field The further away from the mass generating the
field, the weaker the field gets Around a single object, the lines
are always perpendicular to the surface.
Gravitational Field Lines
Gravitational Field lines around Earth are radial
BUT close to the surface they appear to be uniform and
parallel
The Law of Universal Gravitation
The law of universal gravitation mathematically describes the
force of attraction between two objects.
In a system where there are more than 2 gravitational fields,
the overall (net) effect is the vector sum of the individual
forces.
The Law of Universal Gravitation
The r in Newton's Law of universal gravitation refers to the
centre of the point mass.
In reality, the mass is usually a planet which has a real
radius.
The denominator is often replaced with (R0 + h) where h is the
altitude.
The Law of Universal Gravitation
Determine the gravitational force felt by:A 150kg satellite
placed 6000km from the Moon.
A 25T space capsule 30000km from Earth
The Moon placed 385000km from Earth
The Earth placed 150000000km from the Sun
A 250kg satellite at an altitude of 400km above the Earth
A 250kg satellite at an altitude of 30000km above the Earth
A 250kg satellite at an altitude of 30000km above the Moon
A 250kg satellite at an altitude of 30000km above the Sun
Data:
Gravitational Field Strength
The correct name for weight is weight force due to gravity
ThereforeWeight force = Gravitational Force
Given that the Earth has
a radius of 6.38x106 m
and g=9.81 Nkg-1 determine
the mass of the Earth.
The Law of Universal Gravitation
Determine the gravitational field strength at:a point 6000km
above the Moon surface.
a point 36000km above Earth
a point 750000000km from the Sun's surface
A point 750000000km from the Earth's surface
Determine the point where Earth's gravitational field is
balanced by: [Quite Hard]The Sun
The Moon
Data:
Gravitational Potential Energy
On Earth, we experience that whenever we place an object in a
gravitational field, its gravitational potential energy is
converted into other forms e.g. KineticThat is the object will
always fall down towards the Earth!
When an object is allowed to move under the influence of a
gravitational force, its gravitational potential energy will
decrease.
Gravitational Potential Energy
We recall that work done by a force is given by Force x
Displacement.
In a uniform field, this force is the weight.
g
mr
Gravitational Potential Energy
However, this formula gives the change in gravitational
potential energy relative to some point.
This is fine on Earth, but in space there is no reference
point!Which way is UP?
Gravitational Potential Energy
Scientists have agreed that the edge of space has an absolute
gravitational potential energy of 0J
All other absolute gravitational energies are relative to this
AND must be therefore be negative.
Gravitational Potential Energy
Also, experience shows that work must be done to move objects
against the field.
If zero is the edge of the field, and work is added to move the
object to the edge, then all other values must be negative
Gravitational Potential Energy
In a radial field the same rules hold.
Calculate the energy required to just move:A 10T rocket from
Earth to infinity.
A 750kg satellite from the Sun to infinity.
Gravitational Potential Energy
Therefore in a radial field moving a body from point 1 to point
2...
Calculate the energy required to move a rocket from the surface
of the Earth to an orbit of altitude 36000km
Calculate the energy required to move a satellite from an orbit
of altitude 30000km to an orbit of altitude 400km above the
Earth.
Gravitational Potential
Gravitational Potential is the energy required per unit mass to
move an object from infinity to a point in a field.
Like gravitational Field Strength, it is a property of the
field.
Gravitation Summary
All masses cause a gravitational field around themselves.
This attracts all other objects with mass towards them.G is the
Universal Gravitational Constant = 6.67x10-11 Nm2kg-2
Force and acceleration
Potential Energy and Potential
Properties of Objects in the Field
Properties of the Field
