Doc Brown's Physics exam study revision notes: The circular or oval movement of objects under the
effect of a gravitational field, planets circulating around the sun or
moons moving around a planet.
See also Part 6.
Artificial
satellites - their orbits and uses
5.
The
physics of circular motion and the forces involved in solar and planetary systems
Velocity is a vector quantity, it has both
size/magnitude (the
speed) and direction (a reference angle).
If either the speed or direction changes, you have a
change in velocity.
If you
have a continually changing velocity, you have an acceleration!
SO, What velocity are we dealing with? What force are we
dealing with? in terms of one object in circular motion around another
object due to a gravitational field?
So, how do we explain the circular
motion of the objects illustrated above!
To keep a body moving in a circle there must be a force
directing it towards the centre.
This may be a moon or satellite around a
planet or a planet around a star - all apply to planet Earth.
This force is called the centripetal force and produces the continuous change in direction
of circular motion - which means constantly changing velocity of the moon or
planet etc.
Even though the speed may be constant, the object is
constantly
accelerating because the direction is constantly changing via
the circular path - i.e.
the velocity is constantly changing (purple arrows, on the diagram).
For an object to be accelerated, it
must be subjected to a force that can act on it.
Here the resultant centripetal force
of gravity is acting towards the centre, so always directing the
object to 'fall'
towards the centre of motion (blue arrows on the diagram).
But the object is already moving, so
the force of gravity causes it to change direction - speed is
constant, but change in direction means acceleration is taking
place.
In other words the object keeps on
accelerating towards the object it is orbiting and the instantaneous
velocity, at right angles to the acceleration, keeps the object moving
in a circle.
SO, the actual circular path of motion is determined by
the resultant centripetal force (black arrows and circle) ...
... and the circling object keeps
accelerating towards what it is orbiting!
The centripetal force stops the
object from going off at a tangent in a straight line.
The centripetal force will vary with the mass of the objects
in question and the radius of the path the object takes around the other.
You can argue that the path of a
given object in a stable constant orbit depends on its distance from the
object it orbits and the strength of the gravitational field it
experiences.
Summary of the 'rules'
You need to check the text below with the diagram above!
To keep an given object in a
stable orbit (moving at constant speed), the faster it moves or the
smaller the orbital radius, the greater the gravitational centripetal
force needed. See the pattern for the planets of our solar system.
If the speed of an orbiting object
changes the orbital radius must also change.
If an orbiting object initially slows down it is pulled by the gravitational
centripetal force into an orbit of smaller radius and increases
in speed.
Satellites at lower heights
above the Earth may experience tiny friction effects from the
upper atmosphere. Eventually this causes the satellite to slow
down and move to a lower orbit. Ultimately the satellite may be
drawn into a higher speed orbit lower in the atmosphere and burn
up from the heat of friction. This is sometimes done
deliberately to 'safely' remove a defunct satellite.
Conversely, If an object initially speeds up, it partially overcomes the centripetal
gravitational force moves to a higher orbit of greater radius, but
then it slows down in a larger radius stable orbit.
In positioning a satellite
via a 'transporter' rocket, it must be given the correct
velocity to go to the right height and with the right speed into
the desired stable orbit or specified radius.
We can now apply these ideas to the
three situations described below.
P = planet, m = moon
1. Circular motion - velocity & centripetal force
for a moon or a satellite around a planet
P = planet, S = Sun
2. Circular motion - velocity & centripetal force
for a moon around a planet
3.
Artificial satellites
- see the separate section.
The planets move around a star in almost
circular orbits e.g. planet Earth travelling round the Sun once a year.
The same force of gravity keeps a
moon orbiting a planet e.g. our Moon orbiting the Earth.
The same arguments on circular motion apply to the movements
of planets around a sun, a moon around a planet and a satellite orbiting a
planet.
The orbits are usually elliptical, rarely a perfect circle, but the
physics is the same.
In these cases, it is the force of gravitational attraction
that provides the centripetal force and it acts at right angles to the
direction of motion.
You should also realise that they are moving through empty
space (vacuum), so there are no forces of friction to slow the object down.
This is why the planets keep going around
the Sun and the moon keeps going around the Earth.
The pattern in the size of a planet's
orbit around a star
|
8
major PLANETS |
Distance from Sun in Mkm |
Mass relative to Earth |
Size relative to Earth |
Time to orbit Sun (days or years) |
Axis rotation time |
Average surface temperature
oC |
|
Mercury |
58 |
0.05 |
0.4 |
88 d |
58.6
d |
+350 |
|
Venus |
108 |
0.8 |
0.9 |
225 d |
242
d |
+480 |
|
Earth |
150 |
1 |
1 |
365 d |
24 h |
+22 |
|
Mars |
228 |
0.1 |
0.5 |
687 d |
24.7
h |
-23 |
|
Jupiter |
778 |
318 |
11 |
12 y |
9.8
h |
-153 |
|
Saturn |
1430 |
95 |
9.4 |
29 y |
10.8
h |
-185 |
|
Uranus |
2870 |
15 |
4 |
84 y |
17.3
h |
-214 |
|
Neptune |
4500 |
17 |
3.8 |
165 y |
16 h |
-225 |
|
Pluto (dwarf planet) |
5915 |
0.003 |
0.2 |
248 y |
153
h |
-236 |
|
Our 8
major PLANETS |
Distance from Sun in Mkm |
Time to orbit Sun (days or years) |
|
Mercury |
58 |
88 d |
|
Venus |
108 |
225 d |
|
Earth |
150 |
365 d |
|
Mars |
228 |
687 d |
|
Jupiter |
778 |
12 y |
|
Saturn |
1430 |
29 y |
|
Uranus |
2870 |
84 y |
|
Neptune |
4500 |
165 y |
|
Pluto (dwarf planet) |
5915 |
248 y |
The closer an object is to the object
it is orbiting, the stronger the gravitational force of attraction.
The stronger the gravitational force
of attraction, the faster the object must move in order to avoid
crashing into the object it is orbiting.
For any object in a stable orbit, the
radius of the orbit must match the speed the object is travelling.
Faster moving objects must move in
a smaller radius to have a stable orbit.
If the speed changes for some
reason, the radius must change too.
You can see clearly that the further
the planet is for the Sun (our star) the longer it takes for that planet to
orbit the Sun once (relevant data highlighted in bold).
This means, the further out the
planet is from the Sun, the slower it is moving AND in a larger radius
circle with respect to the Sun as its centre - to move in a stable
orbit.
Orbiting objects (planets/moons) -
summary of the connection between gravity, mass and radial distance (size)
of the orbit.
The gravitational field strength
depends on the mass of the object creating the field.
The larger the mass of the object,
the stronger the gravitational field e.g. Jupiter > Earth > our
Moon
The gravitational field strength
experienced by an orbiting object, also varies with its distance from
the object it is orbiting.
The stronger the force an orbiting
object experiences, the greater the instantaneous velocity needed to
balance it e.g. to keep it in stable orbit.
Therefore the closer a planet is to a
star or a moon to a planet, the faster the orbiting object must travel
to stay in orbit.
To have a stable orbit, the object
must have a speed that matches the gravitational 'pull' at a particular
radial distance from the object it orbits.
The smaller the radius, the
faster the object must travel to have a stable orbit.
|
Our 8
PLANETS |
Distance from Sun in Mkm |
Relative speed km/s |
Time to orbit Sun |
|
Mercury |
58 |
47.9 |
88 d |
|
Venus |
108 |
35.0 |
225 d |
|
Earth |
150 |
29.8 |
365 d |
|
Mars |
228 |
24.1 |
687 d |
|
Jupiter |
778 |
13.1 |
12 y |
|
Saturn |
1430 |
9.7 |
29 y |
|
Uranus |
2870 |
6.8 |
84 y |
|
Neptune |
4500 |
5.4 |
165 y |
|
Pluto (dwarf planet) |
5915 |
?
<5.4 |
248 y |
I've already mentioned the
pattern in the distance of planets from our Sun and the speed they
are travelling at - as measured by the length of time for one orbit
of the Sun.
From the table you can see,
the further than planet is from the Sun, the slower the speed it
travels at.
You might think that there
would be greater variation e.g. between Mercury and Neptune, but
remember, the outer planets have a long way to travel in their
orbit!
Because the planets are moving at
different speeds, ancient astronomers had noted the varying
positions of the planets against the relatively constant positions
of real stars. They did not realise until later, that these
'wandering stars', as they called them, were actually what we now
know as planets orbiting a star (our Sun).
See also Part 6.
Artificial
satellites - their orbits and uses
INDEX of my physics notes on
ASTRONOMY
Keywords, phrases and learning objectives for astronomy
Be able to describe and explain the circular oval movement of objects due to
gravitational field e.g. a moon moving around a planet, a planet
moving around a star.
Know that the almost circular motion is due to the
acceleration of the orbiting object being balanced by the
centripetal force of gravity.
Know the speed of the orbiting object does not
necessarily change, but the velocity does, which constantly changes
in direction caused by the gravitational field.
Use your
mobile phone in 'landscape' mode?
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INDEX of my physics notes on
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