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ASTRONOMY: 5. The physics of circular motion and the forces involved in solar and planetary systems

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.

INDEX physics notes on ASTRONOMY

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.


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