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Physics Factsheet
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Number 109
An Inventory of the Solar System: Part I
In this factsheet we will explore circular motion, centripetal acceleration and centripetal force in everyday situations, and apply these ideas
to our solar system.
Our solar system consists of one sun, nine planets, over 150 natural satellites and many small bodies like asteroids and comets. The four
inner planets are relatively small, rocky bodies. The four outer planets are gas giants. Pluto can be considered a bit of an anomaly. All of
the nine planets have elliptical orbits: elongated circles.
The Solar System
Venus
Mars
Mercury
Earth
Saturn
Neptune
Pluto
Jupiter
Uranus
Spin a ball at the end of a piece of string around your head. Someone
cuts the string. What happens next? What would happen to a
planet if the sun disappeared?
Both the ball AND the planet would travel along path C. Why?
If we cut the string or removed the sun, there would be no force
acting on the ball or planet. We know what happens if there is no
resultant force acting: the ball or planet stays still or carries on with
the same steady speed in a straight line (Newton’s 1st Law of motion).
C
D
E
B
Without the string, the ball would follow path C. With the string,
the ball follows path E. There must be a force acting on the ball,
constantly pulling the ball around into a circular path. What is this
force? Which direction does it act?
F
G
A
The force is inwards, towards the centre of the circle. It is caused
by the tension in the string.
If you swing a ball on a string around your head, when the string is cut
where does the ball go?
Any object travelling in a circle will continue in a straight
line at the same steady speed if the inward force is removed.
C
D
E
B
We know acceleration happens when an object changes velocity.
But velocity is a vector: speed in a particular direction. If the
direction of travel changes, we have acceleration, even if the actual
speed remains the same. So an object moving in a circle is always
accelerating towards the centre, even if the speed stays the same.
F
Sun
A
G
This is also true for any object in an orbit. The gravitational attraction
between the sun and the planet keeps the planet in an orbit. The
planet is continually accelerating, but travels at a steady speed!
When something is travelling in a circle, we call the inward
acceleration centripetal acceleration and the inward force
centripetal force. These aren’t NEW forces, just a handy way of
thinking about the forces already involved, like tension in a string,
friction on a road or gravity between a sun and planet.
A planet orbits the sun, if the sun is removed where does the planet
go?
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Physics Factsheet
109. An Inventory of the Solar System: Part I
Centripetal acceleration and centripetal force
An object moving in a circle is always being
accelerated, but the speed DOES NOT change
v2
r
If the radius is small, we need a big acceleration. We need a very
big acceleration if the speed is great because of the v2 term. The
planets closest to the Sun move fastest. A large centripetal
acceleration is required to keep them in orbit.
This is the relationship for centripetal acceleration, speed and
radius.
Centripetal acceleration a =
Example Exam Question
A yo-yo is spun at a steady speed around a person’s head at the
end of a piece of string.
(a) Draw an arrow on the diagram showing where the force is
acting.
(1 mark)
(b) Draw an arrow to show where the yo-yo would travel if the
string were cut.
(1 mark)
(c) Explain why the yo-yo is accelerating, despite travelling with
a steady speed.
(2 marks)
(d) Draw an arrow to indicate the direction of acceleration.
(1 mark)
Newton’s 2nd law of motion tells us F=ma. This gives us a
relationship for centripetal force:
mv2
r
So for the fast moving inner planets, a large centripetal force is
required. The Sun’s gravitational field is strongest nearest the
inner planets, and is the source of this centripetal force.
Centripetal force F =
Answer
b)
For any object moving a circle, the force is ALWAYS
towards the centre
a) and d)
Exam Hint: Q) Does the earth do work keeping the moon in
its orbit? A) The force is always acting at right angles to the
motion. No work is done, because there is no component of the
force in the direction of motion.
Exam Hint: What happens if you twirl a yo-yo around your
head at the end of its string and let go? It will continue in a
straight line in the direction it was travelling when released.
But don’t forget it will ALSO fall down towards the ground:
accelerating due to gravity. Its path will be parabolic in a
vertical plane.
a) 9 b) 9 and d) 9
c) Velocity is speed in a particular direction. 9 But the direction
keeps changing so the yo-yo must be accelerating. 9
Misconception: Centripetal and centrifugal
ƒ
ƒ
ƒ
ƒ
Picture yourself sitting in the passenger seat of a car. What happens to you when the car turns right?
You feel pressed up against the door. Many people say there is a force “throwing you” outwards.
However, there is NO OUTWARD FORCE
Your body is “trying” to obey Newton’s First Law of motion: continue at the same speed in the same direction. The force acts
inwards: forcing your body around the corner
Path that passenger would take
Path of car
Force not acting on
passenger:
centrifugal
✗
✓
Force acting on passenger:
centripetal
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Physics Factsheet
109. An Inventory of the Solar System: Part I
Practice Questions
Show all working, including any rearranging of equations.
1. What is the cause of the centripetal force keeping planets in their orbits? Which direction does it act?
2. Describe and explain what would happen to any object moving in a circular path if the centripetal force were removed.
3. The radius of the moon’s orbit around the earth is 384,000km. Calculate the distance it travels in one orbit. The orbital period of the
moon is 27.3 days. How fast does the moon travel, in metres per second?
4. Calculate the centripetal acceleration of the moon using your answer from question 3.
5. The earth has a mass of 5.98 × 1024kg, an orbital speed of 30kms-1 and orbits 150 million km from the sun. Explain why we can use the
centripetal force equation to calculate the gravitational attraction of the earth to the sun. Calculate this attraction.
6. How can an object be accelerating if it moves at a steady speed in a circular path?
7. If the speed of a car is doubled, how does the centripetal force needed for it to turn a corner change? What happens to required
centripetal force if the radius of the turn is halved? What if the mass of the car is halved?
8. If a circular fairground ride is limited to 4g for safety reasons, with what linear speed can it spin? The radius of the ride is 10m and g
=9.8ms-2.
Answers
1) Gravity provides the centripetal force keeping the planets in their orbits. It acts inwards, towards the centre of the circular path.
2) An object will travel in a straight line in the direction it was travelling at the instant the centripetal force is removed.
3) Circumference of moons orbit = 2πr where r = 3.84 × 108m so circumference = 2.41 × 109m. Period of the moons orbit =27.3 days
= 27.3 × 24 × 60 × 60 = 2.36 × 106 seconds.
distance 2.41 × 109m
Moons orbital speed =
=
= 1020m/s
time
2.36 × 106s
4) Centripetal acceleration =
v2
10202
=
= 2.71 × 10-3ms-2
r
3.84 × 108
5) The centripetal force keeping the earth in its orbit is caused by the gravitational attraction between the earth and the sun.
mv2 5.98 × 1024kg × (30 × 103 m/s)2
F=
=
= 3.59 × 1022N
r
150 × 109m
6) Acceleration is due to a change in velocity. Velocity is speed in a particular direction. A circular path means the direction is constantly
changing and so is the velocity.
mv2
r
If the speed of the car is doubled, the force needed for the turn is quadrupled because F∝v2. If the radius of the turn is halved, the force
required for the turn is doubled because
1
F∝
r
If the mass of the car is halved, the force required for the turn is halved because F∝m.
7) Centripetal force is given by F =
8) If g = 9.8ms-2 then maximum centripetal acceleration = 4g = 39.2ms-2.
a = v2/r so v = √(a × r) = √(39.2 × 10) = 19.8ms-1
Acknowledgements:
This Physics Factsheet was researched and written by Jeremy Carter
The Curriculum Press, Bank House, 105 King Street, Wellington, Shropshire, TF1 1NU
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