1) The document explains that objects can orbit other large bodies like planets due to gravity. While gravity is pulling the objects towards the center, their horizontal movement is fast enough to constantly miss the surface in a curved path. 2) It uses the example of firing a cannon on a very tall mountain to show that with enough initial speed, the cannonball would orbit the Earth instead of hitting the ground. 3) Kepler's Third Law states that the square of an orbiting body's period is proportional to the cube of its average distance from the central body.

2. IN THIS LESSON YOU WILL LEARN WHAT IS
GOING ON HERE…

3. AND HERE…

4. “THERE IS NO GRAVITY”
• Cannot be the answer.
• Gravity is everywhere in the universe.
• You need very large objects to notice it, for example
planets.
• But it is inescapable…..
So what is going on?

5. ORBITAL MOTION
Out into Space Lesson 5

6. LI..
• Understand that objects stay in orbit because of the pull
of gravity and the speed they are moving.
• Describe orbits
• Solve problems about orbits using Newton’s
Gravitational and Kepler’s Laws

7. Here is my thought
experiment. Imagine a
big cannon on a tall
mountain….
The cannon ball
would travel very far
in a curved path

8. An even bigger
cannon and
mountain and the
ball would travel
even further….

9. Always falling
under the effect
of gravity

10. …but the Earth is
curved. So the
cannon ball actually
goes even further

11. What about
a massive
cannon on a
massive
mountain?

12. What if the cannon
and mountain were
even bigger?
The cannon was
above the Earths
atmosphere?
What might
happen?

13. The cannon ball orbits
the Earth!
Continually falling under
the effect of the gravity
field.
Never hitting the ground
because of it’s speed
and the curvature of the
Earth.
Never slowing down
because there is no air
resistance.

14. Things in orbit
are there
because gravity
is pulling them
How clever
towards the
am I?
Earth but they
are travelling
too fast to hit it.
Isaac Newton

15. http://galileo.phys.virginia.edu/classes/109N/m
ore_stuff/Applets/newt/newtmtn.html

16. ROCKETS RATHER THAN MOUNTAINS
•
We put space craft and satellites in orbit around the Earth using rockets rather than
impossibly high mountains.
•
Once the rockets has carried the spacecraft above the atmosphere booster rockets
speed it up to it’s orbit speed.

17. WHAT IS THIS IDEA TO LAUNCH SATELLITES?
• In the 1950’s the USA
had the X-Plane project
it flew planes to the
edge of Earth’s
atmosphere.
• Virgin Galactic launch
small spacecraft from
the back of aeroplanes.

18. SO WHY DO THINGS FLOAT AROUND INSIDE
SPACECRAFT IN ORBIT?
• Orbit is freefall
• The spacecraft and everything in it are falling under gravity
(around the Earth)
• Everything falls with same acceleration.
• Staying the same distance apart (floating)

20. DEMONSTRATE YOUR LEARNING
•
Explain using ideas about gravity and orbits what is happening in this video clip.
•
It was taken by the camera on an astronaut working on the International Space
Station.

21. KEPLER’S LAWS
1. The orbit of every planet is an ellipse with the Sun at one of the two foci.
2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of
time.
3. The square of the orbital period of a planet is directly proportional to the cube of the
semi-major axis of its orbit.
Ellipses are
hard.
We will treat
orbits as
circular motion.

22. FIRST AND SECOND LAWS
NOT THAT RELEVANT FOR CIRCULAR ORBITS
• Circular orbits are types of ellipses (both foci at the same point)
• The speed doesn’t change in a circular orbit.

23. LET’S DERIVE THE THIRD LAW
• What is the only force acting
on a planet orbiting the
Sun?
• What is the expression
for centripetal force?
mv2/r
• And if the planet is moving
at constant speed in a circle
it must have centripetal
force acting on it.
• For the gravitational
force? Gm1m2/r2
• Equating these
expressions, we have
GMm/r2= mv2/r

24. KEPLER’S THIRD LAW
Circle
Circumference
C = 2πr
Period, T
• speed v can be calculated as distance
travelled in one orbit (2πr) divided by the
time taken, T:
v =2πr/T
• Plugging this into the previous equation,
and cancelling the m terms on both sides
gives us:
GM/r2 = 4π2r/T2
• Rearranging again gives:
T2 = (4π2/GM) r3
3.
The square of the orbital period of a planet is directly
proportional to the cube of the semi-major axis of its
orbit.

25. GEOSYNCHRONOUS ORBITS
• We know from Kepler’s third law that the further away a satellite is
from the body it is orbiting, the longer its orbital period.
• If an orbiting satellite had a period of 24 hours, and you saw it
overhead at, say 10.00 am, when would you next see it overhead?
(Because both the Earth would have completed one rotation in the
same time it took the satellite to complete one orbit, it would next be
overhead at 10.00 am the next day. Such a satellite is said to be
geosynchronous.)

26. GEOSTATIONARY ORBITS
•
A difficult question – if you wanted the satellite to remain directly
overhead at all times (not just once per day) where on the Earth
would you have to be?
•
The only points on the Earth’s surface that orbit around the centre
of the Earth are those on the equator. Thus, you would have to be
on the equator.
•
If a satellite has a period of 24 hours and orbits above the equator
such that it always appears to be above one point on the equator,
it is known as a geostationary satellite, and its orbit is a
geostationary orbit.

27. GEOSTATIONARY ORBITS
•
Geostationary satellites are predominantly used for
communications. Satellite TV companies use geostationary
satellites to cover a constant area on the Earth’s surface – hence
you point your satellite dish receiver in the direction of the
geostationary satellite.
•
3 geostationary satellites placed into orbit 120 degrees apart
above the equator would be able to cover the entire Earth (except
for very near the poles).
•
Because geostationary satellites have to be launched so high
(other satellites orbit as low as a few hundred km), the energy and
costs required for launching a satellite into geostationary orbit are
high.