1. Isaac Newton considered what would happen if a cannon ball was shot from a mountain at increasing speeds. He realized that at a certain speed, the projectile would enter into orbit around the Earth due to gravity.
2. Astronauts are not truly weightless in space, but are in a state of constant free fall around the Earth at the same rate as its curvature.
3. To enter into orbit, a satellite must be launched at a velocity less than the escape velocity from Earth, which is around 8km/s. Significant thrust is required to accelerate a satellite to this velocity.
2. Newton’s Thought Experiment
Isaac Newton’s 3 laws of motion and his
law of universal gravitation gave him the
idea of placing objects into orbit.
N1: An object will continue in a straight line
at constant speed unless a force acts.
N2: An unbalanced force causes an
acceleration, i.e. a change in speed or
direction.
NLUG: Any two objects with mass, exert a
gravitational attraction on each other.
3. Newton’s Thought Experiment
• He considered what would happen if a cannon ball were to be
shot at different speeds from the top of a very high mountain on
the equator.
• As the velocity of the projectile increased, so did the range.
• He also noted that the radius of curvature increased as well.
• He proposed that at the correct velocity, the projectile would
curve at the same rate as the Earth’s surface.
• The projectile would orbit the Earth.
• Exceed this speed and the projectile would be able to escape
the Earth’s gravity.
4.
5. Free Falling Spacemen
• Astronauts in space are not really weightless!
• They are not in zero-gravity!
• If they were then there would be no force acting on them.
• So they would, by N1 and N2, continue in a straight line and
not orbit the Earth.
• They are really “Free-falling” around the Earth at the
same rate of curvature as the Earth.
• They are falling towards the Earth but constantly missing.
6. Escaping Earth
•The velocity required for a projectile
to fully escape the Earth’s
gravitational field is called the
escape velocity.
•This can be given by applying the
law of conservation of energy.
•KE of projectile = change in GPE
mv2 = mgDh = G Mm
2
r
1
7. Escaping Earth
v G M
R
2 =
2
v GM
R
2
=
•Notice that the mass of the projectile is
not a factor in determining escape
velocity.
•Use your table of mass and planetary
radius (earlier homework) to calculate the
escape velocity from each of the solar
system planets.
8. Satellites
• To place a satellite into orbit around the Earth,
requires that it be launched with a velocity, less
than the escape velocity.
• The satellite is said to be “bound” by Earth’s gravity.
• This velocity is around 8kms-1!
9. Launching Satellites
• Consider the impulse required to launch a 50kg
satellite into orbit from the Earth’s surface.
• Required velocity = 8kms-1.
• Initial velocity = 0 kms-1.
• Impulse = m (v-u)
= 50 (8000-0)
= 400 000 Ns
10. Launching Satellites
Consider the Force required to
launch a satellite.
Thrust – Weight = ma
T - mg = ma
If the impulse calculated earlier was
applied over a time of 10 seconds
then the trust force would be 40kN
This would mean that the satellite
experiences a force of 40kN and
an acceleration of 790ms-2
Thrust
Weight
11. Launching Satellites
Another way of thinking of
this is the satellite feels a
force of 40000N
This is eighty times its
normal weight of 500N
This can be written as 80g!
This may be fine for a
mechanical object, but
would instantly kill a
human!
Thrust
Weight
12. Launching Humans
Humans can tolerate forces up to 5g for short periods of
time before G-LOC (G loss of consciousness)
Well trained pilots with proper equipment can survive 9g
for short times.
Assume a maximum force of 5g is applied to an 80kg
astronaut.
What is the force required to launch him into space?
What is the impulse required to launch him into orbit?
How long must the launch force be applied for?
13. A Helping Hand
• Most space ports are located close(ish) to the
equator and toward the eastern coast of the
continents.
• This reduces the force required to accelerate
the rocket, as it would already have the speed
of the Earth at take off.
• If the radius of the Earth is 6400km what is the
velocity of a rocket on the equator?
14. Types of Orbit
There are two basic types of satellite orbit:
Geostationary – the satellite orbits with the
same angular velocity as the Earth.
Low Earth Orbit – the satellite orbits closer to
the Earth at high speed.
What could these two orbits be used for?
16. Orbital Decay
The Edge of space is
considered to start at
100km.
But, the edge of the
atmosphere is not a hard
edge!
A few gas molecules extend
outwards into space.
Satellites in low Earth orbit
continually collide with these
molecules, losing energy.
We say that the orbit decays!
17. Orbital Decay
To prevent orbital decay, modern satellites carry
more fuel than is needed to reach orbit.
The extra fuel is used to “boost” the satellite back
up into a stable orbit.
18. Re-entry
In orbit, a spacecraft has high kinetic energy and high
gravitational potential energy relative to the ground.
To safely return to Earth, this excess energy must be
dissipated.
First small “retro-rockets” are used to slow the rocket
down.
Friction with the upper layers of the atmosphere is
allowed to do the rest.
19. Re-Entry
The angle of re-entry is also important.
Too steep and the accelerations may kill the
pilots.
Too shallow could cause the spacecraft to
bounce off the atmosphere.
The correct angle is between 5 and 7 degrees
to the atmosphere!
