Topic 9.2

1.3.1 - Newton, Cannons & Satellites

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.

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.

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.

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 GPEr

MmGhmgmv 22

1

Escaping Earth

•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.

R

GMv

R

MGv

2

22

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!

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

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

Weight

Thrust

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!

Weight

Thrust

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?

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?

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?

Satellite Orbits

NASA Satellite Tracker

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!

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.

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.

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!

Shuttle Re-Entry

http://www.youtube.com/watch?v=qQkqCCRAa38