Dynamics and Space Learning Intention You will be able to: Carry out Calculations involving the relationship between weight, mass and gravitational field strength during Interplanetary rocket flight. Application of Newton’s third law to explain motion resulting from a ‘reaction’ force. Use Newton’s laws to explain free-fall and terminal velocity.

THE EFFECT OF DISTANCE ON GRAVITY As a spacecraft rises from the surface of the Earth, the pull of the Earth’s gravity on it gets smaller and smaller. The table below shows the values of the gravitational field strength at various distances from the Earth. As you can see from the table, the value of “g” quickly decreases with distance from the Earth. You might think that it becomes zero at some point in space – it does, but that point is infinity! However, beyond a few million km, the effect of Earth’s gravitational pull has become very small. Plot a graph of gravitational field strength (y-axis) against the distance from the Earth (x-axis). Use a whole sheet of graph paper, draw in pencil and take care when sketching the free-hand curve through the points. Stick the graph in your jotter. Distance from Earth (km) 1000 2500 5000 7500 10000 Gravitational Field Strength (N/kg) 10 7.3 5.1 3.1 2.2 1.5

1 From the graph, find out how far from the surface of the Earth you would have to travel in order to experience gravitational field strength exactly one quarter of what it is on the surface. 2 A space station, orbits the Earth at a height of 220 km. Use your graph to find the gravitational field strength at this distance from Earth. 3 An astronaut on board the space station has a mass of 60 kg. Find her weight on board the space station.

4 The moon orbits the Earth at a distance of 384000 km from the centre of the Earth. How do we know that the Earth’s gravity must extend at least this distance out into space?

5 When you see videos of people on board space stations, you see them “floating” in the cabin. They appear to be weightless. True weightlessness can only happen where the pull of gravity is zero. Using the figures from the graph, explain why the cosmonauts could not be truly weightless.

A person in a spacecraft in orbit above the Earth clearly appears to be weightless but we know that the gravitational field strength there is not zero. To be truly weightless you must go so far away from any planet or star so that the gravitational field strength is zero. Astronauts in orbit appear to be weightless because they are “falling” to Earth at exactly the same rate as the spacecraft they are in. They are in permanent “free-fall”.  

For example: James is standing still in an aeroplane. In his right hand, he is holding a force meter with a 3 kg mass hanging from it. Due to its weight, the mass exerts a downward force on the force meter. James jumps out the airplane, still holding the force meter with the 3 kg mass hanging from it. Both the force meter and the 3 kg mass are now in free-fall. They are both accelerating downwards towards the Earth at the same rate of10 m/s2. Because the force meter and The 3 kg mass are falling at the same rate, the mass does not exert a downwards force on the force meter - So the reading on the force meter is 0 N. (The 3 kg mass appears to be weightless as it falls freely.)

Newton’s third law is actually very simple. “To every action there is always opposed an equal reaction.” In other words if you push against a wall, the wall pushes against you. When Newton was talking about actions and reactions he was talking about forces. Can you think up any more “Newton pairs” – two forces acting in opposition to each other? Here is one example: The force of a swimmer backwards on the water. The force of the water forwards on the swimmer. Write any more you can think of in your jotter.

For each of the four diagrams, draw arrows clearly showing the two forces acting at the contact point. Name the two forces (eg in diagram 1 the forces will be – the force of the boot on the ball and the forces of the ball on the boot).

1 While driving down the road, Anna Litical observed a fly striking the windshield of her car. Quite obviously, a case of Newton's third law of motion. The fly hit the windshield and the windshield hit the bug. Which of the two forces is greater: the force on the bug or the force on the windshield?

You saw that any action force must have an equal and opposite reaction force. This principle is used in the only type of motor capable of operating in space – the rocket. All other types of motor require air to work.   Propellant gases force the Rocket forwards (action) Rocket motors force the propellant gases backwards (action) For a rocket to escape the Earth’s gravitational pull, it must reach a speed of over 11000 m/s. Modern rockets use paraffin or hydrogen as the fuel. To support the tremendous rate of fuel burn required, a large supply of oxygen is needed. This will be carried in the form of liquid oxygen.

 1 (a) What is the only of motor that can be used in space? (b) Why is this the only form of motor that can be used? Why do rockets carry a supply of liquid oxygen? What advantages might there be in using liquid fuel rather than solid fuel? Explain, using Newton’s 3rd law, how a rocket motor works

What is happening to the force, acting on the people, who are on board the plane vomit comet as it accelerates to the ground at 10 m/s2

SQA I2 2003 Q22. A spacecraft travels through space between planet X and planet Y. Information on these planets is shown in the table below. The spacecraft has a total mass of 2.5x 106 kg. The spacecraft engines produce a total force of 3.8x107 N. (a) The spacecraft is initially on planet X. (i) Calculate the weight of the spacecraft when it is on the surface of planet X.

(ii) Sketch a diagram showing the forces acting on the spacecraft just as it lifts off from planet X. You must name these forces and show their directions. (iii) Calculate the acceleration of the spacecraft as it lifts off from planet X. (b) On another occasion, the spacecraft lifts off from planet Y. The mass and engine force of the spacecraft are the same as before. Is the acceleration as it lifts off from planet Y less than, more than or equal to the acceleration as it lifts off from planet X? You must give a reason for your answer using information contained in the table below.