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9.2 Space: 2. A successful rocket launch

Syllabus reference (October 2002 version)
2. Many factors have to be taken into account to achieve a successful rocket launch, maintain a stable orbit and return to Earth
Students learn to: Students:

Extract from Physics Stage 6 Syllabus (Amended October 2002). © Board of Studies, NSW.
[Edit: 11 June 10]

Prior learning: Preliminary modules 8.4 (subsection 1), 8.5 (subsection 4)

Background: This section is concerned with the context of launching a spacecraft, orbiting it around the Earth and the issues of re-entry. It begins by considering projectile motion, within this context, and then proceeds to rocket launches.

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solve problems and analyse information to calculate the actual velocity of a projectile from its horizontal and vertical components using:    calculation of actual velocity

Here are two sample problems with solutions:

  1. Five seconds after launch, a projectile is tracked on radar moving upwards at 26 m s-1 at an angle of 300 to the horizon. What are the vertical and horizontal components of motion?

    Solution: The vertical component is vy; the horizontal component in this case is vx
    Vx = v cos theta = 13.0ms to -1, Vy = v sin theta = 22.5ms to -1
  2. Five seconds after launch from Earth, a projectile has a horizontal velocity of 23.0 m s-1 and a vertical velocity of 11.5 m s-1 up. Determine its velocity.

    Hint: when calculating velocity, which is a vector quantity, it is usual to show both the magnitude and direction of motion. This is a general rule to use when calculating all vector quantities when no other direction is given in the question.

    Solution:
    equation

Here are two other problems for you to solve:

  1. A test rocket flight is tracked on radar, which displays its horizontal component of velocity at 7.5 m s-1 and its vertical component of velocity at 1.4 m s-1 down. Calculate its actual velocity.

  2. A piece of space junk is being tracked by radar on a ship in the Pacific as it plunges into the ocean. The vertical and horizontal components of the object’s velocity are 7.5 m s-1 and 16 m s-1 respectively. Calculate the actual velocity of the falling object.

Answers

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describe the trajectory of an object undergoing projectile motion within the Earth’s gravitational field in terms of horizontal and vertical components

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describe Galileo’s analysis of projectile motion

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perform a first-hand investigation, gather secondary information and analyse data to calculate initial and final velocity, maximum height reached, range, time of flight of a projectile for a range of situations by using simulations, data loggers and computer analysis

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explain the concept of escape velocity in terms of the:

  • gravitational constant
  • mass and radius of the planet

Background

A useful equation

From the relationship described above, the following expression for escape velocity of a planet can be deduced.

Escape velocity equation

The physics syllabus does NOT require students to know or manipulate this equation.

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outline Newton’s concept of escape velocity

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identify why the term ‘g forces’ is used to explain the forces acting on an astronaut during launch

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identify data sources, gather, analyse and present information on the contribution of one of the following to the development of space exploration: Tsiolkovsky, Oberth, Goddard, Esnault-Pelterie, O‘Neill or von Braun

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discuss the effect of the Earth's orbital motion and its rotational motion on the launch of a rocket

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analyse the changing acceleration of a rocket during launch in terms of the:

  • Law of Conservation of Momentum
  • forces experienced by astronauts
  • Law of Conservation of Momentum
Graphical explanation of Newton's third law -F rocket on gases = F rocket on gases
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analyse the forces involved in uniform circular motion for a range of objects, including satellites orbiting the Earth

Circular motion Source of centripetal force
Ball on a string whirled in a circle Tension in the string
Car driving around a corner Friction between the tyres and the road
Satellite orbiting the Earth Gravitational attraction between the Earth and the satellite
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compare qualitatively low Earth and geo-stationary orbits

Background information outside the syllabus

If you want to work through these figures for yourself, the formulae you need are provided below. They may assist you to understand what is happening in the next activity as well.

Note: the formulae and calculations here are beyond the scope of the syllabus at this point.

The centripetal force to maintain an orbit is provided by gravity.
Fgravity = Fcentripetal

GMms/r2 = msv2/r
M = mass of earth (kg); ms = mass of satellite (kg); G = universal gravitational constant; v = orbital speed in linear terms (ms-1) & r = the orbital radius (m)

The orbital speed (v) can also be calculated from the orbit path (2πr) divided by the period (T) of motion measured in seconds.
v = 2πr/T

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define the term orbital velocity and the quantitative and qualitative relationship between orbital velocity, the gravitational constant, mass of the central body, mass of the satellite and the radius of the orbit using Kepler's Law of Periods

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solve problems and analyse information to calculate centripetal force acting on a satellite undergoing uniform circular motion about the Earth using: F=mv2/r

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solve problems and analyse information using:

r-cubed divided by t-squared = GM divided by 4pi-squared

Sample problem 1: Determine the period of the orbit of the Hubble space telescope, given that its altitude is 600 km. Mass of the Earth = 6 × 1024 kg. Radius of Earth = 6 380 km.

Solution: Radius of the orbit = 6380 km + 600 km = 6.98× 106 m

Solution 1

Sample problem 2 (taken from specimen paper): A planet in another solar system has three moons, all of which travel in circular orbits. Some information about these moons is given in the table.

Moon Radius of orbit (orbs) Period of revolution (reps)
Alpha 4.0 16
Beta 9.0 54
Gamma 2.5

The radius of orbit and period of revolution are measured in orbs and reps respectively, which are not metric units.

  1. Use the data to show that Kepler’s third law is obeyed for the moons Alpha and Beta.
  2. Calculate the speed of moon Gamma in orbs/rep.

Solution:

Solution 2a

The first step is to calculate the period of Gamma’s orbit using Kepler’s third law:

Solution 2b

The orbital speed of Gamma can now be found as the circumference of its orbit divided by the period (remembering from Module 8.4, that the speed is related to distance and time where the distance here is the circumference and the time is the period).

Calculation of orbital speed
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account for the orbital decay of satellites in low Earth orbit

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discuss issues associated with safe re-entry for a manned spacecraft into the Earth’s atmosphere and landing on the Earth’s surface

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identify that there is an optimum angle for re-entry into the Earth’s atmosphere and the consequences of failing to achieve this angle

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