# CBB039 : Numerical Methods

## Question:

Part A

The task is to compare a given planet with the Earth.Your planet is ………………..

Using the data provided in the table, calculate the following values for the Earth and for your planet.

a) Mean density

b) Surface area

c) Speed of rotation at the equator

d) Mean speed of travel around the Sun

e) Gravitational field strength at the planet’s surface

f) Escape velocity at surface

g) Solar constant at the planet’s surface

2.Create 2-dimensional scale models of the Earth and your planet at a scale of 1: 108. [Models will be displayed during Morley Festival in July.]

3.A scale model of the solar system is to be displayed in a corridor of length 24m. Choose an appropriate scale and calculate the position of each planet.

4.Based on these calculations and other information and/or calculations of your own choice, write an account describing the conditions at the surface of your given planet.

Part B

Calculate the atmospheric pressure at different heights above the Earth’s surface using the formula provided. Record your results in the table below.

 Height, h / km Pressure, Ph / Pa 0 10 20 30 40 50 60

#### Find the height at which the pressure is 20 kPa.

Part C

The following data was collected to investigate the orbit of moons of Jupiter.

 Satellite Period of orbit, T / days Radius of orbit, R / x106 m Log T Log R Io 1.77 422 Europa 3.55 671 Ganymede 7.15 1070 Callisto 16.69 1883

 The graph of T against R gives a curve in the shape of a parabola. This suggests that the relationship between T and R is of the form   T = a Rb where a and b are constants   If we take logs of both sides we get   log T = b log R + log a   Comparing this equation with the equation for straight line:   y = m x + c   A graph of log T against log R will have gradient = b

a) Find the values of log T and log R and add them to the table
b) Plot a graph of log Tagainst log R
c) Measure the gradient and find the value of b

Part D

An object is above the surface of your planet at a height equal to the radius of the planet.

a) Calculate the acceleration due to gravity at this height

b) Calculate the distance fallen in 100 seconds (assuming the acceleration is constant during that time).

c) Calculate the speed after 100 seconds.

e) Calculate the new height above the surface of the planet.

f) Calculate the new acceleration due to gravity.

Design a spreadsheet to calculate the time taken for the object to fall to the surface of the planet.

Evaluate the reliability of your model.

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