CBB039 : Numerical Methods

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

h) Radius at the pole

Show all your working and state any assumptions you make in reaching your answers.

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.

Part C

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

Answer:

PART A

a) Mean density for earth and Pluto

 

• Mean density for Earth.

Mass = 5.978 x 10²⁴ kg

 

b) Surface area for earth and Pluto

Surface area of earth

Since the earth is spherical

   

 

c) Speed of rotation at the equator for earth and Pluto

• Speed of rotation of the earth

 

                                     

                                           

 

 

 

d) Mean speed of travel around the sun

 Speed of earth round the sun

                                   

                                                                    

 

e) Gravitational field strength at the planet’s surface

  Gravitational field strength on earth’s surface

                                                 

                                                      

 

 f) Escape velocity at the surface

 Escape velocity on the surface of the earth

                                                           

 

g) Solar constant at the planet’s surface

  Solar constant at the earth’s surface

                                                                                                                                             

If the radiation intensity is inversely proportional to the square of distance from the sun, therefore;

                                              

 

h) Radius at the pole

 Radius of the earth at the pole

                                                         

                                             

 

 

                    

 

4.Question

Comparing the planet earth and Pluto we find that the gravitational strength on the surface of Pluto is less (3.71N/kg) compared to that on the surface of the earth which is 9.81N/kg. The solar intensity on the planet Pluto compared to planet earth is much higher considering solar constant on Pluto is  and that on the surface of the earth is

PART B

Height, h / km	Pressure, Ph / Pa
0	101.3
10	31.24
20	9.63
30	2.97
40	0.96
50	0.28
60	0.087

 

 

                                                         

 

PART C

a)

Satellite	Period of orbit, T / days	Radius of orbit, R / x106 m	Log T	Log R
Io	1.77	422	0.248	2.625
Europa	3.55	671	0.55	2.828
Ganymede	7.15	1070	0.854	3.03
Callisto	16.69	1883	1.22	3.27

 

 

           

                                        

                                                             

(e) new acceleration due to gravity

                                      

                                       

Since the value of R² is 0.99. It can be concluded that the model is reliable since 99% of variation in the acceleration is explained by the variation in time.