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In this coursework I am going to investigate the relationship between the orbital period and the distance of the planet from the sun. Assume that this relationship is a power law of the form: T = KR^n

Extracts from this document...

Introduction

Zahra Balal        A/S Use of Maths        

Planetary Motion

Introduction:

The German astronomer Johann Kepler studied the relative motion of the planets and discovered a relationship between their orbital periods and their means distance from the sun

Aim:

In this coursework I am going to investigate the relationship between the orbital period and the distance of the planet from the sun.

Assume that this relationship is a power law of the form:

T = KR^n

T = the time for full cycle around the sun.

R = Mean distance of the planet from the sun.

K and N are constant.

K = is the gradient

...read more.

Middle

Saturn

1427

3.154423973

10753

4.031529646

Uranus

2870

3.457881997

30660

4.486572151

Neptune

4497

3.652922888

60150

4.779235632

Pluto

5907

3.771366971

90670

4.957463616

After calculating the all of the logs I have insert them into excel spreadsheet and displayed the equation of the line.

image00.png

Now that you have the equation y = 1.5001x – 0.7003

I will transfer it to T = KR^n

1.5001 is the gradient, which is n

-0.7003 is the y intercept (c), which is log K but you should

...read more.

Conclusion

rowspan="1">

2870

30680.93802

30660

4497

60179.6453

60150

5907

90599.87385

90670

Percentage error:

((Actual data -Model) /Actual Data)*100

((88-88.10860661)/88)*100

Model

T

T = 10^-0.7003 x (R)^1.5001

Actual Data

Predicted Error

88

88

0%

224

225

0.444444444%

366

365

0.273972603%

687

687

0%

4330

4329

0.023100023%

10756

10753

0.027899191%

30681

30660

0.068493151%

60180

60150

0.049875312%

90600

90670

0.077203044%

Conclusion:

After doing the above course work I have found out that, I have achieved many things and I can list them as:

  • Calculating the logs of R and T
  • Drawing graph by using the result from R and T logs
  • Determining an accurate linear equation of logs (both R and T)
  • Rearranging log k= 0.7003 into 10^-0.7003 then putting it into the equation of T= kR so it will look like: T= 10^-0.7003* (R) ^1.5001.
  • Applying the rules 1 and 3 to rearrange the equation T= KR
  • Determining the correct equation for the line T= 10^-0.7003*(R ^1.5001)

...read more.

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