• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

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.

This student written piece of work is one of many that can be found in our AS and A Level Core & Pure Mathematics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Core & Pure Mathematics essays

  1. Marked by a teacher

    The Gradient Function

    5 star(s)

    + 12x�h� + 8xh� h h = 2h� + 8x� + 12x�h + 8xh� After doing this so many times, I can tell that every term containing an h will disappear. The one exception to this = 8x�. This is the answer I had previously predicted, and therefore my theory was correct.

  2. Investigation on Boyles law

    all the atoms are in smaller, more compact space so they all hit the sides increasing the pressure. But if you increase the volume then you enlarge the surface area and the atoms have more room to move so less hit the sides and this causes an increase in pressure.

  1. Methods of Advanced Mathematics (C3) Coursework.

    -2.35133 -2.4528 -2.4528 -2.4806 -2.4806 -2.4881 -2.4881 -2.49012 -2.49012 -2.49066 -2.49066 -2.49081 I found with this equation that the Newton-raphson method was the fastest to converge to the route. It was very reliable and it was difficult to find an equation for which it didn't work.

  2. Mathematics Coursework - OCR A Level

    x-value y-value x-y 0.25 0.250858 -0.00086 0.250858 0.249244 0.001614 0.249244 0.252274 -0.00303 0.252274 0.24656 0.005714 0.24656 0.257243 -0.01068 0.257243 0.236932 0.020311 0.236932 0.274423 -0.03749 0.274423 0.200613 0.07381 0.200613 0.332207 -0.13159 0.332207 #NUM! #NUM! #NUM! #NUM! #NUM! From the above table that I made in Microsoft Excel, it is evident that

  1. Arctic Research (Maths Coursework)

    I will start with my base camp in the middle. This is a good position to start as all the observation sites are at equal distances of 50 km (which is the radius) from the base camp. It will also enable me see how the journey times are affected in

  2. Maths - Investigate how many people can be carried in each type of vessel.

    We will substitute them back into the equations that we began with. (20 X 8) + (5 X 5) + (10 X 4) = 225 (10 X 8) + (15 X 5)

  1. The Gradient Fraction

    'y=4x+1' solved by the 'Triangle Method' I will now go on further with straight line graphs. The graph below is a graph of 'y=4x+1'. By looking at the equation, it tells me that the straight line will cross through the +1 in the y axis.

  2. Functions Coursework - A2 Maths

    To illustrate the fact that the root lies in the interval [1.87,1.88], part of the graph of y=f(x) is drawn. The graph crosses the x-axis visibly between x=1.87 and x=1.88. This means that between x=1 and x=2, y=f(x)=0 for a value of x in the interval [1.87,1.88] i.e.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work