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Modelling the Solar System. In this lab we are going to investigate data concerning orbital motion around Saturn. We will work out the centripetal acceleration and the inverse squared of radius.

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Introduction

Maria Cardoso-BotelhoIB PhysicsSt. Dominic’s International Schol

Modelling the solar system

Newton’s Law of Gravitation states that the force of attraction between two bodies is directly proportional to the product of their masses and inversely proportional to the distance between their centres of masses squared.

image00.png

Aim

In this lab we are going to investigate data concerning orbital motion around Saturn. We will work out the centripetal acceleration and the inverse squared of radius.

Data table and processing

First, we will have to convert our units to SI units.

Distance is the average radius

...read more.

Middle

× 106

Iapetus

3.561 × 109

6.854  × 106

Phoebe

1.295 × 1010

4.756  × 107

It is known that centripetal acceleration and velocity are:

image01.png

image02.png

Centripetal acceleration can be therefore described as:

image03.png

The following table describes the centripetal acceleration and the velocity of the satellites.

SATELLITE

VELOCITY (ms-1)

CENTRIPETAL ACCELERATION (ms-2)

Pan

2.030 × 104

3.076

Atlas

1.672 × 104

2.027

Prometheus

1.657  × 104

1.976

Pandora

1.639 × 104

1.892

Epimetheus

1.591 × 104

1.677

Janus

1.592 × 104

1.677

Mimas

1.439 × 104

1.113

...read more.

Conclusion

5,777 × 1026

Enceladus

5,698 × 1026

Tethys

5,701 × 1026

Telesto

5,701 × 1026

Calypso

5,701 × 1026

Dione

5,661 × 1026

Helene

5,661 × 1026

Rhea

5,68 × 1026

SATELLITE

MASS OF SATURN (kg)

Titan

5,711 × 1026

Hyperion

5,690 × 1026

Iapetus

5,692 × 1026

Phoebe

5,688 × 1026

By making an average of the mass of Saturn, we will get 5,708 × 1026.

To make sure these results are accurate, the percentage error will be calculated:

image09.png

The mass of Saturn is 5,685× 1026. Thus:

image10.png

This proves that the data is accurate.

As the distance between the planet and the satellites increases, the centripetal acceleration decreases.

This proves that Newton’s Law of Gravitation is correct, even though this is only an approximation, because for each satellite, there are more forces of attraction acting on than Saturn’s. This can be the force of attraction caused by other satellites.

...read more.

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