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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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.

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 from Saturn to the satellite because the orbit is an ellipse, according to Kepler’s first law. If distance is in thousands of kilometres, then we will have to multiply the values times 106 to get distance in metres.

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The period of motion is in days; therefore, we will have to multiply them by 24, and twice by 60.

It is known that centripetal acceleration and velocity are:

                        

Centripetal acceleration can be therefore described as:

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

To investigate the inverse squared of radius, it is known that:

        and        

We can relate these equations

To find M (mass of Saturn) we can plot a graph where centripetal acceleration is in the y-axis and G ...

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