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Write an equation for the orbit of Saturn in the form x^2/a^2 + y^2/b^2 = 1

*table is given showing Saturn has a semimajor axis (Gm) of 1472 and eccentricity of 0.0560

User Orius
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2.7k points

1 Answer

8 votes
8 votes

Answer:

x²/2166784 +y²/2159989 = 1

Explanation:

The relationship between the semi-axes and the eccentricity of an ellipse is ...

e = √(1 -b²/a²)

In order to write the desired equation we need to find 'b' from 'e' and 'a'.

__

semi-minor axis

Squaring the equation for eccentricity gives ...

e² = 1 -b²/a²

Solving for b², we have ...

b²/a² = 1 -e²

b² = a²(1 -e²)

ellipse equation

Using the given values, we find ...

b² = 1472²(1 -0.056²) = 2166784(0.996864) ≈ 2159989

The desired equation is ...

x²/2166784 +y²/2159989 = 1

Write an equation for the orbit of Saturn in the form x^2/a^2 + y^2/b^2 = 1 *table-example-1
User Edwin De Koning
by
2.4k points
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