Solving Kepler's Laws: Calculating a, b, and f in Mkm

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The discussion focuses on calculating the semi-major axis (a), semi-minor axis (b), and focal length (f) of an ellipse in the context of Kepler's Laws. The semi-major axis is determined by averaging the distances from the Earth (150 Mkm) and Mars (230 Mkm) to the Sun, resulting in a value of 190 Mkm. The focal length is calculated by subtracting the Earth's distance from the semi-major axis, yielding 40 Mkm. The semi-minor axis is derived using the equation b = SQRT(a² - f²), leading to a final value of approximately 189.8 Mkm.

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[SOLVED] Keplers Laws

Please identify the length of the semi-major axis, the semi-minor axis, and the focal length of the ellipse. Specify each of these quantities in millions of km (Mkm).

The semi-major axis (a) is the distance to the center of the ellipse along the major axis. The center of the ellipse is halfway between the two foci (one of which is the Sun).

1. The distance from the Earth to the Sun is 150 million km (Mkm)
2. The distance from Mars to the Sun is 230 million km (Mkm)

Hints:

To determine the length of the semi-major axis first determine the length of the major axis (using the information above) and divide it in half.

To determine the focal length, subtract the Earth's distance to the sun from the semi-major axis.

To determine the length of the semi-minor axis, use the equation below.

f2 = a2 - b2 or b2 = (a2-f2) 1/2 or b = SQRT (a2 - f2)

Totally Lost can you please help me.
 
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Sorry,

I am confused because I am unsure sure if I am supposed to find the Earth's major axis. This is what I did:
By using Kepler's Third law and the mass of the Sun the universal constant G.

2a = cube root of ((GMT^2)/(4pi^2))
which gives me 2.99 x 10^-11 m.

But I'm not sure is this is the correct approach. As I did not take into consideration the distances?

Thanks
 

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