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

• goldfronts1
In summary, the semi-major axis is the distance to the center of the ellipse along the major axis, which can be determined by dividing the length of the major axis (which is the sum of the distances from Earth to the Sun and from Mars to the Sun) by 2. The focal length can be found by subtracting the Earth's distance to the Sun from the semi-major axis. To find the semi-minor axis, the equation b2 = (a2-f2) 1/2 can be used, where a is the semi-major axis and f is the focal length. The approach of using Kepler's Third law and the mass of the Sun with the universal constant G may not be the correct approach as it does not
goldfronts1
[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)

We're not going to do your homework for you. You need to show your work, show us your thoughts, and explain to us exactly why you're stuck.

- Warren

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

## 1. How do you calculate the semi-major axis (a) in Mkm?

The semi-major axis (a) can be calculated using the formula: a = (T2 * G * Ms) / (4 * π2)^(2/3), where T is the orbital period in seconds, G is the gravitational constant, and Ms is the mass of the central body in kilograms.

## 2. What is the formula for calculating the semi-minor axis (b) in Mkm?

The semi-minor axis (b) can be calculated using the formula: b = a * √(1 - e2), where a is the semi-major axis and e is the eccentricity of the orbit.

## 3. How do you determine the focal distance (f) in Mkm?

The focal distance (f) can be determined using the formula: f = √(a2 - b2), where a is the semi-major axis and b is the semi-minor axis. This can also be written as f = a * e, where e is the eccentricity of the orbit.

## 4. Can Kepler's laws be applied to any orbit?

Yes, Kepler's laws can be applied to any orbit, as long as the orbit is elliptical and the central body is much more massive than the orbiting body. These laws do not apply to objects in circular or hyperbolic orbits.

## 5. How can the mass of the central body be determined using Kepler's laws?

The mass of the central body can be determined using the formula: Ms = (4 * π2 * a3) / (G * T2), where a is the semi-major axis and T is the orbital period. This formula assumes that the mass of the orbiting body is much smaller than the central body's mass.

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