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

  • Thread starter goldfronts1
  • Start date
  • Tags
    Laws
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
  • #1
goldfronts1
32
0
[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.
 
Physics news on Phys.org
  • #2
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
 
  • #3
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.

Similar threads

Find the location knowing the resonance using Kepler's third law
    • Introductory Physics Homework Help
Replies
2
Views
442
What is the R^3 in Kepler's 3rd Law?
    • Introductory Physics Homework Help
Replies
7
Views
1K
Calculate the time for a spacecraft to arrive at Mars (No Kepler's law)
    • Introductory Physics Homework Help
Replies
19
Views
3K
Mercury's orbit according to Classical VS Modern Physics
    • Introductory Physics Homework Help
Replies
3
Views
1K
I Kepler orbits for planets of similar masses
    • Classical Physics
Replies
2
Views
803
B How long it takes the Earth to fall halfway to the Sun--ellipse method
    • Classical Physics
Replies
3
Views
982
Gravitation - Period of revolution of planet
    • Introductory Physics Homework Help
Replies
10
Views
5K
How Do You Calculate the Semi-Minor Axis for a Spacecraft's Orbit?
    • Introductory Physics Homework Help
Replies
2
Views
2K
Kepler's laws and proof using angular momentum
    • Mechanics
Replies
1
Views
907
Is This How a Spaceship Enters Mars?
    • Introductory Physics Homework Help
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top