Changes

=='''Orbit eccentricity'''==

=='''Orbit eccentricity'''==

[[Image:Gravitation%20for%20wiki_html_m75870f64.gif|300px|left]] <br>The semi major axis of the ellipse is a and represents the planet's average distance from the Sun. The eccentricity, “e” is defined so that “ea” is the distance from the centre to either focus. A circle is a special case of an ellipse where the two foci coincide. The Earth and most of the other planets have nearly circular orbits. For Earth, “e” = 0.017.<br><br><br>

[[Image:Gravitation%20for%20wiki_html_m75870f64.gif|300px]] <br>The semi major axis of the ellipse is a and represents the planet's average distance from the Sun. The eccentricity, “e” is defined so that “ea” is the distance from the centre to either focus. A circle is a special case of an ellipse where the two foci coincide. The Earth and most of the other planets have nearly circular orbits. For Earth, “e” = 0.017.<br><br><br>

= The Law of Equal Areas =

= The Law of Equal Areas =

Kepler's second law states that each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal periods of time. This can be shown to be true using the law of conservation of angular momentum.

Kepler's second law states that each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal periods of time. This can be shown to be true using the law of conservation of angular momentum.

[[Image:Gravitation%20for%20wiki_html_m4a5ede30.png|300px|left]] <br> If “v” is the velocity of the planet, in time “dt” the planet moves a distance vdt and sweeps out an area equal to the area of a triangle of base “r” and altitude vdt sinα.

[[Image:Gravitation%20for%20wiki_html_m4a5ede30.png|300px]] <br> If “v” is the velocity of the planet, in time “dt” the planet moves a distance vdt and sweeps out an area equal to the area of a triangle of base “r” and altitude vdt sinα.

Hence dA = ½ (r) (“v” x “dt” x sinα)

Hence dA = ½ (r) (“v” x “dt” x sinα)

[[Image:Gravitation%20for%20wiki_html_m290004f7.gif]] <br>

[[Image:Gravitation%20for%20wiki_html_m290004f7.gif]] <br>

G m1 Ms / r12 = m1 (v12)/ r1

<math>G m_1*M_s / (r_1)^2 = m_1*(v_1)^2/ r_1</math>

v1 = 2πr1/T1

<math>v_1 = 2πr_1/T_1</math>

Substituting and rearranging we get

Substituting and rearranging we get

T12/ r13 = 4π2 / G Ms

<math>(T_1)^2)/(r_1)^3 = 4π^2/G*M_s</math>

Deriving this for another planet, we can arrive at the third law.<br><br>

Deriving this for another planet, we can arrive at the third law.<br><br>