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Earth is closer to the Sun in December than in June. In which of these two months is Earth moving...

Question:

Earth is closer to the Sun in December than in June. In which of these two months is Earth moving faster around the Sun?

Kepler's First Law of Planetary Motion

According to this law, the areal velocity of a planet is constant. The areal velocity means the area described by a planet per unit time. This law indicates that a planet represents equal areas in equal interval of time. This law is an application of the law of conservation of angular momentum.

Answer and Explanation:

The Kepler's first law of planetary motion is based upon the law of conservation of angular momentum. According to this law, if there is no external unbalanced torque acting on the object, then its angular momentum is conserved. The statement is known as the law of conservation of angular momentum.

If m is the mass of the planet, which remains constant.

v is the velocity of the planet,

r is the magnitude of the radius vector of the planet,

L is the angular momentum of the planet, then

L= m X v X r.

Let {eq}r_1,\space r_2, r_2>r_1 {/eq} are the magnitudes of the radius vector of the planet from the Sun in December and June respectively.

{eq}v1,\space v_2{/eq} are the magnitudes of the velocities of the planet in December and June respectively.

There is no external torque rating on the planet. hence its angular momentum is constant.

{eq}m \times r_1 \times v_1 = m \times r_2 \times v_2,\\ r_1 \times v_1 = r_2 \times v_2,\\ r_2>r_1, \space hence \space v_1>v_2, \\ {/eq}

Therefore the earth will move faster in the month of December.

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Learn more about this topic:

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Kepler's Three Laws of Planetary Motion

from Basics of Astronomy

Chapter 22 / Lesson 12
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