Question

Calculate the earth's average speed relative to the sun.
b.what is the earth's average velocity over a period of one year?

Answer 1

a).  The Earth travels around the sun in a path that's nearly a circle, with a radius of roughly 93 million miles.

The circumference of the circle is (2 · π · radius) = about  5.843 x 10⁸  miles.

Average Speed = (distance covered) / (time to cover the distance)

The time to cover the distance is 1 year.

Speed = (5.843 x 10⁸ mile/year) (year / 365 day) (day / 24 hour)

Speed = (5.843 x 10⁸ / 365·24) (mile · year · day / year · day · hour)

Average speed = 66,705 miles/hour .

b). The Earth's average velocity over a period of 1 year is zero.

Velocity = (displacement) / (time)

Displacement = (distance and direction between start-point and end-point). After one year, the Earth is located at the point where it started, so its displacement over the period of 1 year is zero.

Answer 2

The correct values are;

a. The average speed of the Earth relative to the Sun is approximately 29,785.68 m/s

b. The average velocity of the Earth over a period of one year is 0

The reason the above values are correct are given as follows;

$a. \ Average \ speed = \dfrac{Total \ distance}{Total \ time}$

The total distance traveled by the Earth relative to the Sun, is given by the length of the orbit of the Earth around the Sun ≈ 2 × $R_{ave}$ × π

Where;

$R_{ave}$  = The average distance at which the Earth orbits around the Sun = 149.60 million km

Distance traveled by Earth ≈ 2 × 149.6 × 10⁹ × π

The time it takes to revolve once around the Sun = 365.25 days

365.25 days = ${365.25 \ days}\times \dfrac{24 \ hours}{1\ Day} \times \dfrac{3,600 \ s}{1 \ hour} = 31,557,600 \ s$

$Average \ speed \ of \ the \ Earth = \dfrac{2 \times 149.6 \times 10^9 \times \pi \ m}{31,557,600 \ s} \approx 29,785.68 \ m/s$

The average speed of the Earth relative to the Sun ≈ 29,785.68 m/s

b. $Average \ velocity= \dfrac{Total \ displacement}{Total \ time}$

The Earth's average velocity over a period of one year is given as follows;

Total displacement of the Earth = Final position - Initial position

The motion of the Earth round the Sun is circular, and in a period of one year, the Earth revolves once round the Sun

Therefore, after exactly one year, relative to the Sun;

Final position of the Earth = Initial position of the Earth

Relative to the Sun, in one year, we have;

Displacement = Final position of the Earth - Initial position of the Earth = 0

Therefore;

$Average \ velocity \ of \ the \ Sun= \dfrac{0 }{31,557,600 \ s} = 0$

The Earth is located in the same place relative to the Sun after a period of one year

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