Question

At its closest approach to the sun (perihelion), the Earth is approximately 1.46 E 8 km away from our closest star. At aphelion, the point furthest away in its orbit, the Earth is approximately 1.52 E 8 km away. Which of the following is a true statement?The speed at aphelion and perihelion are equal.At aphelion, the Earth is traveling at its highest speed.At perihelion, the Earth is traveling at its highest speed.At perihelion, the Earth is traveling at its lowest speed.

Answer 1

Given:

The distance between the sun and earth at perihelion, p=1.46×10⁸ km

The distance between the sun and the earth at aphelion, a=1.52×10⁸ km

To find:

Which of the given option is a true statement?

Step-by-step explanation:

The gravitational force between the sun and the earth keeps the earth in its orbit around the sun by providing the necessary centripetal force.

Thus,

`\begin{gathered} (GMm)/(r^2)=(mv^2)/(r) \\ \Rightarrow v^2=(GM)/(r) \end{gathered}`

Where m is the mass of the earth, M is the mass of the sun, G is the gravitational constant, v is the velocity of the earth and r is the radius of the earth's orbit.

From the above equation, it is clear that the speed is inversely proportional to the radius or the distance between the sun and the earth.

Thus the speed of the earth will be the highest when the distance between the earth and the sun is lowest. And the speed will be the lowest when the distance between the earth and the sun is highest.

Final answer;

Thus the speed of the earth will be highest at perihelion.

Therefore the correct answer is option C.