# Question about the sun and the earth

• alias_none
In summary: Earth in the course of a year is 0. This is because the Earth's displacement is 0, as it travels in a circular path around the sun, and the force exerted by the sun is always perpendicular to the displacement. Therefore, the dot product of force and displacement is 0, resulting in no work being done. This is a fundamental principle of centripetal forces, which do not do work to displace a rotating object. In summary, the sun does no work on the Earth in its annual orbit due to the nature of centripetal forces and the circular path of the Earth's orbit.
alias_none
The sun exerts a force of 4.0 X 10^28 N on the earth, and the Earth travels 9.4 X 10^11 m in its annual orbit around the sun. How much work is done by the sun on the Earth in the course of a year? Explain.

This is a trick question. The one year length shouold tip you off that displacement is zero, but even if it wasn't, the force is always perpendicular to the displacement by definition. This means that a centripetal force of any kind does no work to displace the rotating object.

turdferguson said:
This is a trick question. The one year length shouold tip you off that displacement is zero, but even if it wasn't, the force is always perpendicular to the displacement by definition. This means that a centripetal force of any kind does no work to displace the rotating object.
Not quite. The work done is the dot product of force and displacement:

$$dW = \vec{F}\cdot \vec{ds} = Fds\cos\theta$$

Unless the orbit is perfectly circular (the Earth orbit is close to circular but is slightly elliptical) the force is not always perpendicular to velocity or displacement of the Earth (hence $\cos\theta \ne 0$ and $dW \ne 0$). However, over a period of a full year, as you have correctly pointed out, the total work is 0.

AM

## 1. How does the sun affect the Earth?

The sun affects the Earth in many ways. It provides light and heat, which are essential for life on our planet. The sun's gravity also keeps the Earth in its orbit, and its magnetic field protects us from harmful solar winds.

## 2. What is the distance between the sun and the Earth?

The average distance between the sun and the Earth is about 93 million miles or 149.6 million kilometers. This distance is also known as 1 astronomical unit (AU).

## 3. How does the Earth's tilt affect seasons?

The Earth's tilt on its axis is what causes the change in seasons. When the Northern Hemisphere is tilted towards the sun, it experiences summer, while the Southern Hemisphere experiences winter. As the Earth orbits the sun, the tilt changes, causing the seasons to shift.

## 4. How long does it take for the Earth to orbit the sun?

It takes the Earth approximately 365.24 days to orbit the sun. This is why we have a leap year every four years to account for the extra quarter of a day.

## 5. Is the sun getting bigger?

Yes, the sun is getting bigger. As it burns through its hydrogen fuel, it expands and becomes a red giant. However, this process takes billions of years, and it's not something we need to worry about in our lifetime.

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