# Finding the period of the satellite's orbital motion

• rwssman
In summary, the period of a satellite's orbital motion is the time it takes for the satellite to complete one full orbit around its parent body. It can be calculated using Kepler's third law and is important for predicting the satellite's position, determining its coverage area, and calculating task completion time. The period can change due to various factors, but it typically has an inverse relationship with the satellite's speed.
rwssman

## Homework Statement

I want to find the period of the satellite.

mg = mv^2/r

## The Attempt at a Solution

I derive the equation
mg = mv^2/r
v = sqrt(gr)
v = ωr and ω = 2π/T

T = 2π/ω = 2πr/v

Then, T = 2πr/sqrt(gr)

But the answer is 2πr/R * sqrt(r/g). I don't know why? Is there anyone can give an explanation to me why it is not correct.

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Hi,

From the text: ##g## at the surface is not ##g## far away ...

## 1. What is the period of a satellite's orbital motion?

The period of a satellite's orbital motion refers to the time it takes for the satellite to complete one full orbit around its parent body, such as a planet or moon.

## 2. How is the period of a satellite's orbital motion calculated?

The period of a satellite's orbital motion can be calculated using Kepler's third law, which states that the square of a satellite's orbital period is proportional to the cube of its average distance from the parent body, or by using the satellite's orbital velocity and distance from the parent body.

## 3. What factors affect the period of a satellite's orbital motion?

The period of a satellite's orbital motion is primarily affected by the satellite's distance from the parent body and the mass of the parent body. Other factors that may influence the period include the presence of other celestial bodies, atmospheric drag, and the shape of the satellite's orbit.

## 4. Can the period of a satellite's orbital motion change?

Yes, the period of a satellite's orbital motion can change due to various factors such as changes in the parent body's mass or gravitational pull, collisions with other objects, or external forces acting on the satellite, such as atmospheric drag or thrust from a spacecraft.

## 5. Why is understanding the period of a satellite's orbital motion important?

Understanding the period of a satellite's orbital motion is important for predicting the satellite's location and trajectory, as well as for planning space missions. It also provides valuable information about the parent body's mass and gravitational force, and can help scientists study the dynamics of celestial bodies and their interactions.

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