# Spinning satellite - the velocity in the central mass

• Ante
In summary, the problem involves a satellite spinning clockwise with four low-mass panels sticking out. A tiny meteor rips through one of the panels, reducing its speed. The question asks for the vx and vy components of the center-mass velocity of the satellite. To solve this, the values for mass and radius are defined and a coordinate system is created. The central mass position is calculated using the formula R= total summ of (ri*m)/totalsum of m. It is assumed that the meteor's impact on the satellite's velocity is negligible according to Newton's third law. The velocity in the x-direction can be calculated using the formula vcm= total sum of m*vi/total sum of m, but the velocity in the
Ante

## Homework Statement

A satellite is spinning clockwise and has four low-mass panels sticking out. A tiny meteor rips through one of the panels and continues in the same direction, but with reduced speed. Afterward, calculate vx and vy components of the center-mass velocity of the satellite. Here is a picture I made in paint that demonstrates the problem. http://img529.imageshack.us/f/satellite.png/

## Homework Equations

Position of central mass R= total summ of (ri*m)/totalsum of m
vcm= total sum of m*vi/total sum of m

## The Attempt at a Solution

Since the question doesn't mention any values I decided to define the values as:

Mass of satellite = 2000kg
Radius of the satellite = 15m

Mass of one panel = 100kg
Radius of the panel = 10m

First, I made a coordinate system, where the origo is in the center of the satellite (so its centermas cancels out). I used the definition of the central mass (I assumed the masses are uniform) to prove the central mass is l/2. I calculated the central mass position with the formula R= total summ of (ri*m)/totalsum of m and showed its position in the center of the satellite. So in my graph, the positions of the panels central mass is the satellites radius + (l/2) where l is the length of the panels.

When the meteor hits one of the panels, it transfer one of its own energies according to momentum conservation $$\Delta$$Psys = $$\Delta$$P1+$$\Delta$$P2= 2, which is proved to the reduced speed of the meteor.

However, I assumed that the meteors effect on the satellites velocity is negligble according to Newtons third law. The meteor does go in high speed, but its mass is relative low compared to the satellite, and since it breaks through one of the panels, no "real" collision is happening.

I know that the velocity is vcm= total sum of m*vi/total sum of m which I assumed is the velocity in the X direction? How do I get the velocity in the y-component?

Do I need to calculate the velocity of each panel and then calculate the velocity of the central mass?Any help is appreciated.

## 1. What is a spinning satellite?

A spinning satellite is a man-made object that orbits around a celestial body while rotating on its own axis at a constant speed.

## 2. How does a spinning satellite maintain its velocity?

A spinning satellite maintains its velocity through the conservation of angular momentum, which is the product of its moment of inertia and its angular velocity.

## 3. What is the velocity in the central mass of a spinning satellite?

The velocity in the central mass of a spinning satellite is determined by its distance from the central body and its rotational speed. The closer the satellite is to the central body, the higher its velocity will be.

## 4. Can the velocity in the central mass of a spinning satellite change?

Yes, the velocity in the central mass of a spinning satellite can change if external forces such as gravity or atmospheric drag act upon it. However, as long as these forces are balanced, the velocity will remain constant.

## 5. What is the purpose of a spinning satellite?

The purpose of a spinning satellite is to perform various tasks such as communication, navigation, weather monitoring, and scientific research. They also help us gather information about our planet and the universe.

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