# Atmospheric drag on an artificial satellite orbiting the Earth

• Cristiano
In summary, the conversation discusses the calculation of x, y, and z components of atmospheric drag on an artificial satellite orbiting Earth. The Earth's rotation adds complexity to the calculation, but it is possible to find the relative velocity by subtracting the atmospheric motion from the satellite's velocity. The formula for the atmospheric rotation speed is also provided, but the exact method for calculating the x and y components is not mentioned. Further details such as the satellite's altitude and size are also needed for a complete calculation.
Cristiano
Consider an artificial satellite orbiting the Earth and suppose that the atmosphere co-rotates with the Earth.

I need to calculate x, y and z components of the atmospheric drag.

I know how to calculate the drag in a non-spinning atmosphere and I have all the data to do that, but the Earth’s rotation confuses me.

I know the x, y and z components of the satellite state (position and velocity). The z-axis is the Earth’s rotation axis and the x-axis and y-axis lie on the equatorial plane. The exes do not rotate (it’s an inertial reference frame).

The altitude of the satellite is not stated. Atmospheric drag is only significant for objects in low Earth orbits. The shape, size, and orientation of the satellite are also not stated.

You can calculate the x/y/z motion of the atmosphere at the position of the satellite and subtract that from the satellite velocity to find the relative velocity.

mfb said:
You can calculate the x/y/z motion of the atmosphere at the position of the satellite and subtract that from the satellite velocity to find the relative velocity.

There is no doubt, but how to calculate x/y of the atmosphere (rotating frame) in the satellite reference frame (inertial frame)?
I know that the atmosphere rotates with speed (with an adequate accuracy for me):
Vrot= (6378.137 + alt_satellite) * (2 * PI) / 86162 * cos(lat_satellite) [km/s]
the z component is always 0, but how to calculate x/y components?

##\vec v = \vec r \times \vec \omega## with the cross product.

## 1. What is atmospheric drag and how does it affect an artificial satellite?

Atmospheric drag is the resistance that an object experiences as it moves through the Earth's atmosphere. It is caused by the air molecules colliding with the object and creating a force in the opposite direction of motion. This force can significantly affect the orbit and trajectory of an artificial satellite, causing it to lose altitude and eventually fall out of orbit.

## 2. How do scientists measure atmospheric drag on a satellite?

Scientists use various methods to measure atmospheric drag on a satellite, including computer simulations, ground-based observations, and data collected by the satellite itself. They also take into account factors such as the satellite's mass, size, and shape, as well as the density and composition of the Earth's atmosphere at different altitudes.

## 3. Can atmospheric drag be predicted and accounted for in satellite orbits?

Yes, atmospheric drag can be predicted and accounted for in satellite orbits. Scientists use mathematical models and data from previous observations to estimate the amount of drag that a satellite will experience in its orbit. This information is then used to make adjustments to the satellite's trajectory and ensure that it stays in its intended orbit.

## 4. How does atmospheric drag affect the lifespan of a satellite?

Atmospheric drag is one of the main factors that determines the lifespan of a satellite. As a satellite experiences drag, it loses energy and gradually descends to lower altitudes. This can eventually lead to the satellite burning up in the Earth's atmosphere. To maintain a stable orbit and prolong its lifespan, satellites may need to periodically use thrusters to counteract the effects of atmospheric drag.

## 5. Are there any ways to reduce the impact of atmospheric drag on satellites?

Scientists and engineers have developed various techniques to reduce the impact of atmospheric drag on satellites. These include using materials that can withstand high temperatures and designing satellites with streamlined shapes to minimize drag. Some satellites may also use solar panels or other surfaces to increase the drag and slow down their descent, prolonging their lifespan in orbit.

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