How Is Satellite Orbit Speed Calculated with Atmospheric Resistance?

[Bjarne]

When a satellite is affected by resistance against orbit motion,
for example from thin atmosphere or solar wind, it will as a result of this decelerates -
but in that process it will decrease slightly toward the earth, and therefore following accelerate too.
How can the new orbit speed be calculated?

 

[Filip Larsen]

You may want to search and read up on the concept of "orbital decay" to get an idea of how orbital mechanics works in the presence of drag forces.

 

[Bjarne]

You may want to search and read up on the concept of "orbital decay" to get an idea of how orbital mechanics works in the presence of drag forces.

I tried, and found how to calculate a lot related to that question, but now how to calculate orbit speed change.

Let's say the resistance against motion is 1E-10m/s^2
Due to the resistance the satellite will decrease towards the Earth, and hence the orbit speed will also increase, as well as it will decrease due to the resistance.

 

[Filip Larsen]

From an assumed constant deceleration due to drag you can find the change in speed due to this deceleration simply by multiplying with time. In a more detailed calculation you would instead (numerically) integrate the instantaneous deceleration over a period of time, along with other accelerations, in order to get a more accurate trajectory of the satellite.

But I'm not sure why you'd want to know this? In general, as long as the change in speed is low enough for the satellite still to be in orbit, then the most significant effect of the drag at any particular point in the orbit is to reduce the orbital height at the opposite side of the orbit. This means that low drag generally acts to first circularize the orbit and then, when the orbit is mostly circular, to lower the overall height. Thus, the change in orbital speed due to drag is closely connected to the change in orbital height, and it is usually the orbital height, rather than speed, that is in primary interest when you look at orbital decay.

 

[pmacias]

The new orbit speed can be calculated by using the conservation of energy and angular momentum principles. The decrease in altitude due to the deceleration will result in a decrease in potential energy, while the increase in velocity due to the acceleration will result in an increase in kinetic energy. By equating the changes in potential and kinetic energy, we can solve for the new velocity. Additionally, the angular momentum of the satellite will also change due to the change in altitude, so we can use the equation for angular momentum to calculate the new velocity as well. It is important to also take into account the effects of any external forces, such as drag from the atmosphere or gravitational pull from other objects, when calculating the new orbit speed. This calculation can be complex and may require advanced mathematical techniques, but it is crucial for accurately predicting the trajectory and behavior of satellites in orbit.