4.5. Decelerating Spacecraft

When a spacecraft is landing on the surface, it decelerates. The rate of change of the momentum flux within the control volume is equal to the net outflux of momentum flux passing through the control surface, in the absence of external forces.

This chunk explains the principle of momentum conservation within a control volume during the landing of a spacecraft. When no external forces act upon the spacecraft, the change in momentum is only due to the fuel or thrust operations. It's essential to consider both the incoming and outgoing momentum fluxes when analyzing how the craft decelerates.

Think of a skateboarder coming to a stop. As they push backward against the ground with their foot, they are exerting a force to slow down. In this case, the skateboard is the control volume, the skateboarder's foot is the thrust (or propulsion), and the ground is the surface applying a force against the momentum of the skateboard. Just as the skateboarder slows down by pushing against the ground without any external help from another force, the spacecraft decelerates by managing its thrust.

In this scenario, the spacecraft has a mass of 15000 kg, descending at 600 meters per second. It uses solid fuel that expels gases at a rate of 90 kg per second, with those gases moving at 2500 meters per second relative to the spacecraft.

This chunk provides specific details about the spacecraft. The mass and speed are crucial for calculating the momentum. The mass of the fuel expelled as burst gases and their speed relative to the spacecraft create thrust which affects the spacecraft's deceleration. The parameters indicated will help us apply the necessary calculations to determine the change in velocity and the thrust experienced during deceleration.

Imagine a heavy balloon filled with air that someone is trying to slow down as it falls. Each time the balloon releases air, it pushes against the forces acting on it. Similarly, the gases sprayed out of the spacecraft act like the balloon releasing air, helping it slow down.

Using the thrust generated by the combustion of gases, we can calculate the deceleration of the spacecraft. The net outflux of momentum due to the expelled gases results in negative acceleration, acting against the current velocity.

The thrust created by the expelled gases affects the spacecraft's acceleration. To find the deceleration, we can use the formula derived from Newton’s second law, F = m * a, where the force is given by the momentum change resulting from the expelled gases. This will allow us to determine how quickly the spacecraft is slowing down during landing.

Recall the experience of a car braking to stop. The brake pads push against the wheels, generating friction and slowing the car down. Similarly, the spacecraft's expulsion of gases generates a thrust that acts to decelerate it just like brakes act to slow down a car.

After calculating the acceleration of the spacecraft due to thrust, we can find the change in velocity over the duration of fuel burn. This momentum change reveals how effectively the spacecraft has decelerated.

In this chunk, we discuss finding the change in velocity due to the thrust generated during the fuel burning period. By knowing the initial velocity and calculating the deceleration, we can determine how much the velocity decreases over a specific time. This calculation is vital for ensuring the spacecraft can safely land.

Consider throwing a ball upward. As it rises, gravity causes it to decelerate, and eventually, it stops and then falls back down. Similarly, the spacecraft experiences a deceleration when it expels gas, leading to a decrease in its speed until it safely touches down.

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