The Orion MPCV's mass is constant but its weight varies depending on the gravitational potential. To calculate the required burn time for the de-orbit, we divide the thrust force by the mass to find the acceleration, determine the change in altitude, calculate the average acceleration, and finally, rearrange the equation to solve for the burn time. Plugging in the given values, the de-orbit burn should last approximately 146,689 seconds.
The difference between the Orion MPCV's mass and weight is that mass is a measure of the amount of matter in an object, while weight is the force of gravity acting on an object. Mass is constant, meaning it does not change from place to place, whereas weight can vary depending on the strength of the gravitational field. In the case of the Orion MPCV, its mass remains the same but its weight is less while in orbit than on Earth's surface due to the decreased gravitational potential.
To calculate the required burn time for the de-orbit, we can use the equation:
- Using Newton's Second Law (F = ma), we find the acceleration (a) by dividing the thrust force (F) by the mass (m) of the Orion MPCV.
- Next, we determine the change in altitude by subtracting the new perigee altitude from the original perigee altitude and convert it to meters using the conversion factor 0.379 km.
- The average acceleration is then found by dividing the change in velocity (AV) by the burn time (t).
- Rearranging the acceleration equation, we solve for the burn time (t) by dividing the change in velocity (AV) by the average acceleration.
Plugging in the values given:
- Force (F) = 53,000 N
- Mass (m) = 25,848 kg
- Change in altitude = 397 km - 96.5 km = 300.5 km = 300,500 m
Using these values, we can calculate the burn time:
- Acceleration (a) = F / m = 53000 N / 25848 kg = 2.051 m/s^2
- Average acceleration (a) = AV / t
- Rearranging to solve for burn time (t): t = AV / a = 300500 m / 2.051 m/s^2 ≈ 146,689 seconds.
Therefore, the de-orbit burn should last approximately 146,689 seconds to achieve the desired change in altitude.