Question

The Orion MPCV must reduce its velocity at a pre-calculated point in its orbit in order to return to Earth after its mission to the moon.

During a de-orbit burn, a pre-calculated AV (delta V, change in velocity) will be used to decrease the Orion MPCV's altitude. The Orion MPCV's Orbital Maneuvering Syster (OMS) engines provide a combined thrust force of 53,000 Newtons. The Orion MPCV has a mass of 25,848 kg when fully loaded.
What is the difference between the Orion MPCV's mass and weight? An object's mass does not change from place to place, but an object's weight does change as it moves to a place with a different gravitational potential.
For example, an object on the moon has the same mass it had while on the Earth but the object will weigh less on the moon due to the moon's decreased gravitational potential. The Orion MPCV always has the same mass but will weigh less while in orbit than it does while on Earth's surface.
CALCULATION: Calculate how long a de-orbit burn must last in seconds to achieve the Orion MPCV's change in altitude from 397 kilometers to 96.5 kilometers at perigee.
Use the equations and conversions provided to find the required burn time.
Equations to use:
1. Newton's Second Law: F = ma
Where:
a = acceleration is in meters per second per second (=) units
F = force is in Newtons 1N = 1(km
M = mass is in kg finits
Solve for a = m
2. Determination of AV (DeltaV):
Find the change in altitude (Original Perigee - New Perigee)
0.379 5
Use the conversion factor of (-
-). This conversion factor is the approximation of orbital velocity for the altitude difference, only valid for Earth's gravity and atmospheric drag for
1km
the altitudes of this problem.
Equation should read A/ = (Change in Altitude x 0.379
3. Equation that defines average acceleration, the amount by which velocity will change in a given amount of time: a =
AK
4. Rearranging the acceleration equation above to find the time required for a specific velocity change given a specific acceleration, where t=-
AV = change in velocity in meters per second
a = acceleration is in meters per second per second
t= required time in seconds (this is the value you are solving for)
Please include at least two decimal places in your answer.

Answer 1

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:

1. 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.
2. 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.
3. The average acceleration is then found by dividing the change in velocity (AV) by the burn time (t).
4. 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:

1. Force (F) = 53,000 N
2. Mass (m) = 25,848 kg
3. Change in altitude = 397 km - 96.5 km = 300.5 km = 300,500 m

Using these values, we can calculate the burn time:

1. Acceleration (a) = F / m = 53000 N / 25848 kg = 2.051 m/s^2
2. Average acceleration (a) = AV / t
3. 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.