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 System (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 357.3 kilometers to 96.5 kilometers at
perigee. Use the equations and conversions provided to find the required burn time.
Equations to use:
Newton's Second awF=ma
Where•
a = acceleration is in meters per second per second (') units
F= force is in Newtons 1N = 1(k8-m )
M= mass is in ka units
Solve for a = E
2. Determination of AV (DeltaV):
Find the change in altitude (Original Perigee - New Perigee)
0.379 m
Use the conversion factor of (- Tm
-). This conversion factor is the approximation of orbital velocity for the altitude difference, only valid for Earth's gravity and atmospheric drag for
the altitudes of this problem.
Equation should read AV = (Change in Altitude) × 0.379
3. Equation that defines average acceleration, the amount by which velocity will change in a given amount of time: a =
AV
AV
4. Rearranaina the acceleration equation above to find the time required for a soecific velocity change given a soecific acceleration. where † =
AV = change in velocitv in meters per second m
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 vour answer.

Answer 1

The Orion MPCV's mass is constant, while its weight varies with gravity. To calculate the burn time for a change in altitude, use the change in altitude to find the change in velocity (ΔV), then use Newton's Second Law to find acceleration, and finally find the required burn time (t) using t = ΔV / a.

Step-by-step explanation:

The difference between the Orion MPCV's mass and weight is that mass is a measure of the amount of matter in an object and does not change regardless of location, while weight is the force exerted on the mass due to gravity and can change depending on where the object is. To calculate the de-orbit burn time to achieve the required change in altitude for the Orion MPCV:

1. Firstly, calculate the required change in velocity (ΔV) using the given change in altitude and the conversion factor. Here, ΔV = (357.3 km - 96.5 km) × 0.379 m/s/km.
2. Next, determine the acceleration (a) produced by the Orion MPCV's OMS engines using Newton's Second Law, F = ma, solving for a = F/m.
3. Last, rearrange the acceleration equation to solve for the required time (t) using t = ΔV / a.

Following these steps will yield the time in seconds required for the de-orbit burn.