During a de$-$orbit burn, a pre$-$calculated $$V $($delta V$,$ change in velocity$)$ will be used to decrease the Orion MPCV$$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 deorbit burn must last in seconds to achieve the Orion MPCV$\text{'}$s change in altitude from $375\mathrm{.}9$ kilometers to $96\mathrm{.}5$ kilometers at

perigee. Use the equations and conversions provided to find the required burn time.

Equations to use:

Newton's Second Law F$=$ma

Where$$

a $=$ acceleration is in meters per second per second $($m$/$s$^2)$ units

F$=$ force is in Newtons $1$N $=1($k$8-$m$/$s$^2)$

M$=$ mass is in ka units

Solve for a $=$ F$/$m

$2.$ Determination of AV $($DeltaV$)$:

Find the change in altitude $($Original Perigee $-$ New Perigee$)$

Use the conversion factor of $(((0\mathrm{.}379$ m$/$s$)/1$km$)$

Equation should read AV $($deltaV$)=($Change in Altitude$)0\mathrm{.}379$

$3.$ Equation that defines average acceleration, the amount by which velocity will change in a given amount of time: a $=$deltaV$/$t

$4.$ Rearrange the acceleration equation above to find the time required for a specific velocity change given a specific acceleration. where t $=$detlaV$/$a

AV$($deltaV$)=$ change in velocity in meters per second m$/$s

a $=$ acceleration is in meters per second per second m$/$s$^2$

t$=$ required time in seconds $($this is the value you are solving for$)$