Question

NASA

satellite orbits the earth every 90 minutes. During anorbit,

the

satellite's electric power comes either from solar array

wings,

when these are illuminated by the sun, or from batteries.

The

batteries discharge whenever the satellite uses more

electricity

than the solar array can provide or whenever the satelliteis

in

the shadow of the earth (where the solar array cannot beused).

If

the batteries are overused, however, they can be

damaged.

"font-family:'comic sans ms',

sans-serif;font-size:medium;">You are

to determine whether the batteries could be damaged ineither

of

the following operations. You are told that the batterycapacity

is

50 ampere-hours. If the total battery discharge does notexceed

40%

of battery capacity, the batteries will not be

damaged.

(a)

Operation 1 is performed by the satellite while orbiting the

earth.

At the beginning of a given 90-minute orbit, the satellite

performs

a 15-minute maneuver which requires more current than the

solar

array can deliver, causing the batteries to discharge. The

maneuver

causes a sinusoidally varying battery discharge of period 30

minutes with a maximum discharge of ten amperes at 7.5minutes.

For

the next 45 minutes the solar array meets the total

satellite

current demand, and the batteries do not discharge. Duringthe

last

30 minutes, the satellite is in the shadow of the earth and

the

batteries supply the total current demand of 30

amperes.

(i)

The battery current in amperes is a function of time. Plot

the

function, showing the current in amperes as a function oftime

for

the 90-minute orbit. Write a formula (or formulas) for the

battery

current function.

(ii)

Calculate the total battery discharge (in units of

ampere-hours)

for the 90-minute orbit for Operation 1.

(iii)

What is your recommendation regarding the advisability of

Operation

1?

"font-family:'comic sans ms',

sans-serif;font-size:medium;">(b)

Operation 2 is simulated at NASA's laboratory in Houston.

The

following graph was produced by the laboratory simulation of

the

current demands on the battery during the 90-minute orbit

required

for Operation 2.

(i)

Calculate the total battery discharge (in units of

ampere-hours)

for the 90-minute orbit for Operation 2.

(ii)

What is your recommendation regarding the advisability of

Operation

2?