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**Unformatted text preview: **lVIAE146: Astronautics Homework #3 Assigned: Saturday: January 26‘”; 2009 Due (late: Monday . February 2”". 2009. (at the beginning of the lecture) Please justify all of your“ answers and explain your reasoning it’ll/ll sentences. Assignment: Solve exercises # l, 2, IL 5 in your textlmok, as copied below. 1. The total Av required for transfer from a low earth orbit at 28"" inclination to geosyn—
chronous equatorial orbit is Vt :- 4.29 km/s. A space tug with a restartable hydrogen—
oxygen engine has an [Sp z 453 5, ml, : 16, 000 kg, and my. :- 1300 kg. How much
payload can the tug deliver to geosynchronous orbit? Can the tug make a round trip
without payload? if it can, how much payload could it carry to geosynchronous orbit
and still return empty to low earth orbit? 2. Engine performance may sometimes be upgraded in a multistage rocket. Show that the
trade—off ratio for engine improvement in stage k is given by firm ﬂ ’gcln(m01</mfk) { .. i (7.87)
(”SM (Haze 21:] V€j(l/’n0j " l/mfj) Evaluate arm/815M and amt/ENSPJ for the space shuttle. Use the quantities pertaining
to individual components (in parentheses) in Table 7.3. Should effort be placed into
improving the solid«rocket boosters or the main engines ﬁrst? 4. For the sounding rocket in Table 7.5, calculate the approximate burnout speed (ignoring
the effects of burn time) and maximum altitude achieved with a 250-kg payload. Suppose
that instead of immediately igniting the second stage when the ﬁrst burns out, we allow
the second stage to coast to its maximum altitude and then ignite it. Calculate the
maximum altitude achieved by the payload for this burn—coast~burn—coast strategy. Why
is there such a large difference? TA 3 L E 7.5
Sounding rocket k 13p, 5 mp. kg my. kg l 282 l 167 l 13
2 282 415 4]
>i< 250 5. The solid-rocket boosters of the space shuttle have an ISp 2 290 s, a dry mass of
81.900 kg each, and a full mass of 584,600 kg each. The external tank has a dry mass
of 35,000 kg and contains 703,000 kg of propellant. Space-shuttle main engines have
an [SP 2 455 s. (a) Consider a vehicle consisting offaur solid—rocket boosters burning together as the
ﬁrst stage. and an external tank with two main engines as; the second stage, as
shown in Figure 7.13. Approximately how much payload can this vehicle deliver to low earth orbit (V; 2: - 1.000 ft/sec)? Set up the problem explicitly, and put in
all numbera. (b) The mass of the payload can be ignored in some places. Where and why? (0) Calculate an approximate mt to low earth orbit and compare to the shuttle payload
(approximately 30.000 kg, or 65,000 lb). ...

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