Sunday Math Circle: Rocket Science 101
April 26, 2015
1. The distances between various places are shown in the table below. Determine how many
orders of magnitude each distance is.
Places
Austin to Dallas
Distance (in miles)
200
Austin to New York City
1700
Austin to Center of the Earth
4000
Earth to Moon
Orders of Magnitude
234,000
Each to Sun
93,000,000
2. The masses of various objects are shown in the table below. Compare the masses of these
objects to each other by finding the number of orders of magnitude in their ratios:
Object
apple
textbook
car
schoolbus
Earth
Ratio
mtextbook
=
mapple
mcar
=
mapple
mschoolbus
=
mtextbook
mearth
=
mcar
1
.1
= 10
Mass (in kg)
.1
1
1,500
12,000
6 · 1024
Orders of Magnitude
1
3. Estimate to one decimal place the following values of y = log(x).
log(1) =
0
log(2) =
.3
log(3) =
log(4) =
log(5) =
log(6) =
log(7) =
log(8) =
log(9) =
4. Calculate the following values of y = log(x), correct to one decimal place (hint: use the
estimations above!).
log(20) =
log(10 · 2) = log(10) + log(2) = 1 + .3
1.3
log(70) =
log(500) =
log(6000) =
log(40, 000) =
5. Calculate the ∆v for the following rockets. Remember the rocket equation:
total mass
∆v = ve · log
empty mass
(a) Rocket 1 has an unfueled mass of 60kg and holds 300kg of fuel. The engine for the
rocket has an effective exhaust velocity of 2500m/s.
(b) Rocket 2 has an unfueled mass of 500kg and a fully fueled mass of 50,000kg. The
engine for the rocket has an effective exhaust velocity of 4000m/s.
(c) Rocket 3 has two stages. The second stage (this one is on top!) is Rocket 1. The first
stage (this is the bottom one!) has mass of 1000kg and can hold 7640kg of fuel. The
engine for the first stage has an effective exhaust velocity of 2000m/s.
Don’t forget: The mass of the second stage needs to be added to the first stage!
6. ∆v map: plan out your trip!
Earth5
Surface
9700
(Free)
Low5Earth5
Orbit5(ISS)
500
4000
Hubble5
Telescope
700
Lunar5
Orbit
1600
Lunar5
Surface
My trip goes to:
It takes this much ∆v in total:
6100
Low5Mars5
Orbit
(Free)
4100
Martian5
Surface
7. Build a rocket from these parts:
BigRtank:
100Rempty
2500Rfull
Medium:
45Rempty
1000Rfull
MedumRtank:
40Rempty
600Rfull
SmallRtank:
8Rempty
100Rfull
Lander
2Rempty
5Rfull
Satellite
1
ReturnRVehicle
CforRpeople)
15
SolidRfuelRengine:
massR8
SolidRFuel
LiquidRfuelRengine:
massR2
LiquidRFuel
RepairRcraft
CnoRpeople)
3
ChooseRone
My rocket:
My rocket’s ∆v: