PARTS 1-2PARTS 1-2

Writing/Developing/Calculating a Formula

Part 1: Writing/Developing a Formula۞ How many feet are in a mile? 5280 ft.

۞ How would you convert 15 ft to miles?

۞ How Would you represent h feet in miles?

۞A. Use the Pythagorean Theorem to write an equation relating r, d, & h.

۞B. Solve for d.

۞C. In the equation found in part b, replace the h with the answer from #3.

milesftft

ft

352

1002.0

5280

15

milesh

5280

2

22

22

222

22

222

2

528052802

2

2

))((

)(

hrhd

hhrd

hrhd

hrhrdr

hrhrdr

hrdr

222 hrdr

2

528052802

hhrd

Part 2: Calculating the Formula

• Explain why the formula found in Part 1c in approximately

equivalent to

It is approximately equivalent because if you would to

plug in something for h to the original equation found in

Part 1: 4c , the number would be too small to

take into consideration.

.2640

rhd

2

5280

h

PARTS 3PARTS 3

Researching Planet RadiiResearching Planet Radii

Planet RadiiPlanet Radii

PlanetPlanet RadiusRadius

MercuryMercury 1515.52 mi1515.52 mi

VenusVenus 3760.54 mi3760.54 mi

EarthEarth 3963.11 mi3963.11 mi

MarsMars 2110.80 mi2110.80 mi

JupiterJupiter 44423.07 mi44423.07 mi

SaturnSaturn 37448.80 mi37448.80 mi

UranusUranus 15881.63 mi15881.63 mi

NeptuneNeptune 15387.64 mi15387.64 mi

Pluto*Pluto* 720.79 mi720.79 mi

PARTS 4PARTS 4

Using the Formula

2640

rhd 1. Using the formula and the radius of the Earth in Part 3,

determine how far you can see on a clear day. (Hint: Plug in your height for h)

2. Solve the formula for h.

3. Using the formula from #2 and radii found in Part 3, determine how tall a person would have to be on Saturn to see 7 mi to the horizon.

940543770706.0

2640

172.20608

2640

2.511.3963

2640

rhd

hr

d

r

rh

r

drhd

rhd

222

2

2 264026402640*

2640*2640

2640

mih 3311.3963

)7(26409 2

4. Using the formula from #2 and radii found in Part 3, determine how tall a person would have to be on Saturn to see 7 mi to the horizon.

5. Could a person possible see 7 mi to the horizon on Saturn? Why or why not?

No, because there is no person that is that tall.6. Could a person possibly see 7 mi to the horizon on Saturn? Why or

why not? No, because people can not live there

ftmih 184805.3

8.39448

72640 2

PARTS 5-6PARTS 5-6

Graphing Formulas & Visual Display

Interesting Facts about Mars….

dr

h

2)(2640

mi531.328.2110

)1.5(2640 2

Mars: Formula & Graph

2640

8.2110 hd

Jupiter #5

Distance from Sun Approximately 466 million milesNumber of Moons 62 moons have been identified Ganymede is the largest moon -- it is bigger than both Mercury and PlutoDiameter 85,788 miles the largest planet -- more than 12 Earths could line up across it! scientists use the planet's gravity to accelerate spacecraft so they can reach Saturn, Uranus and NeptuneComposition a giant ball of mostly hydrogen and heliumLength of Day 9 hours, 55 minutes in Earth time (the length of one rotation)Length of a Year 12 Earth years (the length of one orbit around the sun)Name named for the king of the Roman gods.Visited by Pioneer 11, Viking, Galileo, Cassini and others feetd

milesd

d

rhdFormula

ft

miles

miles

176.49390

3542.92640

)2.5(8.44423

2640:

________________

8448

607.1

66069488218.107.44423

)2.5(2640 2Part 5 & 6:

Jupiter’s FORMULA & GRAPH

2640

07.44423 hd

=4.84763.15881

2)4.5(2540

4.847miles

= 25592.16 feet :D

Facts: Uranus is the seventh planet from the Sun.

Uranus is a giant gas planets which is made up of mostly rock and various ices.

Uranus has been visited by only one spacecraft, Voyager 2 on Jan 24 1986.

Uranus spins differently from most planets. It seems to be tilted "sideways" instead of right-side up. At the time of Voyager 2’ passage, Uranus' south pole was pointed almost directly at the Sun.

Uranus has 15 known moons. Voyager 2 discovered 10 small moons in addition to the 5 large ones already known. It is likely that there are many more tiny moons within the rings.

2640

)4.5(63.15881 2

d

=13.2446

2640

63.15881 hd

Neptune

24.29346

5580.52640

)3.5(64.15387

Facts of Neptune

Neptune's Great Dark SpotNeptune's rings

Facts about NeptuneTopic Data

Diameter 49,572 kmDensity 1.64 g/cm3

Mass 1.024 x 1026 kgVolume 6.379 x 1013 km3

Temperature Range -223° C to >-220° CAtmosphere Hydrogen, Helium, Methane

Winds Up to 2400 m/sMoons 13

Average Distance from Sun 4,504,300,000 kmOrbital Period 164 Years, 288 Days, 13.0 Hours

Rotation 0 Days, 16.11 HoursTilt 28.31°

Rings YesComposition Hydrogen and Helium

Magnetic Field Up to 20 times its radius

False-color image of Neptune. Red areas are semitransparent haze covering planet. Cloud systems in

Neptune's southern hemisphere.

Formula

2640

64.15387 hd

Graph