This is Pre-Calc! Please help and Thank you! Please click the pics for the background infoDirections: Answer questions 1-8 based on the information on Table 1. Round all answers to the nearest thousandth and label with the appropriate units.1. According to Table 1, what is the closest distance between Earth and Mars?2. According to Table 1, what is the farthest distance between Earth and Mars?3. Based on your answers from #2 and #3, what is the average distance between the two planets?4. Based on your answers from #2 and #3, what is the amplitude of the distances?5. The distance has a period of 772 days. Write a sinusoidal equation relating the number of days and distance from Earth to Mars.6. Based on the equation from #5, what is the distance between our planets on Mr. Schutt’s birthday (day 187)?7. Write a sinusoidal equation relating the number of days and the one-waycommunication between Earth to Mars.8. What is the one-way communication time delay between our planets on Mr. Schutt’s birthday (day 187)? UNIT 4, LESSON 8: EXPLORING SPACE THROUGH MATHBACKGROUNDThis problem applies mathematical principles in NASA's human spaceflight program.Since 1964, NASA has been exploring Mars. The Mars Exploration Program began in the 1960'sand has made and documented some remarkable findings about the "Red Planet". The firstphase of the Mars Exploration Program consisted of activities known as “flybys", which involvedsatellites flying by the planet and taking as many pictures as possible. The satellite series wascalled Mariner. The Mariners' cameras have captured some surprisingly great images of giantvolcanoes and a grand canyon on the planet's surface. Still in orbit around Mars today, theMars Odyssey spacecraft, with its onboard camera, has captured images that have been used tocreate an accurate Martian map.Figure 1: Mariner SatellitesOn July 30, 2020, NASA launched an Atlas-V rocket with the Mars rover "Perseverance"on it, and on February 18, 2021 Perseverance landed on the surface of Mars. The rover ismoving about the surface of the planet collecting full color images of the terrain andmicroscopic images of the rock and soil.INSTRUCTIONAL OBJECTIVES• You will use trigonometric functions to model periodic behavior of real-life data;• You will make predictions based on the properties of a function;• You will graph a sinusoid curve; and• You will determine the domain and range of functions using graphs and tables. MartOrbitEarthOrbit1 Earth Year = 365 days1 Mars Year - 687 Earth days or 669 sols (martian days)PROBLEMInformation sent from Mars to Earth is carried on radio waves that travel at the speed oflight in space. However, at its closest distance from Earth, Mars is 55 million kilometers away,and at its farthest distance, is over 400 million kilometers. Because the distance between thetwo planets is, on average, over 100 million kilometers, there still is a significantcommunication time delay. NASA's engineers and scientists are working to understand thisdelay by collecting data and modeling the distance between Mars and Earth in 26-month cycles.This is the time required for Mars to make its closest approach to Earth.Elapsed TimeMars-EarthDistance(x10° km)One WayCommunicationTime (min)(days)2.2712.6522.8515.92223.9922.24222.2712.66000.5573.17722.2712.6Table 1: Mars-Earth Distance & Communication Delay 2002 – 2004 (approximately 26 months), where day zero isthe start of the distance and communication delay tracking.

From the given table 1 at elapsed time 600 days and one way communication time of 3.1 minutes, the…

Answered: Directions: Answer questions 1-8 based…

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Chapter1: Units, Trigonometry. And Vectors

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This is Pre-Calc! Please help and Thank you! Please click the pics for the background info

Directions: Answer questions 1-8 based on the information on Table 1. Round all answers to the nearest thousandth and label with the appropriate units.

1. According to Table 1, what is the closest distance between Earth and Mars?

2. According to Table 1, what is the farthest distance between Earth and Mars?

3. Based on your answers from #2 and #3, what is the average distance between the two planets?

4. Based on your answers from #2 and #3, what is the amplitude of the distances?

5. The distance has a period of 772 days. Write a sinusoidal equation relating the number of days and distance from Earth to Mars.

6. Based on the equation from #5, what is the distance between our planets on Mr. Schutt’s birthday (day 187)?

7. Write a sinusoidal equation relating the number of days and the one-way
communication between Earth to Mars.

8. What is the one-way communication time delay between our planets on Mr. Schutt’s birthday (day 187)?

UNIT 4, LESSON 8: EXPLORING SPACE THROUGH MATH
BACKGROUND
This problem applies mathematical principles in NASA's human spaceflight program.
Since 1964, NASA has been exploring Mars. The Mars Exploration Program began in the 1960's
and has made and documented some remarkable findings about the "Red Planet". The first
phase of the Mars Exploration Program consisted of activities known as “flybys", which involved
satellites flying by the planet and taking as many pictures as possible. The satellite series was
called Mariner. The Mariners' cameras have captured some surprisingly great images of giant
volcanoes and a grand canyon on the planet's surface. Still in orbit around Mars today, the
Mars Odyssey spacecraft, with its onboard camera, has captured images that have been used to
create an accurate Martian map.
Figure 1: Mariner Satellites
On July 30, 2020, NASA launched an Atlas-V rocket with the Mars rover "Perseverance"
on it, and on February 18, 2021 Perseverance landed on the surface of Mars. The rover is
moving about the surface of the planet collecting full color images of the terrain and
microscopic images of the rock and soil.
INSTRUCTIONAL OBJECTIVES
• You will use trigonometric functions to model periodic behavior of real-life data;
• You will make predictions based on the properties of a function;
• You will graph a sinusoid curve; and
• You will determine the domain and range of functions using graphs and tables.

Mart
Orbit
Earth
Orbit
1 Earth Year = 365 days
1 Mars Year - 687 Earth days or 669 sols (martian days)
PROBLEM
Information sent from Mars to Earth is carried on radio waves that travel at the speed of
light in space. However, at its closest distance from Earth, Mars is 55 million kilometers away,
and at its farthest distance, is over 400 million kilometers. Because the distance between the
two planets is, on average, over 100 million kilometers, there still is a significant
communication time delay. NASA's engineers and scientists are working to understand this
delay by collecting data and modeling the distance between Mars and Earth in 26-month cycles.
This is the time required for Mars to make its closest approach to Earth.
Elapsed Time
Mars-Earth
Distance
(x10° km)
One Way
Communication
Time (min)
(days)
2.27
12.6
52
2.85
15.9
222
3.99
22.2
422
2.27
12.6
600
0.557
3.1
772
2.27
12.6
Table 1: Mars-Earth Distance & Communication Delay 2002 – 2004 (approximately 26 months), where day zero is
the start of the distance and communication delay tracking.

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