How Do You Calculate the Altitude and Distance of Spacecraft Using Trigonometry?

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In summary, the conversation involved a person requesting help with a problem involving the International Space Station and Space Shuttle, tracking stations, and various distances and altitudes. They provided their work so far, but were unsure if it was correct.
  • #1
mks
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I know this is simple, but I need help. I've attached the image (of ISS and SS with angles, etc..)


Based upon the information provided on International Space Station (I.S.S.) and Space Shuttle (S.S.), and tracking stations C and D, answer following questions:

a) What are the altitudes of the space station and space shuttle?
b) How far apart are they? (horizontal and vertical distances)
c) How far is each space vehicle from each of the tracking stations?
 

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  • #2
can someone please help?

anyone..?
 
  • #3
You need to show us some of your work in order for us to help you (PF homework forum rules). How would you go about starting these problems?
 
  • #4
I did it this far, but I'm not sure if I even did it right:

Solution:

Laws used: Sin = Opposite / Hypotenuse, Cos = adjacent / hypotenuse and A / sina = B/ sin b = C / sin c

< A = 180 - 33 - 72
= 75

< B = 180 - 31 - 81
= 68

d --> d/sin72
= 1418/sinA
= 1418/sinA*sin72
= 1418/sin75*sin72
= 1418/0.9659*0.95105
= 1418/0.918619
= 1543.62
c --> c/sin31
= 1418/sinB
= 1418/sin31*sin68
= 1418/0.51503*0.92718
= 1418/0.4775255
= 2969.475

a1 (altitude 1) => sin33 = a1/d
a1 = sin33*d
= 0.544639*1543.62
= 840.7
a2 (altitude 2) => sin81 = a2/c
a2 = sin81*c
= 0.9877*2969.475
= 2932.5
f --> cos33 = f/d
f = cos33*d
= 0.8387*1543.54
= 1294.6
g --> cos81 = g/c
g = cos81*c
= 0.15643*2969.475
= 464.44

b) H (horizontal distance) = 1418 - f - g
= 1418 - 1294.6 - 464.52
= -341.12
V (vertical distance) = a2 - a1
= 2932.5 - 840.715
= 2091.785
 
  • #5
c) Distance from ISS to Houston = d => 1543.62
Distance from SS to Houston = c => c/sin33
= 1418/sinB
= 1418/sinB*sin33
= 1418/sin68*sin33
= 1418/0.92718*0.544639
= 1418/0.504978
= 2808.04
 
  • #6
I think you made a mistake when you rearranged your equations using the sine law to find d and c, giving you the wrong values to work with for the rest of the question (ex. d=(1418*sin72)/sin75). You repeat this mistake in part (c), as well as mixing up some angles I think.
 

FAQ: How Do You Calculate the Altitude and Distance of Spacecraft Using Trigonometry?

1. How do you calculate the altitude of an object?

The altitude of an object can be calculated by using the trigonometric functions of sine, cosine, and tangent. The formula for calculating altitude is altitude = distance x tangent (angle of elevation).

2. What is the difference between altitude and elevation?

Altitude refers to the height of an object above sea level, while elevation refers to the height of an object above ground level. Altitude is a fixed measurement, while elevation can vary depending on the location of the object.

3. Can altitude be negative?

No, altitude cannot be negative. It is always a positive value representing the height above sea level.

4. How accurate are altitude calculations?

The accuracy of altitude calculations depends on the accuracy of the distance and angle measurements used in the calculation. Generally, altitude calculations can be accurate to within a few meters.

5. What factors can affect the accuracy of altitude calculations?

The accuracy of altitude calculations can be affected by factors such as atmospheric conditions, equipment used, and human error. It is important to use precise measurements and account for any potential sources of error to ensure accurate results.

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