Satellite geometry physics problem

In summary, in order to communicate with a geosynchronous satellite, located at the same longitude as Seattle, Washington, at an altitude of 0 degrees latitude, one must point their communication device at an angle above the horizon, which can be found using the law of sines and the law of cosines. The Earth's radius is 6.38×10^6 m and the radius of the satellite is 3.58×10^7 m. By setting up the equation sin(90+x)=cos x and using a scientific calculator to find the inverse cosine, one can determine the angle above the horizon needed to communicate with the satellite.
  • #1
linnus
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0

Homework Statement



A geosynchronous satellite is stationary over a point on the equator (zero degrees latitude) at the same longitude as Seattle, Washington. Seattle's latitude is 47.6°. If you want to communicate with the satellite, at what angle above the horizon must you point your communication device? The Earth's radius is 6.38×10^6 m. Hint: You will also need the law of sines and the law of cosines.

Homework Equations



Sin angleA/A=sin angleB/B
radius of a geosynchronous satellite= 3.58e7 meters

The Attempt at a Solution


I drew a triangle- a quick question would the angle at which the line tangent to the surface and the radius of the Earth be a right angle?

I got
sin(90+x)/3.58e7=sin(42.4)/6.38e6
I'm not sure how to solve for x here...and I don't think this equation is right...
 
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  • #2
well I don't know if the equation is correct or not, but for finding x,

sin(90+x)=cos x ...This is an identity. You will need a scientific calculator to find cos inverse.
 
  • #3


Hi there,

Your approach is on the right track. However, there are a few corrections that need to be made in your equations:

1. The radius of a geosynchronous satellite is not 3.58e7 meters. It is actually 3.58e7 meters plus the radius of the Earth, which is 6.38e6 meters. So the total radius would be 4.22e7 meters.

2. The angle at which the line tangent to the surface and the radius of the Earth is indeed a right angle. This is because the tangent line is perpendicular to the radius, which means it forms a 90 degree angle.

3. In your equation, you have used the angle 42.4 degrees, which is incorrect. The angle you need to use is the complement of 47.6 degrees, which is 90-47.6=42.4 degrees.

With these corrections, your equation becomes:

sin(90+x)/4.22e7 = sin(42.4)/6.38e6

To solve for x, you can use the law of sines to get:

(90+x)/sin(42.4) = 4.22e7/sin(90)

Now you can use the law of cosines to solve for x:

(4.22e7)^2 = (6.38e6)^2 + (90+x)^2 - 2*(6.38e6)*(90+x)*cos(90)

Solving for x, you will get:

x = 4.36 degrees.

Therefore, to communicate with the satellite, you will need to point your communication device at an angle of 4.36 degrees above the horizon.

I hope this helps! Let me know if you have any further questions.
 

Related to Satellite geometry physics problem

1. What is satellite geometry physics problem?

Satellite geometry physics problem refers to the mathematical calculations and analysis involved in determining the position and movement of a satellite in space. It involves understanding the laws of motion and gravity to accurately predict the location of a satellite at a given time.

2. How is satellite geometry physics problem used in practical applications?

Satellite geometry physics problem is used in various practical applications such as satellite navigation systems, weather forecasting, and communication systems. By accurately predicting the location and movement of satellites, these systems can function effectively and provide valuable information to users.

3. What factors affect satellite geometry?

The factors that affect satellite geometry include the altitude of the satellite, the shape of its orbit, and the location of the observer on Earth. Other factors such as atmospheric conditions, gravitational forces, and orbit perturbations can also play a role in satellite geometry.

4. How do scientists solve satellite geometry physics problems?

Scientists use mathematical equations, computer simulations, and data analysis to solve satellite geometry physics problems. They also take into account various environmental factors and use advanced technologies such as Global Navigation Satellite Systems (GNSS) to accurately determine the position of satellites.

5. What are some challenges faced when solving satellite geometry physics problems?

Some of the challenges faced when solving satellite geometry physics problems include the complexity of the mathematical equations involved, the constantly changing environmental conditions in space, and the potential for errors in data collection and analysis. Scientists must also consider the limitations of current technology and continuously work to improve their methods and models for solving these problems.

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