How Do You Solve Challenging Polar Coordinate Problems?

In summary: However, if you are stuck on either problem, you could try calculating the force on the satellite using problems 3 and 4 and then using the force law to find the mass of the sun.
  • #1
imsoconfused
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HELP! I just got this assignment over the email a couple hours ago and it's due in the morning and I have no clue how to do these problems! I've spent a few hours trying to figure this stuff out on my own, but I'm down to these last few and I just can't do it. if you can answer one or more, I really appreciate anything AT ALL. I'm sorry I don't have much done already, but I've got a brain block and I'm starting to panic. please help!


2. If a satellite circles the Earth at 9000 km from the center, estimate its period T in seconds.

3. Convert 1/r = C - Dcos(theta) or 1= Cr-Dx into the xy equation of an ellipse.

5. The Earth takes 365.25 days to go around the sun at at distance d = 93 million miles = 150 million km. find the mass of the sun.
F=ma=constant/r^2.
 
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  • #2
imsoconfused said:
2. If a satellite circles the Earth at 9000 km from the center, estimate its period T in seconds.

Hi imsoconfused! :smile:

2. Either compare t with the period of the moon (erm … that's one month! :wink:) …*that only works if you know how far away the moon is, of course.

Or work out the gravitational force on it, by comparing it with g at the Earth's surface … that only works if you know the radius of the Earth … and then use centripetal acceleration :smile:
 
  • #3
imsoconfused said:
HELP! I just got this assignment over the email a couple hours ago and it's due in the morning and I have no clue how to do these problems! I've spent a few hours trying to figure this stuff out on my own, but I'm down to these last few and I just can't do it. if you can answer one or more, I really appreciate anything AT ALL. I'm sorry I don't have much done already, but I've got a brain block and I'm starting to panic. please help!


2. If a satellite circles the Earth at 9000 km from the center, estimate its period T in seconds.

3. Convert 1/r = C - Dcos(theta) or 1= Cr-Dx into the xy equation of an ellipse.
Multiply through by r first. r= [itex]\sqrt{x^2+ y^2} and r cos(theta)= x. You may need to square both sides of an equation to get rid of the square root and get the (standard)equation of an ellipse.

5. The Earth takes 365.25 days to go around the sun at at distance d = 93 million miles = 150 million km. find the mass of the sun.
F=ma=constant/r^2.

Problems 2 and 5 are not mathematics problems. They are physics problems and I would be surprised if your book does not have formulas that apply directly.
 

FAQ: How Do You Solve Challenging Polar Coordinate Problems?

What are polar coordinates?

Polar coordinates are a way of representing points in a two-dimensional space using a distance from the origin and an angle from a reference axis.

How are polar coordinates different from Cartesian coordinates?

Cartesian coordinates use the x and y axes to represent points, while polar coordinates use a distance and angle from the origin. This allows for a different way of visualizing and solving problems in a two-dimensional space.

What are some common applications of polar coordinates?

Polar coordinates are commonly used in physics and engineering, particularly in problems involving circular motion and forces. They are also used in navigation and mapping, as well as in graphing and plotting equations.

How do you convert between polar and Cartesian coordinates?

To convert from polar coordinates to Cartesian coordinates, you can use the formulas x = rcosθ and y = rsinθ, where r is the distance from the origin and θ is the angle from the reference axis. To convert from Cartesian coordinates to polar coordinates, you can use the formulas r = √(x^2 + y^2) and θ = tan^-1(y/x).

What are some common mistakes to avoid when working with polar coordinates?

One common mistake is using degrees instead of radians for the angle in polar coordinates. It is important to remember that the angle is measured in radians, not degrees. Another mistake is using the wrong reference axis, which can result in incorrect calculations. It is also important to ensure that the distance and angle are correctly labeled and used in the correct order when solving problems.

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