Why do you need a tracking telescope mount?

When you are photographing deep sky objects, you take many long exposure photos and stack them on top of each other to get a final image. However, the earth keeps spinning, and that makes the sky paper rotate around the north pole. normally this movement is noticeable to the naked eye, but your telescope is so zoomed in that streaking can appear after just a. minute of exposure. Normally astronomers use very expensive equatorial tracking mounts that can cancel out that rotation.

this is a form of photography called star trails and it represents the movement of the sky really well

Calculus Industry Connection

In astrophotography, calculus is used for everything from predicting the positions of the planets to calculating the brightness of variable stars over time, the rate at which the universe is expanding, and the rate at which the positions of the stars change due to Earth's rotation.

Theory

For this project, I wanted to explore the mathematics behind the change in the apparent position of the stars and how that mathematics could be applied to a goto tracking mount. I will measure the target object's right ascension (RA), the local sidereal time (LST), and the telescope's location to accurately predict the position of a star or deep-sky object over time.

Calculations for the rate of change of the Right Acension

These are the inputs that are required for the equation(s) to work.

Calculations for the rate of change of the Right Acension

This calculates the local sidereal time or LST using the current attitude and the GST or Greenwich serial time. The LST time zone is dependent on the position of the stars, not the position of the sun.

Calculations for the rate of change of the Right Acension

This calculates the hour angle or the RA. The hour angle is the rate of change of the position of the stars.

Calculations for the rate of change of the Right Acension

Now we can convert that to the rate of change of the star's position in degrees instead

LoFi scale-prototypes of the physical system

Key Takeaways

• The hour angle is the rate of change of the hours (one hour is 15 degrees) over time
• The RA is the angle from the vernal equinox to the deep sky/celestial object
• GST and the location of the observer are used to calculate the LST
• LST is a time zone dependent on the position of the stars not the position of the sun

Next Steps

• Finish working out the math
• Make a larger mount that can bear heavier weights.
• Modify the design of that mount so that it can be motorized
• Then implement the math to control the motorized mount

Our goal is to measure the rate of change of the distance traveled with respect to time of a paper airplane and a paper ball.

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How does Calculus Apply to

Air Traffic Controllers?

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Key Takeaways/Learnings

Next Steps

• Create and measure more planes

• Control the plane

• Incorporate other math

Houdini had his feet shackled to the top of a concrete block which was placed on the bottom of a giant laboratory flask. The cross-sectional radius of the flask, measured in feet, was given as a function of height y from the ground by the formula

with the bottom of the flask at y=1 foot.

The flask was then filled with water at a steady rate of 22 cubic feet per minute. Houdini's job was to escape the shackled before he was drowned by the rising water in the flask.

Now Houdini knew it would take him exactly 10 minutes to escape the shackles. For dramatic impact, he wanted to time his escape so it was completed precisely at the moment the water level reached the top of his head. Houdini was exactly six feet tall.

Your task is to find out how high this block should be. Express the volume of the water in the flask as a function of the

height of the liquid above ground level. What is the volume when the water level reaches the top of Houdini’s head? (Neglect

Houdini’s volume and the volume of the block.) What is the height of the block?

Left Hand Rule

Right Hand Rule

Mid Point Rule