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Space Flight Engineering & Calculus
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Space Flight Engineering
- designing a shuttle
- space shuttle ascent: first and second derivative
- center of gravity: triple integral
- shape of trajectory: differentials and integrals
- Acceleration curves: derivatives
- spiral orbits
- maximum area of satellites
Works Cited
Calculus is everywhere!
"Applications of Calculus." WyzAnt: Find Private Tutors at Affordable Prices, In-Person & Online. N.p., n.d. Web. 24 May 2016.
"A Brief History of Calculus." WyzAnt: Find Private Tutors at Affordable Prices, In-Person & Online. N.p., n.d. Web. 24 May 2016.
"Life at Spaceflight (Engineering)." Spaceflight. N.p., 5 Mar. 2014. Web.
N.p., n.d. Web. 24 May 2016.
- language of engineers, scientists, and economists
- plays a huge role in our daily lives
Problem #2
Problem #1
The integral of the dose rate formula D(T) with respect to time is the accumulated total dose.
A) Perform this integration for one 10-hour orbit of the spacecraft assuming that the total dose over the time interval T: [0h, 10h] is equal to twice the dose rate over the time interval T: [0h, 5h].
B) How many years will it take for the spacecraft total dose to equal 1000 Grays?
Answer #2
A)
Suppose the radial distance between the center of Earth and the spacecraft can be modeled as a simple linear function during the time the shielded spacecraft is inside the Van Allen belts, and the radiation dose rate is modeled by a simple power-law function:
Path: R(T) =7000 + 3000T kilometers, where T is the elapsed time in hours.
Dose Rate: D(R) = 60(R/25000)^2 milliGrays/hour, where R is in kilometers.
What is the dose rate formula re-written so that the dose rate is a function of time D(T)?
Example
Answer #1
Answer: Substitute the formula R(T) in the equation for D to get
B) The spacecraft accumulates 0.22 Grays every 10 hours, so in one year it accumulates 0.22 Grays/10 hours x (24 hours /1day)x(365 days/1 year) = 192 Grays/year,
then 1000 Grays/ (192 Gy/yr) = 5.2 years.
- Van Allen Probes orbiting Earth
- Radiation in the environment contains high energy electrons and protons that can damage satellite solar panels and electronics
- typical spacecraft becomes unreliable after 1000 grays of radiation
- 1 gray = 1 joule of energy delivered to 1 kilogram of material
The History of Calculus
- Created in 17th century
- Isaac Newton
- geometrical and related to the physical world
- orbiting planets
- Gottfried Leibniz
- change in graphs