Universal Gravitation Equation and Graphing Calculator

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SUMMARY

The discussion centers on applying Newton's law of universal gravitation to derive an equation for gravitational acceleration based on distance from Earth's center. The equation is expressed as y = c(1/x²), where x represents the distance in kilometers and y represents the acceleration due to gravity in m/s². Participants are tasked with calculating gravitational acceleration at various distances, including sea level (6400 km), Mt. Everest (6410 km), and typical satellite orbits (6500 km) up to higher orbits (6600 km). The universal gravitational constant (G), mass of Earth (M), and mass of the object (m) are essential constants in these calculations.

PREREQUISITES
  • Understanding of Newton's law of universal gravitation
  • Familiarity with the equation y = c(1/x²)
  • Basic graphing calculator skills
  • Knowledge of gravitational acceleration and its units (m/s²)
NEXT STEPS
  • Learn how to use a graphing calculator for plotting equations
  • Study the derivation of gravitational force equations in physics
  • Explore the implications of gravitational acceleration at different altitudes
  • Investigate the effects of mass on gravitational force
USEFUL FOR

Students studying physics, educators teaching gravitational concepts, and anyone interested in the practical applications of Newton's law of universal gravitation.

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Homework Statement



Use Newton's law of universal gravitation to find an equation where x is equal to an object's distance from Earth's center, and y is its acceleration due to gravity. Use a graphing calculator to graph this equation, using 6400-6600 km as the range for x and 9-10 m/s2 as the range for y. The equation should be of the form y = c(1/x2).
(a) Trace along this graph and find y at sea level, 6400 km.


(b) Trace along this graph and find y on top of Mt. Everest, 6410 km.


(c) Trace along this graph and find y in a typical satellite orbit, 6500 km.


(d) Trace along this graph and find y in a much higher orbit, 6600 km.


i got no idea how to solve any help or the answers would help greatly
 
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For a start you could read
http://csep10.phys.utk.edu/astr161/lect/history/Newtongrav.html

G= universal gravitational constant
M = mass of Earth (a constant)
m = mass of your object (a constant)
g = gravitational acceleration experienced by the object (a variable)
r = distance of object from the centre of the Earth (a variable)

G*M*m/r*r = m*g

<< complete solution deleted by berkeman >>
 
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