Using calculus to find gravity in space (dynamics)

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SUMMARY

The discussion focuses on calculating gravitational acceleration at the International Space Station (ISS) using the formula g=GM/R^2, where G is the gravitational constant and R is the distance from the center of the Earth. The user calculates the gravitational acceleration at 400 km above Earth's surface to be approximately 8.7 m/s². They express confusion about the application of calculus in this context, questioning the necessity of integration when the mass of the Earth can be easily referenced. The conversation highlights the distinction between direct calculation and the conceptual understanding of gravitational changes with distance.

PREREQUISITES
  • Understanding of gravitational formulas, specifically g=GM/R^2
  • Basic knowledge of calculus, particularly integration
  • Familiarity with the concept of gravitational acceleration
  • Knowledge of the Earth's radius and distance measurements
NEXT STEPS
  • Study the derivation and implications of the gravitational formula g=GM/R^2
  • Learn about the application of calculus in physics, focusing on dynamics
  • Explore the concept of gravitational potential energy and its relation to distance
  • Investigate the effects of altitude on gravitational acceleration using real-world examples
USEFUL FOR

Students in physics, particularly those studying dynamics, educators teaching gravitational concepts, and anyone interested in the mathematical applications of calculus in real-world scenarios.

Veirian
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I am currently solving a problem where I need to find the gravity in the ISS (distance 400km from Earth with Radius 6371km). I am using the formula g=GM/R^2 . One way to solve it would be to find GM by multiplying g(which is 9.81) and R^2 (which is known) and then to use it in GM/(R+400)^2 and get 8.7m/s^2.

I was wondering whether there was a way to use calculus to get this. If I integrate with respect to the distance (From 6371 to 6371+400) I get something around -1.02. Does that mean that the value changes from R to R+400 by -1.02 ?
I am having some trouble in deciding when and how to use calculus in physics (more specifically dynamics).
 
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I don't understand what the difficulty here is, and why you need to use calculus.

Why can't you just plug in the numbers and find g? Is it because you don't know "M", the mass of Earth? This is something you can easily look up. I don't understand why you're making it more difficult than it is.

Zz.
 

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