Elliptical orbit around a massive spherical planet

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SUMMARY

The discussion centers on the dynamics of a small satellite S in an elliptical orbit around a massive spherical planet P. Key conclusions include that the total potential energy (PE) plus kinetic energy (KE) at position 4 is greater than at position 9, and the potential energy of S varies with position. The force on S at position 2 is less than at position 8, while the speed of S at position 2 is also less than at position 8. Additionally, it is confirmed that the torque exerted on S is not constant, and S has its minimum speed at position 10.

PREREQUISITES
  • Understanding of gravitational potential energy and kinetic energy in orbital mechanics.
  • Familiarity with elliptical orbits and their properties.
  • Knowledge of torque and its implications in rotational dynamics.
  • Basic principles of satellite motion and forces acting on satellites.
NEXT STEPS
  • Study the principles of gravitational potential energy and kinetic energy in orbital mechanics.
  • Learn about the characteristics of elliptical orbits and how they affect satellite motion.
  • Investigate the concept of torque in relation to satellite dynamics.
  • Explore the mathematical modeling of satellite motion using Kepler's laws.
USEFUL FOR

Students studying physics, particularly those focusing on orbital mechanics, as well as educators and anyone interested in understanding the dynamics of satellites in elliptical orbits.

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Homework Statement


The path of a very small satellite S in an elliptical orbit around a massive spherical planet P is shown in the figure. The distance from 3 to 4 is the same as from 4 to 5, 9 to 10, and 10 to 11.
(Select T-True, F-False, G-Greater than, L-Less than, E-Equal to, If the first is T and the rest F, enter
TFFFFFF).

https://cats.lsa.umich.edu/msuphysicslib/Graphics/Gtype30/prob02a_ellipse2na.gif

A) The total PE + KE of S at `4' is ... that at `9'.
B) The magnitude of the force on S at `2' is ... at `8'.
C) The PE of S varies with position.
D) The torqe exerted on S is constant
E) S has its minimum speed at `10'.
F) The speed of S at position `2' is ... at `8'.
G) P could be at position X for the orbit of S shown.


Homework Equations





The Attempt at a Solution



A) The total PE + KE of S at `4' is ... that at `9'. GREATER THAN
B) The magnitude of the force on S at `2' is ... at `8'. LESS THAN
C) The PE of S varies with position. TRUE, depends on R
D) The torqe exerted on S is constant NOT SURE, FALSE?
E) S has its minimum speed at `10'. LESS THAN
F) The speed of S at position `2' is ... at `8'. LESS THAN
G) P could be at position X for the orbit of S shown. TRUE
 
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I doubt too many people here go to the university of michigan. Could you upload the diagram somewhere we don't need to log into?
 

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