Elliptical orbit/ determine speed & potential energy

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SUMMARY

In the discussion regarding Jupiter's elliptical orbit around the Sun, three key statements were evaluated. Statement I is true: Jupiter achieves its greatest speed when it is closest to the Sun. Statement II is also true, as gravitational potential energy increases with distance from the Sun. However, Statement III is false; the magnitude of Jupiter's acceleration is not constant and varies with distance, being maximum when closest to the Sun. The gravitational force, acceleration, and velocity all increase as Jupiter approaches the Sun.

PREREQUISITES
  • Understanding of gravitational force as defined by Fg = GMm/r^2
  • Knowledge of velocity calculation using v = √(GM/r)
  • Familiarity with the concept of gravitational potential energy
  • Basic principles of elliptical orbits in celestial mechanics
NEXT STEPS
  • Study the implications of Kepler's laws of planetary motion
  • Explore the relationship between orbital speed and distance from the Sun
  • Investigate the effects of gravitational forces on celestial bodies
  • Learn about energy conservation in orbital mechanics
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Astronomy students, physics enthusiasts, and educators seeking to deepen their understanding of celestial mechanics and gravitational interactions.

YMMMA
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Homework Statement


True statements about Jupiter as it moves in its elliptical orbit around the Sun include which o the following?
I. It has its greatest speed when closest to the Sun.
II. It has its greatest potential energy when farthest from the Sun.
III. The magnitude of its acceleration is constant.

Homework Equations


Gravitational force Fg = GMm/r^2, where M is the mass of sun, m is the mass of jupiter, and r is the distance between the two masses.

Velocity v= √GM/r

Acceleration due to gravity a = GM/r^2

Gravitational potential energy = mass * acceleration due to gravity * height

The Attempt at a Solution


The closest it is from the sun the greater the speed, gravitational force, and acceleration. So, as the distance decreases, the Fg, a, and v increase.
I correct
II gravitational potential energy is proportional to the height and so it is proportional to the distance between the masses, the fathest it is the greater the potential energy.
III it’s not constant it has maximum and minimum values depending on the distance between the masses.

Is there something I misunderstood?
 
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I'd say you were correct on all counts.
 
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