Solving Planetary Motion: X & Y's Circular Orbits

In summary, planet X has rotated 92.6 degrees after 5 years, while planet Y has traveled an unknown number of degrees in the same amount of time. The ratio of the radii of their orbits is 5:2, and this can be applied to their angular velocities using Kepler's third law. The formula for angular velocity is W=phix/t for planet X and Wy=phiy/t for planet Y, and the angular position can be found using the formula phix=angular of X after t time and phiy=angular of Y after t time. Remember that Kepler's third law can be derived from the F=GMm/r^2 formula.
  • #1
lempkema
7
0

Homework Statement



Planets X & Y travel in circular orbits around the same star. The ratio of the radii of their orbits is 5:2. 5 years after the planets were aligned, planet x has rotated 92.6 degrees. how many degrees has y traveled in the same amount of time?

Homework Equations



v^2=GM/R

Wx=phix/t; Wy=phiy/t

phix= angular of X after t time
phiy= angular of X after t time

The Attempt at a Solution



I just keep getting the wrong answer. I try transferring the ratio of radii to the angular velocities, but i must be doing it wrong.
 
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  • #2
Check Kepler's third law.
 
  • #3
thank you so much, that made to ratio a lot less difficult to apply!
 
  • #4
Note, that third law can be derived from the F=GMm/r^2.
 

Related to Solving Planetary Motion: X & Y's Circular Orbits

1. What is the significance of solving planetary motion?

Solving planetary motion allows us to understand and predict the movement of planets in our solar system, which is crucial for space exploration, navigation, and studying the history of our universe.

2. How do we determine the X and Y coordinates of a planet's circular orbit?

The X and Y coordinates of a planet's circular orbit can be determined using mathematical equations such as Kepler's laws of planetary motion and Newton's law of universal gravitation. These equations take into account the mass, distance, and velocity of the planet in relation to its central star.

3. What factors affect the circular orbits of planets?

The circular orbits of planets are affected by the gravitational pull of their central star, as well as the presence of other nearby planets and objects. The shape and orientation of a planet's orbit can also be influenced by its own mass, velocity, and distance from the central star.

4. Can we accurately predict the circular orbits of planets?

Yes, with the use of advanced technology and mathematical calculations, we can accurately predict the circular orbits of planets. However, small variations in factors such as mass and velocity can lead to slight deviations from the predicted orbit over time.

5. How does solving planetary motion help us understand the universe?

By studying the circular orbits of planets, we can gain a better understanding of the laws of gravity and motion that govern our solar system. This knowledge can then be applied to other celestial bodies and help us understand the formation and evolution of the universe.

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