Calculating Orbit Time of a Hypothetical Planet in the Asteroid Belt

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SUMMARY

The discussion focuses on calculating the orbital period of a hypothetical planet located in the asteroid belt, which is approximately three times the distance from the Sun to Earth. The relevant equation for this calculation is T = 1.4 * sqrt((a/r)^3), where "T" represents the orbital period, "a" is the radius of the hypothetical planet's orbit, and "r" is the radius of Earth's orbit. Participants also inquire about the origin of the constant 1.4 and whether the planet can be assumed to have the same density as Earth to deduce its mass.

PREREQUISITES
  • Understanding of Kepler's laws of planetary motion
  • Familiarity with orbital mechanics and gravitational theory
  • Basic algebra and square root calculations
  • Knowledge of density and mass relationships in celestial bodies
NEXT STEPS
  • Research Kepler's Third Law of Planetary Motion
  • Explore the concept of orbital radius and its impact on orbital period
  • Investigate methods for calculating the mass of celestial bodies based on density
  • Learn about the historical context and formation theories of the asteroid belt
USEFUL FOR

Astronomy students, astrophysicists, and educators looking to deepen their understanding of orbital mechanics and the dynamics of celestial bodies in the asteroid belt.

Phys221
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Just looking for a place to start, not all the work.

Homework Statement


3 The asteroid belt between Mars and Jupiter consists of many fragments (which some
space scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the radius of the asteroid belt (where the orbit of the planet would have been) is
about three times larger than the distance between the Sun than the Earth, how long
would it have taken this hypothetical planet to orbit the Sun? (b) Can we use these data to
deduce the mass of this planet

Homework Equations


T=1.4sqrt((a/r)^3) this is for Earth.
sqrt = square root

The Attempt at a Solution


No idea where to start. I'm assuming we say it has the same density as Earth.

Thanks in advance.
 
Last edited:
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Phys221 said:
...

Homework Equations


T=TE sqrt((a/r)^3)...
"a" is the radius of the hypothetical planet.

Where does the 1.4 come from?
 

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