Help with Calculating Planet's Orbital Period

In summary, the conversation is about predicting the period of a newly discovered planet based on its distance from the sun. The conversation includes equations and references to Kepler's third law, with the assumption that all orbits are circular. The final conclusion is that the predicted period is 16 times the Earth's period, represented as T = 16√2.
  • #1
tinksy
5
0
hi, could someone please help me with this problem??

If a small planet were discovered with a distance from the sun eight times that of the Earth, what would you predict for its period in (Earth) years. (i.e. how many times longer would it take to go round the sun than the Earth does.)
 
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  • #2
i will not give you the answer straight away, but here's the hint---
get orbital velocity v as a function of radius r

dynamics of the system(*) :

from Newton's second law and law of gravitation,
(m*v^2)/R = (G*M*m)/R^2


get v(r) and substitute in the kinemetical relation which you got correct,that is, T=2(pi)r/v

this will give you T(r) which is usually called "kepler's third law".


*assumption: all orbits are circular

justification : though the orbits that actually elliptical ,the eccentricity is very small.(dont worry if you don't understand this,take this as a side remark).

cheers :smile:
 
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  • #3
thanks teddy...

could u tell me if I'm right?

i've used kepler's law T^2 (directly proportional to) R^3
so if R = 8R (as for Earth, R = 1AU so for the planet, R = 8AU)
kepler's law: R^3/T^2 = 1
therefore, T^2 = 8^3/1
so T = (root)512 = 16(root)2 ...? is that correct?
 
  • #4
yup,its right.
bye :smile:
 
  • #5
yaaaaaay! thanks
 

1. What is a planet's orbital period?

A planet's orbital period is the time it takes for a planet to complete one orbit around its parent star. This is also known as the planet's year.

2. How is a planet's orbital period calculated?

A planet's orbital period is calculated using Kepler's Third Law, which states that the square of a planet's orbital period is proportional to the cube of its semi-major axis. This equation is T^2 = (4π^2a^3)/GM, where T is the orbital period, a is the semi-major axis, G is the gravitational constant, and M is the mass of the parent star.

3. What factors can affect a planet's orbital period?

A planet's orbital period can be affected by its distance from the parent star, the mass of the parent star, and any gravitational influences from other planets or objects in the system.

4. Can a planet's orbital period change over time?

Yes, a planet's orbital period can change over time due to various factors such as tidal forces from other objects, changes in the planet's distance from the parent star, and gravitational interactions with other planets in the system.

5. Why is calculating a planet's orbital period important?

Calculating a planet's orbital period is important because it allows us to understand the dynamics of the planet's orbit and its relationship with its parent star. It also helps us to predict future positions and movements of the planet, which is crucial for studying its atmosphere and potential habitability.

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