Consider a moon that is 1.15 x 10^6 km from the planet it is orbiting .

In summary, the orbital period of the satellite at a distance of 4.10 x 10^6 km from the planet is approximately 181.8 days. This was calculated using the formula T^2/r^3 = k constant and correcting a computation error. The given choices for the orbital period were a)96.3 d b)181.8 d c)63 d d)4.01 d.
  • #1
vipson231
23
0
Consider a moon that is 1.15 x 10^6 km from the planet it is orbiting...

Homework Statement



Consider a moon that is 1.15 x 10^6 km from the planet it is orbiting. This moon makes one complete orbit every 27 days. What is the orbital period of a satellite orbiting the planet at a distance of 4.10 x 10^6 km?

a)96.3 d
b)181.8 d
c)63 d
d)4.01 d
I was given a formula T^2/r^3 = k constant

So i set up the equation (27)^2/(1.15 x 10^6)^3= T^2/ (4.10 x 10^6)^3 and got T^2= 3.30 x 10^22 and take square root of that which gives me T=1.87151521 x 10^11. However my answer is not a choice above. Did i do something wrong with my calculation?
 
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  • #2


vipson231 said:
...Did i do something wrong with my calculation?

Yes. T2 is not equal to 3.3x1022.
 
  • #3


:O Thx I'll go back and see what I did wrong
 
  • #4


Oh I made a careless computation error I input all the values at once in my calculator and got 181.75 ≈181.8.
(27^2)(4.10x10^6)^3/ (1.15 x 10^6)^3 = 33035.85699

radical of 33035.85699 = 181.75 = 181.8 Cheers! =)
 
  • #5


I would like to point out that you have correctly used the formula T^2/r^3 = k constant to solve for the orbital period of the satellite. However, your final answer is not in the correct units. The units for the constant k are in seconds squared per cubic meters, so your final answer should also be in seconds. Therefore, your final answer should be 1.87151521 x 10^11 seconds. To convert this to days, we can divide by 86,400 seconds (the number of seconds in a day), which gives us approximately 2.167 days. This is not one of the given answer choices, so there may be a mistake in the given problem or the answer choices. I would suggest double checking your calculations and units to ensure accuracy.
 

What is the distance between the moon and the planet it is orbiting?

The distance between the moon and the planet it is orbiting is 1.15 x 10^6 km.

How big is the moon compared to the planet it is orbiting?

The size of the moon compared to the planet it is orbiting cannot be determined solely based on the distance between them. Other factors such as mass and density also play a role in determining the size of a celestial object.

What is the orbit of the moon around the planet like?

The moon's orbit around the planet is likely to be elliptical, with the planet located at one of the two foci of the ellipse. The exact shape and parameters of the orbit would depend on the masses of the moon and the planet, as well as their distance and relative velocities.

What are the potential effects of the moon's distance from the planet?

The distance between a moon and its planet can affect various factors such as the strength of the moon's gravitational pull on the planet, the tidal forces exerted on the moon, and the potential for the moon to have a stable atmosphere or liquid water on its surface. Additionally, the distance can also impact the likelihood of the moon being habitable for potential life forms.

How is the distance between a moon and its planet measured?

The distance between a moon and its planet can be measured using various methods such as radar ranging, parallax measurements, and astrometry. These techniques involve using precise instruments and calculations to determine the distance between two celestial objects.

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