How to Calculate the Orbital Period of a Satellite Around Planet Zeta?

  • Thread starter Thread starter EskShift
  • Start date Start date
  • Tags Tags
    Radius
AI Thread Summary
To calculate the orbital period of a satellite around planet Zeta, the gravitational force and orbital mechanics equations are applied. The satellite is in orbit at a distance of 2R from the surface, leading to confusion about the correct period calculation. Initial attempts yield a period of 540 days, which, when square-rooted, approximates 23 days, but the expected answer is 40 days. This discrepancy raises questions about the problem statement's accuracy and whether the orbital radius was miscalculated. Clarification from a teacher may be necessary to resolve the confusion regarding the correct orbital parameters.
EskShift
Messages
20
Reaction score
0
A satellite is being prepared for take-off on the surface of the fictitious planet Zeta. The planet Zeta has a radius of R and the satellite experiences a gravitational force, F, from the planet at the surface. A single moon, Eta, completes one orbit of the planet every 50 days at a distance of 5R from the center of the planet.
The satellite is now placed into orbit 2R from the surface of the planet.

Determine the Period of the satellite.


Homework Equations


Well i assume you use (R^3 / T^2)A = (R ^ 3 / T ^ 2)B



The Attempt at a Solution


Therefore
5R ^3 / 50^2 = 3R^2 / T^2
T is what we need, but i seem to always get 540 and am not exactly sure as to how to work it out.
Am i using the wrong equation? or is my working out wrong?

thanks.
 
Physics news on Phys.org
EskShift said:
A satellite is being prepared for take-off on the surface of the fictitious planet Zeta. The planet Zeta has a radius of R and the satellite experiences a gravitational force, F, from the planet at the surface. A single moon, Eta, completes one orbit of the planet every 50 days at a distance of 5R from the center of the planet.
The satellite is now placed into orbit 2R from the surface of the planet.

Determine the Period of the satellite.

Homework Equations


Well i assume you use (R^3 / T^2)A = (R ^ 3 / T ^ 2)B

The Attempt at a Solution


Therefore
5R ^3 / 50^2 = 3R^2 / T^2
T is what we need, but i seem to always get 540 and am not exactly sure as to how to work it out.
Am i using the wrong equation? or is my working out wrong?

thanks.

Welcome to PF.

Don't you need to take the square root of 540?
 
LowlyPion said:
Welcome to PF.

Don't you need to take the square root of 540?

I thought so too, but that is approximately 23. The answer says 40 days? I still don't understand what I'm doing wrong, and i have an exam tomorrow!
 
Working backwards from 40 days that suggests an orbital radius of 4.3R from the center doesn't it?
 
LowlyPion said:
Working backwards from 40 days that suggests an orbital radius of 4.3R from the center doesn't it?

It certainly does, possibly the answer is a miss-type, everyone i have asked have all said they don't understand. but i haven't asked my teacher yet, he might know. but ill be happy if my working is correct at least?
 
EskShift said:
It certainly does, possibly the answer is a miss-type, everyone i have asked have all said they don't understand. but i haven't asked my teacher yet, he might know. but ill be happy if my working is correct at least?

Perhaps there is a misstatement in the problem?
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

A satellite in orbit in a system with one planet and two moons
Replies
1
Views
1K
Time taken for a planet to collide with the Sun
Replies
10
Views
802
Calculating Angle & Speed to Reach Planet's Moon from Station Orbit
Replies
1
Views
2K
Find Density Given Period of Orbit
Replies
12
Views
5K
Satellite Motion Homework: Find 2nd Satellite Speed
Replies
2
Views
2K
How Does the Time Period Change with Orbit Radius in Satellite Motion?
Replies
10
Views
2K
Finding r of a Jovian-synchronous orbit and escape velocity
Replies
7
Views
2K
How do I find way of comparing the density of the Earth and the Moon?
Replies
9
Views
2K
What is the Correct Radius and Mass of Earth for Satellite Orbit Calculations?
Replies
1
Views
2K
Finding Orbital Period of Unknown Planet
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top