How Long Will It Take the Aimless Wanderer to Orbit Planet Mongo?

[anthonym44]

Homework Statement

Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As chief scientist-engineer, you make the following measurements: a 2.50-kg stone thrown upward from the ground at 11.0 returns to the ground in 9.00 ; the circumference of Mongo at the equator is 2.00×10^5 ; and there is no appreciable atmosphere on Mongo. I found the mass to be 3.71*10^25, now part B asks me for..."If the Aimless Wanderer goes into a circular orbit 3.00×104 above the surface of Mongo, how many hours will it take the ship to complete one orbit?"

Homework Equations

F_g = (GM1M2)/R^2, g= GM/R^2, T^2=R^3, V=(2piR)/T

The Attempt at a Solution

I attempt to use the propotions rule where (T1^2/R1^3) = (T2^2/R^3) using this i have to calculate the period of the planet some how. I figured in order to do this i must need velocity of the planet. if the mass of the ship was given i would also be able to solve the problem so i attempted to use the equation F_g=(GM1M2)/R^2 but do not know F_g, I thought maybe this was F=ma therefore F=(3.71*10^25)(2.44) (2.44 was solved for a using kinematics.) Any help would be appreciated thanks.

 

[Shooting Star]

At the given altitude,

Fc = GMm/(R+h)^2, where Fc = mw^2(R+h). Find w and hence T directly.

 

[Moetasim]

As a scientist, it is important to first understand the problem and the given information before attempting to solve it. In this scenario, we are given the mass of the stone (2.50 kg), the time it takes for the stone to return to the ground (9.00 s), the circumference of Mongo at the equator (2.00×10^5 m), and the fact that there is no appreciable atmosphere on Mongo. From this information, we can use the equation for gravitational force to determine the mass of Mongo (3.71*10^25 kg).

In order to solve part B, we need to use the equation for orbital period, T^2 = R^3, where T is the period and R is the distance from the center of the planet. However, in this case, we are given the altitude of the orbit (3.00×10^4 m) instead of the distance from the center of the planet. To solve this, we need to add the radius of the planet (2.00×10^5 m) to the altitude to get the distance from the center of the planet (2.30×10^5 m).

Now, we can use the equation for orbital period to calculate the time it takes for the ship to complete one orbit around Mongo. Since we are given the altitude (3.00×10^4 m) and the radius of Mongo (2.00×10^5 m), we can use the equation V=(2piR)/T to calculate the velocity of the ship in orbit (7.12×10^3 m/s).

Finally, we can use this velocity to calculate the orbital period using the equation T = 2piR/V, which gives us a period of approximately 10.95 hours. Therefore, it would take the Aimless Wanderer approximately 10.95 hours to complete one orbit around Mongo at an altitude of 3.00×10^4 m.