Calculating Orbital Velocity and Period Using Kepler's Laws

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In summary, the conversation discusses the orbit of a ship 155 mi above the earth. Using the equations v=(G*(m/r)).5 and (2*PI*r)/T=v, the velocity is calculated to be 7757.8 m/s and the time for one orbit is about 1 hour and 30 minutes. However, a more direct approach using the equation T² = 4π²R³/(GM) yields a more accurate time of 5358 seconds.
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Homework Statement


A ship is in orbit 155 mi. above the earth, (a) what is its velocity? (b) How long will it take the ship to orbit the earth?



Homework Equations


v=(G*(m/r)).5, (2*PI*r)/T=v


The Attempt at a Solution


I added 155 mi to 3963 mi and got 4118 mi and that is about 6627359 m, which is how high the ship is from the center of the earth. I plugged that into the first equation I gave, and got a velocity of about 7757.8 m/s, which seems pretty logical to me. However, I'm not sure about the time. I solve for T in the second equation (ex. (2*PI*6627359)/7757.8) and get about 5367.6 seconds, about 1 hour and 30 minutes, and that seems way to short. Any ideas on where to point me?
Thanks in advanced :)
 
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  • #2
I found the period directly.
Fc = Fg
4π²mR/T² = GMm/R²
T² = 4π²R³/(GM)
Using R = 6619448 m I got T = 5358 s.
It is a reasonable time.
 

Related to Calculating Orbital Velocity and Period Using Kepler's Laws

1. What are Kepler's laws?

Kepler's laws are a set of three laws that describe the motion of planets around the sun. They were discovered by astronomer Johannes Kepler in the early 17th century.

2. What is Kepler's first law?

Kepler's first law, also known as the law of ellipses, states that the orbit of a planet around the sun is in the shape of an ellipse, with the sun located at one of the foci.

3. How do I calculate the period (T) of a planet's orbit using Kepler's third law?

To calculate the period (T) of a planet's orbit, you can use the formula T^2 = (4π^2/GM) * a^3, where G is the gravitational constant, M is the mass of the sun, and a is the semi-major axis of the planet's orbit.

4. What is Kepler's second law?

Kepler's second law, also known as the law of equal areas, states that a line connecting a planet to the sun will sweep out equal areas in equal time intervals. This means that a planet will move faster when it is closer to the sun and slower when it is farther away.

5. How do I calculate the velocity (V) of a planet in its orbit using Kepler's laws?

To calculate the velocity (V) of a planet in its orbit, you can use the formula V = √(GM * (2/r - 1/a)), where G is the gravitational constant, M is the mass of the sun, r is the distance between the planet and the sun, and a is the semi-major axis of the planet's orbit.

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