Kepler's Third Law satellite problem

In summary, the altitude of the synchronous orbit of an orbiting satellite over a fixed spot on the equator of rotating Pluto can be calculated using the equation r = [(G*M*T^2)/4pi^2]^(1/3) and then subtracting the radius of Pluto from the result. The final answer in kilometers is (1.77e^4 km). However, the system may show this as incorrect despite being the correct solution.
  • #1
bonekrushur
3
0

Homework Statement



An orbiting satellite stays over a certain spot on the equator of (rotating) Pluto. What is the altitude (in km) of the orbit (called a "synchronous orbit")?


Homework Equations


r = [(G*M*T^2)/4pi^2]^(1/3)
h= r-radius of pluto


The Attempt at a Solution


I have plugged in the numbers (6.67e^-11) for G, (1.31e^22 kg) for M, and (551852 s) for T. I get (1.89e^7 m) for the radius. Then I subtract 1,153,000 meters from my answer to account for the radius of Pluto. My final answer in meters is (1.77e^7 m). My final answer in km is (1.77e^4 km). However, when I input this, the system shows this is wrong. I've tried several variations of the answer, but nothing works. Does anyone know if I've overlooked something in the equation? Thanks.
 
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  • #2
Seems right.
 
  • #3
I get the same answer.
 

Related to Kepler's Third Law satellite problem

What is Kepler's Third Law satellite problem?

Kepler's Third Law satellite problem, also known as the Third Law of Planetary Motion, is a mathematical relationship that describes the motion of objects in orbit around a central body. It states that the square of the orbital period of a satellite is directly proportional to the cube of the semi-major axis of its orbit.

What does Kepler's Third Law satellite problem help us understand?

Kepler's Third Law satellite problem helps us understand the relationship between an object's orbital period and its distance from the central body. It allows scientists to calculate the orbital period of a satellite based on its semi-major axis or vice versa.

How is Kepler's Third Law satellite problem used in space exploration?

Kepler's Third Law satellite problem is used in space exploration to help scientists determine the optimal orbit for satellites and other spacecraft. It also allows for the prediction and calculation of satellite trajectories and helps ensure the stability and longevity of space missions.

What factors can affect the accuracy of Kepler's Third Law satellite problem?

The accuracy of Kepler's Third Law satellite problem can be affected by various factors, such as the gravitational pull of other celestial bodies, the shape and size of the central body, and the presence of external forces like solar wind or atmospheric drag. These factors can cause slight deviations from the predicted orbit.

How does Kepler's Third Law satellite problem relate to Newton's laws of motion?

Kepler's Third Law satellite problem is based on Newton's laws of motion, specifically the law of universal gravitation. It uses these laws to mathematically describe the motion of objects in orbit around a central body. Additionally, Kepler's Third Law can be derived from Newton's laws of motion and the law of conservation of angular momentum.

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