Calculating the period of a low Earth satelite using Kepler

In summary, to find the period of a low Earth orbiting satellite using Kepler Laws, you must use the equation T^2/R^3 for Earth = 2.97E-19 (sec^2/m^3). However, this constant is incorrect and a different one must be used for orbits around the Earth. The correct value can be calculated using the mass of the Earth and the radius of the orbit.
  • #1
barryj
854
51

Homework Statement


Find the period of a low Earth orbiting satellite using Kepler Laws
earth radius = 6.38E6 meters
T^2/R^3 for Earth = 2.97E-19 (sec^2/m^3)

Homework Equations



2.97E-19 = T^2/(6.38E6)^3
T^2 = (2.97E-19)(6.38^6)^3 = 77.1
T = 8.72 sec

The Attempt at a Solution


This is not correct since I know the period of a low earther is about 90 minutes or about 5600 seconds.
?
 
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  • #2
barryj said:
T^2/R^3 for Earth = 2.97E-19 (sec^2/m^3)
Hello. The number on the right doesn't look correct. How did you get that value?
 
  • #3
The number came from a chart that was supplied with a homework set for physics.
I realize that there are other variants of this number with different units such as
3.35 10E24km^3/yr^2) this shyulkd be the same value if the units are converted.
Maybe there is an error in one of he documents.
 
  • #4
The value given in your table is incorrect. You can calculate the correct value yourself in terms of the mass of the earth.

See http://pvhslabphysics.weebly.com/keplers-3rd-law.html

Here ##a## is the radius of the orbit if the orbit is circular. If the orbit is elliptical, then ##a## is the length of the semi-major axis of the ellipse.
 
  • #5
The value of the constant that you used appears to be for orbits around the sun rather than around the earth.
 
  • #6
barryj said:
T^2/R^3 for Earth = 2.97E-19 (sec^2/m^3)

Your constant is wrong
 
  • #7
I get it now. Yes, I need a different constant for around earth. I was confused but better now. thanks
 

1. How is the period of a low Earth satellite calculated using Kepler's laws?

The period of a low Earth satellite can be calculated using Kepler's third law, which states that the square of a satellite's orbital period is proportional to the cube of its semi-major axis. This can be expressed as P^2 = (4π^2 / GM) * a^3, where P is the period, G is the gravitational constant, M is the mass of the central body, and a is the semi-major axis of the satellite's orbit.

2. What is the semi-major axis and how is it related to the period of a low Earth satellite?

The semi-major axis is the average distance between the satellite and the center of the Earth. It is related to the period of a low Earth satellite through Kepler's third law, where the cube of the semi-major axis is directly proportional to the square of the orbital period.

3. Can the period of a low Earth satellite change over time?

Yes, the period of a low Earth satellite can change over time due to factors such as atmospheric drag, gravitational perturbations from other bodies, and changes in the satellite's altitude or orbit. These changes can be calculated and predicted using mathematical models.

4. How does the mass of the central body affect the period of a low Earth satellite?

The mass of the central body, in this case the Earth, affects the period of a low Earth satellite through Kepler's third law. As the mass of the central body increases, the period of the satellite will also increase, assuming all other factors remain constant.

5. What is the relationship between the period of a low Earth satellite and its altitude?

The period of a low Earth satellite is inversely proportional to its altitude. This means that as the altitude of the satellite increases, its period will decrease. This is because a higher altitude will result in a larger semi-major axis, which in turn increases the orbital period according to Kepler's third law.

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