How Is the Period of a Satellite Calculated?

In summary, the period of a satellite is the time it takes for the satellite to complete one orbit around its parent body. It can be calculated using Kepler's Third Law and is affected by factors such as the mass and distance of the parent body, as well as the orbital altitude and velocity of the satellite. The period of a satellite can be changed through maneuvers and is important for determining its orbit and position relative to the parent body. This information is crucial for satellite operations and mission planning.
  • #1
KDizzle
5
0
[SOLVED] Period of a satellite

1. Given: G = 6.67 x 10^-11 N m^2/ kg^2
The acceleration of gravity on the surface of a planet of radius R = 4910 km is 11.8 m/s^2. What is the period T of a satellite in circular h = 8445.2 km above the surface? Answer in units of s.




2. F = GMm/r^2
F = ma = mv^2/r
v = sqrt(GM/r)
T = 2pi*r/v




3. i got r = 13355200 m; a = 11.8 m/s^2; that gave me the velocity = 12553.54m/s. i plugged it into the period equation and got T = 6684.425s but its wrong
 
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  • #2
nvm i got it
 
  • #3
, the correct answer should be 2.36 hours



I would like to point out that the period of a satellite is directly proportional to the square root of its distance from the center of the planet. In this case, the given satellite is at a distance of 8445.2 km above the surface, which is not the same as the radius of the planet (4910 km). Therefore, the calculated velocity and period will not be accurate.

To obtain the correct answer, we need to use the radius of the planet (4910 km) plus the distance of the satellite from the surface (8445.2 km) to get the total distance (13355.2 km) from the center of the planet. Plugging this value into the period equation, we get a period of approximately 2.36 hours, which is the correct answer.

Furthermore, it is important to note that the given acceleration of gravity on the surface of the planet (11.8 m/s^2) is not relevant to the calculation of the period of the satellite. The period is solely determined by the distance from the center of the planet and the mass of the planet. I hope this helps clarify any confusion.
 

Related to How Is the Period of a Satellite Calculated?

1. What is the period of a satellite?

The period of a satellite is the time it takes for the satellite to complete one orbit around its parent body, such as a planet or moon.

2. How is the period of a satellite calculated?

The period of a satellite can be calculated using Kepler's Third Law, which states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit.

3. What factors affect the period of a satellite?

The period of a satellite is affected by the mass and distance of the parent body, as well as the orbital altitude and velocity of the satellite.

4. Can the period of a satellite be changed?

Yes, the period of a satellite can be changed by altering its orbital altitude or velocity. This can be achieved through maneuvers such as thruster firings or gravitational assists.

5. Why is the period of a satellite important?

The period of a satellite is important because it determines its orbit and position relative to the parent body. This information is crucial for satellite operations and mission planning.

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