Calculating Satellite Orbit Height Above Earth's Surface

In summary, to determine the height of communications satellites placed in orbits that rotate the Earth once every 24 hours, you can use the equation GM/4(3.14 squared) times T squared, where M is the mass of the Earth. Subtract the Earth's radius from the calculated radius to get the height above the Earth's surface.
  • #1
livblue23
6
0

Homework Statement


Communications satellites are placed in orbits such that they rotate the Earth once every 24.0 hours. Determine how high above the Earths surface these satellites must be placed.


Homework Equations


GM/4(3.14 squared) times T squared


The Attempt at a Solution


so i know that first i have to get the radius by using GM/4(3.14 squared) times T squared, and then subract the Earth's radius from that, but what would be the M in that equation?
 
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  • #2
Hi livblue23! :smile:

(have a pi: π :wink:)

I'm not sure what equation you're using,

but anyway M would be the mass of the Earth. :smile:
 
  • #3


I would like to clarify that the equation you have mentioned is the formula for calculating the period of an orbit (T) in terms of the mass of the central body (M) and the radius of the orbit (r). This formula is derived from Kepler's third law of planetary motion and is not directly related to calculating the height of a satellite above Earth's surface.

To determine the height of a satellite above Earth's surface, we can use the following equation: h = R + r, where h is the height of the satellite, R is the radius of Earth (6371 km), and r is the radius of the satellite's orbit.

To calculate the radius of the satellite's orbit, we can use the following equation: r = (G*M*T^2/4π^2)^(1/3), where G is the gravitational constant (6.67x10^-11 Nm^2/kg^2), M is the mass of Earth (5.97x10^24 kg), and T is the orbital period (24 hours = 86400 seconds).

Plugging in these values, we get r = (6.67x10^-11 * 5.97x10^24 * 86400^2 / 4π^2)^(1/3) = 42165 km.

Therefore, the height of the satellite above Earth's surface would be h = 6371 km + 42165 km = 48536 km.

It is important to note that this calculation assumes a circular orbit and does not take into account any atmospheric drag or other factors that may affect the satellite's orbit. The actual height of a satellite above Earth's surface may vary depending on these factors.
 

1. How is the height of a satellite's orbit above Earth's surface calculated?

The height of a satellite's orbit above Earth's surface is calculated using the following formula:

Height = (GM / (2π)^2) * (T^2 / R^3), where GM is the gravitational constant times the mass of Earth, T is the orbital period of the satellite, and R is the radius of Earth plus the desired orbit height.

2. What is the significance of calculating a satellite's orbit height?

Calculating a satellite's orbit height is important because it determines the satellite's trajectory and coverage area, as well as its communication and data transmission capabilities. It also affects the amount of fuel needed for the satellite to maintain its orbit.

3. How does the orbit height of a satellite affect its speed?

The higher the orbit height, the slower the satellite's speed will be. This is because the gravitational pull of Earth decreases with distance, so the satellite needs to travel at a slower speed to maintain its orbit.

4. Can the orbit height of a satellite be changed?

Yes, the orbit height of a satellite can be changed by using thrusters or other propulsion systems to adjust its speed and trajectory. This is often done to account for changes in the satellite's mission or to avoid collisions with other space objects.

5. How accurate are calculations of satellite orbit height?

The calculations of satellite orbit height are highly accurate, with a margin of error of only a few meters. However, factors such as atmospheric drag and gravitational anomalies can affect the satellite's actual orbit height, so constant monitoring and adjustments may be necessary.

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