What Is the Magnitude of Satellite Acceleration Due to Gravity?

In summary, the magnitude of the acceleration due to gravity at a circular orbit 3.59 x 10^7 m above the Earth's surface is 0.233 m/s^2, calculated using Newton's law of gravity with the given values for G, ME, and r.
  • #1
Cursed
39
0

Homework Statement



Synchronus communications satellites are placed in a circular orbit that is 3.59 x 107 m above the Earth's surface. What is the magnitude of the acceleration due to gravity at this distance?

F=?
G=6.67259 x 10-11 N*m2/kg2
ME (Mass of Earth)= 5.98 x 1024 kg
r = 3.59 x107m

Homework Equations



F = (G*m1*m2)/(r2)
F = MA

The Attempt at a Solution



1) F = G * (ME2/r2) = 1.8514...N
2)F = MA --> (1.8514...N) = (5.98 x 1024)A
3) A = 0.309 m/s2

CORRECT ANSWER: 0.233 m/s2
 
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  • #2
In Newton's law of gravity, r is the distance from the center of the earth, not the distance from the surface.
 
  • #3
Doc Al said:
In Newton's law of gravity, r is the distance from the center of the earth, not the distance from the surface.

Ah, there's the problem. :P

Thanks. :D
 

FAQ: What Is the Magnitude of Satellite Acceleration Due to Gravity?

What is the Satellite Acceleration Problem?

The Satellite Acceleration Problem refers to the discrepancy between the calculated and observed acceleration of an orbiting satellite. According to Newton's laws of motion, the acceleration of a satellite should be constant and equal to the gravitational force exerted by the Earth. However, in reality, there are various factors that can cause the acceleration to deviate from the expected value.

What causes the Satellite Acceleration Problem?

There are several potential causes for the Satellite Acceleration Problem. One factor is the non-uniform distribution of mass within the Earth, which can create variations in the gravitational force. Additionally, atmospheric drag, solar radiation pressure, and the gravitational pull of other celestial bodies can also contribute to the acceleration discrepancy.

How is the Satellite Acceleration Problem addressed?

To address the Satellite Acceleration Problem, scientists use mathematical models and simulations to predict and account for the various factors that can affect satellite acceleration. These models are constantly refined and updated as new data is collected from satellite missions.

What are the implications of the Satellite Acceleration Problem?

The Satellite Acceleration Problem has significant implications for satellite missions and their accuracy. Inaccurate predictions of satellite acceleration can lead to errors in orbit determination and navigation, which can impact the functionality and success of the mission.

Are there any ongoing efforts to solve the Satellite Acceleration Problem?

Yes, there are ongoing efforts by scientists and engineers to better understand and mitigate the effects of the Satellite Acceleration Problem. This includes the development of more accurate mathematical models, as well as the use of advanced technologies and techniques such as drag-free satellites and precision tracking systems.

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