Centripetal force satellite orbiting problem

[pokeefer]

Homework Statement

Question 1: What speed must a satellite have to orbit the Earth at a distance 7.8 x 10^7 m/s from the Earth's centre, where the acceleration due to gravity is 0.065 m/s^2?

Question 2: An object orbits the Earth at a constant speed in a circle of radius 6.38 x 10^6 m, very close to but not touching the Earth's surface. What is its centripetal acceleration?

Homework Equations

Ac = v^2 / r
Fc = mv^2 / r

V = 2(pie)r / T

The Attempt at a Solution

For the first question I assumed that the centripetal acceleration was the force of gravity and so I got:

Ac = v^2 / r
0.065 = v^2 / 7.8 x 10^7
V = 2252 m/s

I don't even know if that is right.

And then the next question is really touch and making me confused. There are too many satellite questions in my homework assignment and its frustrating me. What do I do! :/

 

[gneill]

You could say that the centripetal acceleration was due to the force of gravity, or equal to the acceleration due to gravity. But not equal to the force of gravity. Force is not acceleration.

Your approach on the first question is good. So, keeping that in mind, what is the acceleration due to gravity close to the surface of the Earth?

 

[pokeefer]

That did not help me much at all.

I feel like i don't have enough given information to work with on these questions.

 

[gneill]

What assumption did you make for the first question?

 

[rwisz]

Hello,

I would like to clarify a few points about the centripetal force satellite orbiting problem.

Firstly, in the first question, the centripetal acceleration is not equal to the acceleration due to gravity. The centripetal acceleration is the acceleration towards the center of the circle, while the acceleration due to gravity is the acceleration towards the Earth's center of mass. They are not the same thing.

To solve the first question, you can use the equation Fc = mv^2 / r, where Fc is the centripetal force, m is the mass of the satellite, v is its speed, and r is the radius of its orbit. You can also use the equation V = 2(pie)r / T, where T is the period of the satellite's orbit. By equating these two equations, you can solve for the speed of the satellite.

In the second question, the centripetal acceleration can be calculated using the equation Ac = v^2 / r, where v is the constant speed of the object and r is the radius of its orbit. Again, this is not the same as the acceleration due to gravity. The acceleration due to gravity would be calculated using the equation Fg = GmM / r^2, where G is the gravitational constant, m is the mass of the Earth, and M is the mass of the object.

I understand that there may be many satellite questions in your homework assignment, but it is important to differentiate between the different concepts and equations involved in each problem. I suggest reviewing the equations and concepts related to satellite motion and practicing with different types of problems to improve your understanding.

I hope this helps. Keep up the good work!