What is the gravitational force on the satellite?

[lollypop]

hello everybody:

A satellite of mass m used in a cellular telephone network is in a circular orbit at a height of h above the surface of the earth.

What is the gravitational force on the satellite? Take the gravitational constant to be G , the mass of the Earth to be m_e , and the radius of the Earth to be r_e.
for this question i get the following:
F_g= (G*m*m_e)/(r_e+h)^2

now, for this question
What fraction is this of its weight at the surface of the earth? Take the free fall acceleration to be g.
i'm going to use just the mass of the Earth not the one from the satellite right? but what does it mean "what fraction"?? what formula do i use?

 

[cookiemonster]

They want you to find the ratio of the force of gravity acting on the satellite in orbit to the force of gravity acting on the satellite on the surface of the Earth, i.e.

$$\frac{F_g(r_e + h)}{F_g(r_e)}$$

cookiemonster

 

[M98Ranger]

Hello there,

To answer your first question, the gravitational force on the satellite can be calculated using Newton's Law of Universal Gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In this case, the satellite is in orbit around the Earth, so the equation would be:

F_g = (G*m*m_e)/(r_e+h)^2

Where G is the gravitational constant, m is the mass of the satellite, m_e is the mass of the Earth, and r_e+h is the distance between the satellite and the center of the Earth.

Now, for your second question, "what fraction" is referring to the ratio of the gravitational force on the satellite to its weight at the surface of the Earth. The weight of an object is the force of gravity acting on it, and it is given by the equation:

W = m*g

Where m is the mass of the object and g is the acceleration due to gravity. So to find the fraction, we can divide the gravitational force on the satellite by its weight at the surface of the Earth:

Fraction = F_g / W

= (G*m*m_e)/(r_e+h)^2 / (m*g)

= (G*m_e)/(r_e+h)^2 / g

Hope this helps clarify things for you. Let me know if you have any other questions.