the acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force. true and false
True. The acceleration of a satellite can be derived by equating the universal gravitational force between the satellite and the planet with the centripetal force required to keep the satellite in circular orbit. This allows us to solve for the satellite's acceleration.
True.
The acceleration of a satellite can indeed be derived by equating the universal gravitational force with the centripetal force.
The gravitational force between the satellite and the celestial body it orbits provides the centripetal force necessary to keep the satellite in orbit. The centripetal force is given by the formula Fc = m * a, where Fc is the centripetal force, m is the mass of the satellite, and a is the centripetal acceleration.
On the other hand, the gravitational force is given by the formula Fg = G * (m1 * m2) / r^2, where Fg is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the satellite and the celestial body, respectively, and r is the distance between their centers.
By equating these two forces, we get m * a = G * (m1 * m2) / r^2. Rearranging the equation, we find that the acceleration of the satellite (a) is given by G * (m1 * m2) / r^2m.
So, indeed, the acceleration of a satellite can be derived by equating the universal gravitational force and the centripetal force.
True. The acceleration of a satellite can indeed be derived by equating the universal gravitational force and the centripetal force.
To understand how this is done, let's go through the process step by step.
Firstly, we need to understand the forces acting on a satellite. The primary force acting on a satellite is the gravitational force due to the planet or object around which it is orbiting. According to Newton's law of universal gravitation, this force is given by:
F_grav = G * (m_s * m_p) / r^2
Where:
- F_grav is the gravitational force
- G is the gravitational constant
- m_s is the mass of the satellite
- m_p is the mass of the planet or object
- r is the distance between the satellite and the planet or object
Next, for a satellite to stay in orbit, there also needs to be a centripetal force acting on it. This force is directed towards the center of the orbit and is responsible for keeping the satellite moving in a circular path. The centripetal force is given by:
F_cent = (m_s * v^2) / r
Where:
- F_cent is the centripetal force
- m_s is the mass of the satellite
- v is the velocity of the satellite
- r is the radius of the orbit
Now, in order for the satellite to maintain its orbit, the gravitational force and the centripetal force must be equal. Therefore:
F_grav = F_cent
By substituting the respective formulas for F_grav and F_cent, we get:
G * (m_s * m_p) / r^2 = (m_s * v^2) / r
Now, we simplify this equation by canceling out the mass of the satellite, which gives:
G * m_p / r^2 = v^2 / r
Finally, we can solve for the acceleration, which is given by the centripetal force divided by the mass of the satellite:
a = v^2 / r
Therefore, based on the derivation, we can conclude that the acceleration of a satellite can be found by equating the universal gravitational force and the centripetal force.