An Earth satellite in a circular orbit is at an altitude of 3185.5 km. The acceleration due to

step 1 So here in this question firstly the radius of orbit is the sum of mean radius of the earth and

An Earth satellite in a circular orbit is at an altitude of...

An Earth satellite in a circular orbit is at an altitude of $3185.5 \mathrm{~km}$. The acceleration due to gravity at that distance is $4.36 \mathrm{~m} / \mathrm{s}^{2}$, and the mean radius of the Earth is $6371 \mathrm{~km} .(a)$ What is the radius of the orbit? (b) Find the speed of the satellite.

Key Concepts

Circular Orbits

Circular orbits describe the motion of an object that travels around a central body at a constant distance. In this type of orbit, the gravitational force acts as the centripetal force, keeping the satellite on its circular path without changing its speed.

Gravitational Acceleration and the Inverse Square Law

Gravitational acceleration decreases with distance from the center of a mass according to the inverse square law. This concept is crucial in orbital mechanics as it allows us to relate the acceleration due to gravity at a given distance to the overall gravitational influence of the central body.

Relationship between Altitude and Orbital Radius

The altitude of a satellite is the distance above the surface of the central body, such as the Earth. The orbital radius is the sum of the central body's radius and the satellite’s altitude. Understanding this relationship is essential for converting between measurements relative to the surface and those relative to the center of mass.

Centripetal Force and Orbital Speed

In a stable circular orbit, the centripetal force required to keep the satellite moving in a circle is provided by the gravitational force. This leads to the relationship v²/r = g, where v is the orbital speed and g is the gravitational acceleration at that distance. This principle enables the calculation of orbital speed when the radius of the orbit and gravitational acceleration are known.

Transcript

Please give Ace some feedback