91Ó°ÊÓ

Gravitational field strength, often denoted by the symbol \( g \), is a measure of the force exerted by gravity on a unit mass at a point in space. At the surface of the Earth, it measures approximately \( 9.8 \ m/s^2 \), indicating that a 1 kg object experiences a gravitational force of 9.8 N towards the Earth's center.

This concept is crucial because it helps us calculate the gravitational force acting on any object in proximity to the Earth. The formula for gravitational field strength is \( g = \frac{F}{m} \), where \( F \) is the force due to gravity and \( m \) is the mass.

The gravitational field strength decreases with increasing distance from the surface of the Earth. This is because the gravitational force is inversely proportional to the square of the distance from the center of the Earth, described by the formula \( g = \frac{GM}{r^2} \), where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, and \( r \) is the distance from the Earth's center. As the satellite orbits at a distance \( 3.5R \) from the Earth's center, the gravitational field it experiences is considerably weaker than that at Earth's surface.

Orbital motion refers to the motion of an object as it travels around a larger body due to the influence of gravity. For a satellite in orbit around the Earth, the gravitational force acts as a centripetal force, keeping the satellite in a stable path around the planet.

This centripetal force is crucial for maintaining the satellite's orbit and is calculated using the expression \( F_c = \frac{mv^2}{r} \), where \( m \) is the mass of the satellite, \( v \) is its orbital velocity, and \( r \) is the orbital radius.

As derived from the problem, when a satellite orbits at \( 3.5R \) from Earth's center, the centripetal force acting on it due to gravity is given by \( F_g = mg \times \frac{R^2}{(3.5R)^2} \). This position causes the force to significantly decrease compared to when the object is at the Earth's surface.

Earth's gravitational field is the region of space around the planet in which an object experiences a force that pulls it towards the Earth's center. This field is responsible for the phenomena we experience such as objects falling and satellites remaining in orbit.

The strength and effect of Earth's gravitational field change with distance. It diminishes as we move further from the planet. For a satellite orbiting at a distance of \( 2.5R \) above the Earth's surface, this means it is sensing a weaker gravitational pull compared to objects on the surface.

Earth's gravitational field can be quantified using the formula \( g = \frac{GM}{r^2} \). This allows us to compute the necessary conditions for a satellite to stay in orbit at a specific altitude. The decrease in field strength as the distance increases explains the difference in the gravitational force exerted on a satellite compared to that on an object on Earth's surface.