Problem 776 - JEE Physics

Question

The weight of an astronaut, in an artificial satellite revolving around the earth is (A) zero (B) Equal to that on the earth (C) more than that on earth (D) less than that on the earth

Step-by-Step Solution

Answer

The correct answer is (D) The weight of an astronaut in an artificial satellite revolving around the Earth is less than that on the Earth. This is because the astronaut's weight is technically less in the satellite due to the decreased gravitational force, as they are farther from the Earth's center than when they are on the surface.

Step 1: Understand the concept of weight in physics.

Weight is the force exerted on an object due to gravity. It is the product of mass and acceleration due to gravity. On Earth, this acceleration is about \( 9.8 \, m/s^2 \), while in space it is less.

Step 2: Compare the weight of an astronaut on Earth and in an artificial satellite.

When an astronaut is in an artificial satellite around the Earth, they are farther from the Earth's center than when they are on the surface. As gravitational force decreases with distance from the center of the mass causing the gravity (in this case, Earth), the astronaut's weight would be less in the satellite than on Earth.

Step 3: Consider the perception of weight.

Although the astronaut's weight is technically less in the satellite due to the decreased gravitational force, the astronaut would feel weightless. This is because the satellite is in constant free fall around the Earth, resulting in a sensation of zero gravity.

Step 4: Choose the correct answer based on the definitions of weight.

If weight is defined as the force of gravity on an object, then the weight of an astronaut in an artificial satellite revolving around the Earth is less than that on Earth (Answer D). However, if weight is defined as the perceived or measurable effect of gravity, then the astronaut would feel weightless, or have a perceived weight of zero (Answer A). Based on the most typical definition of weight in physics as a measure of the force of gravity on an object, the correct answer would be (D) The weight of an astronaut in an artificial satellite revolving around the Earth is less than that on the Earth.

Key Concepts

Gravity

Gravity is a fundamental force of nature that draws two masses toward each other. It gives weight to physical objects and causes them to fall to the ground when dropped. On earth, this force is strong enough to keep us firmly on the ground. When discussing weightlessness, it's essential to understand that, while the force of gravity remains present, its effects can be mitigated by physical circumstances, such as free fall.
Gravity is not constant everywhere. At the Earth's surface, it provides a downward acceleration of about 9.8 meters per second squared (\(9.8 \, \text{m/s}^2\)). However, as we move away from the Earth's surface, such as in an artificial satellite orbiting the Earth, this force weakens. This weakening is because gravitational force decreases with the square of the distance from the mass exerting the gravity. Simply put, the farther you are from Earth, the less gravity you feel.

Artificial Satellite

An artificial satellite is a man-made device orbiting the Earth or another celestial body. Examples include communication satellites, weather satellites, and the International Space Station (ISS). When such a satellite is in orbit, it is in a constant state of free fall toward Earth but with enough tangential velocity to keep missing it. This leads to a stable orbit around the planet.
Living conditions in an artificial satellite present unique situations. For instance, an astronaut inside the satellite experiences microgravity, which means they feel almost weightless. This condition occurs not because there is no gravity, but because both the satellite and the astronaut are falling toward Earth at the same rate, creating a sensation of weightlessness.

Gravitational Force

Gravitational force is the attractive force between two masses. The larger the mass, the stronger the force it exerts. This force operates universally, from large celestial bodies like planets to smaller objects like apples. It is always an attractive force and is one of the fundamental interactions within physics.
The equation governing gravitational force is given by Isaac Newton's law of universal gravitation:\[F = \frac{G \cdot m_1 \cdot m_2}{r^2}\]where:

• \(F\) is the gravitational force between two objects
• \(G\) is the gravitational constant
• \(m_1\) and \(m_2\) are the masses of the objects involved
• \(r\) is the distance between the centers of the two masses

When it comes to orbiting objects like artificial satellites, this force provides the necessary centripetal force to keep them in orbit despite their high velocities.

Free Fall

Free fall is when an object is falling solely under the influence of gravity, with no other forces acting upon it. In this state, objects experience acceleration due to gravity and nothing else. Importantly, during free fall, all objects fall at the same rate regardless of their mass as long as only gravity acts upon them and other factors like air resistance are negligible.
An artificial satellite in orbit is in a constant state of free fall. Although it is moving forward at high speed, it is also constantly 'falling' toward the Earth. However, because of its forward momentum, it keeps missing the Earth, resulting in an orbit. Inside such a satellite, astronauts experience what is commonly described as weightlessness. This happens because both they and the satellite are falling together, leading to a condition where they feel no force of support on their bodies and thus perceive no weight.