Problem 66 - Master Resource Book in JEE Main Physics

Question

A space ship moves from earth to moon and back. Th. greatest energy required for the space ship is \(t\) overcome the difficulty in (a) entering the earth's gravitational field (b) take off from earth's field (c) take off from lunar surface (d) entering the moon's lunar surface

Step-by-Step Solution

Answer

(b) Take off from Earth's field.

Step 1: Identify the Concept

To solve this problem, we need to understand the concept of gravitational fields and energy requirements when moving between celestial bodies. The energy required to overcome a gravitational field is directly related to the gravitational pull of the body involved. This problem involves comparing the gravitational forces of the Earth and the Moon.

Step 2: Analyze Gravitational Fields

Earth has a much stronger gravitational field compared to the Moon. This is because Earth's mass is significantly larger, making the gravitational force stronger. Therefore, overcoming Earth's gravitational field requires more energy than overcoming the Moon's.

Step 3: Consider Space Ship Movements

The spaceship faces the greatest energy requirement during take-off from the Earth's surface because it needs to overcome Earth's strong gravitational pull. Moving away from the Moon requires less energy due to its weaker gravity. Entering gravitational fields themselves require less energy compared to take-off.

Step 4: Examine All Options

Evaluate each option based on the gravitational energy requirements analyzed in the previous steps: (a) Entering Earth's gravitational field requires less energy because it's a passive process. (b) Taking off from Earth's field requires significant energy due to strong gravity. (c) Taking off from the lunar surface requires less energy due to weaker gravity. (d) Entering the Moon's gravitational field requires the least energy, as it is also a passive process.

Step 5: Choose the Correct Option

Based on the evaluation, the greatest energy requirement is for overcoming Earth's gravitational field during take-off because the spaceship must exert a force greater than Earth's gravitational attraction, which is stronger than any other gravitational force encountered in this trip.

Key Concepts

Energy Requirements

When a spaceship embarks on a journey from the Earth to the Moon and back, understanding the energy requirements is crucial. The energy needed for space travel is largely dependent on the gravitational fields of the celestial bodies involved. Gravitational fields can be thought of as the invisible force fields that every planet and moon generates.
Earth's gravitational field is relatively strong due to its large mass. Because of this, when a spaceship needs to take off from the Earth's surface, it must overcome Earth's strong gravitational pull. This substantial energy necessity is due to the fact that the spaceship has to work against this powerful force. As a result of the Earth's larger mass, a large amount of fuel and energy is required to break free from its grip.

• Taking off from Earth: High energy requirement
• Entering other gravitational fields: Lower energy requirement

On the other hand, the Moon's gravitational field is much weaker. The lower gravitational pull means that less energy is needed for a spaceship to escape its gravity compared to the Earth. Therefore, taking off from the lunar surface requires considerably less energy.

Space Travel

Space travel involves moving a spacecraft from one celestial body to another and wisely managing energy resources. When planning a space mission, one has to account for the energy needed at various stages.
During take-off from Earth, the energy demand reaches its peak. This is due to the need to overcome the strong gravitational attraction of Earth. Once the spacecraft has left the Earth's gravitational influence, the journey becomes less energy-intensive. This phase of the travel is more about guided movement towards a destination rather than raw power exertion.

• Phase of peak energy use: Take-off from Earth
• Later phases: Energy-efficient trajectories

As the spaceship approaches the Moon, it enters the Moon's gravitational field, mostly passively drifting closer with little energy required to "enter" it. After landing, taking off from the Moon uses significantly less energy, thanks to its weaker gravitational attraction. Hence, understanding these energy dynamics is fundamental for efficient space travel.

Celestial Bodies

Celestial bodies like Earth and the Moon have distinct gravitational fields, influencing the energy needed for spacecraft to move between them.
These bodies can be thought of as large objects in space that exert gravity. The mass of a celestial body directly affects its gravitational strength. Earth, with its significantly larger mass compared to the Moon, has a much stronger gravitational pull. This means activities such as launching a spacecraft from Earth require a lot of effort and energy due to this strong gravitational force.

• Earth: Strong gravitational pull
• Moon: Weaker gravitational pull

When a spaceship approaches a celestial body, it naturally starts to "fall" toward it, entering its gravitational field with minimal energy use. Both understanding and calculating these gravitational impacts are crucial to planning space missions, as the forces will dictate how much energy is required for various maneuvers, such as take-offs and landings.