Question bank: Gravitation: Escape Velocity

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Question 1:

Medium

An artificial satellite is about to be launched into space to orbit around the Earth. To ensure that the satellite remains in orbit without falling back to the surface, it needs to reach escape velocity when launched. Escape velocity is the minimum speed required for an object to overcome Earth's gravitational attraction and avoid falling. Consider Earth's mass (M) as 5.97 × 10²⁴ kg, its radius (R) as 6.371 × 10⁶ m, and the gravitational constant (G) as 6.674 × 10⁻¹¹ m³/kg.s². (a) To determine the escape velocity for the satellite, use the escape velocity formula: v = √(2GM/R). Calculate Earth's escape velocity. (b) The rocket fuel responsible for launching the satellite provides a specific energy per unit mass (E) equal to 4 × 10⁷ J/kg. Determine the minimum amount of fuel needed to reach escape velocity, considering the satellite's mass (m) as 500 kg and using the formula: m₁ = m × (1 - e^(-Δv/E)), where Δv is the change in velocity needed to reach escape velocity and m₁ is the minimum amount of fuel. (c) Analyze the relationship between escape velocity and the amount of fuel needed for the successful launch of the satellite. Do you think the amount of fuel affects the choice of orbit or the distance of the satellite from Earth? Justify your answer.

Gravitation: Escape Velocity

Question 2:

Easy

What is the escape velocity of Earth?

Gravitation: Escape Velocity

Question 3:

Medium

Gravitation: Escape Velocity

Question 4:

Easy

What are the factors that affect the escape velocity?

Gravitation: Escape Velocity

Question 5:

Medium

During a Physics class, the teacher explained to the students that escape velocity is the minimum speed required for an object to overcome the gravitational force of a planet and thus escape its attraction. Consider that a student wants to calculate Earth's escape velocity. For this, he has the following information: Earth's mass (M) is approximately 5.97 x 10^24 kg, and Earth's radius (R) is approximately 6,371 x 10^6 m; the gravitational constant (G) is 6.674 x 10^-11 N m²/kg². Find the gravitational force (F) exerted by Earth on an object of mass m on the Earth's surface in terms of M, R, G, and m. Using gravitational potential energy (U) and kinetic energy (K), write an equation that relates the energies involved when the object reaches escape velocity. Calculate Earth's escape velocity using the provided data and the equations found in the previous items.

Gravitation: Escape Velocity

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