Find minimum energy to escape an orbit

In summary, the Apollo 11 spacecraft had a mass of 7170 kg, a period of 121 min, and an orbital distance of 1.87167 × 106 m when it orbited the Moon. Assuming a circular orbit and the Moon as a uniform sphere with a mass of 7.36 × 1022 kg, its orbital speed was 1619.837645 m/s. To escape the Moon's gravitational field, the minimum energy required would be zero, which is the sum of the kinetic and potential energies of the spacecraft. Using the equation E = m\left(\frac{v^2}{2} - \frac{GM}{r}\right), we can calculate the escape energy by setting E
  • #1
trivk96
47
0

Homework Statement


When it orbited the Moon, the Apollo 11 spacecraft ’s mass was 7170 kg, its period was 121 min, and its mean distance from the Moon’s center was 1.87167 × 106 m. Assume its orbit was circular and the Moon to be a uniform sphere of mass
7.36 ×1022 kg. Its orbital speed was 1619.837645 m/s

What is the minimum energy required for the craft to leave the orbit and escape the Moon’s
gravitational field?
Answer in units of J



Homework Equations


Don't know of any
maybe UG=-Gm1m2/r


The Attempt at a Solution


UG=(6.67259*10−11*7.36*1022*7170)/1.87167*106

But I do not think this is right
 
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  • #2
It has to have energy zero to escape. How much energy does it have now?
Notice the minus sign in your UG=-Gm1m2/r.
Of course it has kinetic energy, too.
 
  • #3
You're on the right track, but you need one more piece of the puzzle. The total mechanical energy of a body in orbit is given by the sum of the kinetic and potential energies. In particular,
[tex] E = m\left(\frac{v^2}{2} - \frac{GM}{r}\right) [/tex]
The orbit becomes unbound (escape happens) when E ≥ 0.
 

1. What is the minimum energy to escape an orbit?

The minimum energy required to escape an orbit, also known as the escape velocity, is the amount of energy needed to break free from the gravitational pull of a planet or celestial object. This energy is dependent on the mass and radius of the object.

2. How is the minimum energy to escape an orbit calculated?

The minimum energy to escape an orbit can be calculated using the formula: Escape Velocity = √(2GM/R), where G is the gravitational constant, M is the mass of the planet or celestial object, and R is the radius of the object. This formula is derived from the law of conservation of energy.

3. Can the minimum energy to escape an orbit be changed?

Yes, the minimum energy required to escape an orbit can be changed by altering the mass or radius of the object. For example, a planet with a larger mass or smaller radius will have a higher escape velocity, while a planet with a smaller mass or larger radius will have a lower escape velocity.

4. What is the relationship between the minimum energy to escape an orbit and the escape velocity?

The minimum energy to escape an orbit is directly related to the escape velocity. The higher the escape velocity, the more energy is required to escape the orbit. Similarly, a lower escape velocity will require less energy to break free from the orbit.

5. Why is the minimum energy to escape an orbit important?

The minimum energy to escape an orbit is important because it determines whether an object can break free from the gravitational pull of a planet or celestial object. It is also crucial in space exploration and satellite missions, as it helps scientists and engineers determine the amount of energy needed for spacecrafts to leave the Earth's orbit and travel to other planets.

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