Minimum energy required to escape the grav field

In summary, the Apollo 11 spacecraft had a mass of 13400 kg and orbited the Moon at a mean distance of 2.56393 X 10^6 m. Using the gravitational constant G of 6.67259 X 10^-11 N m^2/kg^2, the orbital speed of the spacecraft was calculated. To escape the Moon's gravitational field, the minimum energy required would be the work needed to move the craft from its orbit to the point where the gravitational forces from the Moon and Earth are equal and opposite.
  • #1
lizzyb
168
0

Homework Statement



When it orbited the Moon, the Apollo 11 spacecraft 's mass was 13400 kg, and its mean distance from the Moon's center was 2.56393 X 10^6 m. Assume its orbit was circular and the Moon to be a unform sphere of mass 7.36 X 10^22 kg.

a) Given the gravitational constant G is 6.67259 X 10^-11 N m^2/kg^2, calculate the orbital speed of the spacecraft . DONE

b) What is the minimimum energy required for the craft to leave the orbit and escape the Moon's gravitational field? Anser in units of J.

Homework Equations



[tex] KE = \frac{1}{2}m v^2[/tex]

[tex]v_{esc} = sqrt{ \frac{2 G M}{R}}[/tex]

The Attempt at a Solution



I did this: [tex] KE = \frac{1}{2} m_c v^2 = \frac{1}{2} m_c \frac{2 G M_m}{R} = \frac{G M_m m_c }{R}[/tex]

Where M_m is the mass of the moon and m_c is the mass of the spacecraft .

I plugged in the numbers but the anser was wrong. What else would they mean by energy required? Thanks.
 
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  • #2
Perhaps they wanted you to find the work required to move the craft from its orbit to the point at which the gravitational force from the moon and Earth are equal and opposite.
 
  • #3
how do i go about doing that?
 
  • #4
Solve for where the forces are equal. Then, find the work required to move from your current radius to the calculated height.
 

Related to Minimum energy required to escape the grav field

1. What is the minimum energy required to escape the gravitational field of an object?

The minimum energy required to escape the gravitational field of an object is known as the "escape velocity." This velocity depends on the mass and radius of the object and can be calculated using the formula: v = √(2GM/r), where G is the gravitational constant, M is the mass of the object, and r is the distance from the center of the object.

2. How is the escape velocity related to the gravitational field?

The escape velocity is directly related to the strength of the gravitational field. The stronger the gravitational field, the higher the escape velocity will be. This means that objects with a larger mass or a smaller radius will have a higher escape velocity.

3. Can the escape velocity be exceeded?

Yes, it is possible to exceed the escape velocity of an object. This can be achieved by adding additional energy, such as through rocket propulsion, to overcome the gravitational pull of the object. However, this requires a significant amount of energy and is not feasible for most objects in our universe.

4. How does the escape velocity differ on different planets?

The escape velocity varies on different planets depending on their mass and radius. For example, the escape velocity on Earth is approximately 11.2 km/s, while on the Moon it is only 2.4 km/s. This is due to the Moon having a smaller mass and radius compared to Earth.

5. Does the escape velocity change with altitude?

Yes, the escape velocity does change with altitude. As an object moves further away from the center of the gravitational field, the escape velocity decreases. This is because the gravitational force becomes weaker at higher altitudes, making it easier for objects to escape the gravitational pull of the object.

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