Escape velocity and acceleration from gravity

In summary, the escape velocity of a body is equal to the maximum velocity that can be achieved from gravitational acceleration. In the given scenario, the spacecraft would reach a maximum velocity of 11 km/sec due to the Earth's gravity. However, in the real world, other gravitational forces, such as the sun's, would need to be taken into account for accuracy. This is because the escape velocity is calculated by setting the total energy equal to zero, neglecting the influence of other bodies. Additionally, meteorites can have higher velocities than 11 km/s, indicating surplus energy that does not solely come from the Earth's gravity. Therefore, the example is correct in theory but incorrect in the real world due to other gravitational forces at play.
  • #1
Cpt. Bob
Ive heard that the escape velocity of a body is the same as the maximum velocity that can be achieved from gravitational acceleration from the same body. Like say it requires a spacecraft to be moving at about 11 km/sec to escape Earth's gravity, and we isolated the Earth and spacecraft , so that the only force acting on the spacecraft is Earth's gravity. Then if the spacecraft was placed stationary any distance from the earth, the maximum velocity it could ever achieve is 11 km/sec. Is this correct, and if so why? Would it be incorrect in the example above, but correct in the real world because of other more powerful gravitational forces, such as the suns, countering acceleration due to Earth's gravity till the spacecraft is very near earth, or near enough for Earth's gravity to become dominant? Thx in advance for any clarification.
 
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  • #2
Originally posted by Cpt. Bob
Is this correct, and if so why?

It is correct, and it is due to the conservation of energy. The escape velocity is calculated by setting the total energy equal to zero. That is, if you start at r=∞ from rest and let go, you would return to the Earth at the escape velocity.

Would it be incorrect in the example above, but correct in the real world because of other more powerful gravitational forces, such as the suns, countering acceleration due to Earth's gravity till the spacecraft is very near earth, or near enough for Earth's gravity to become dominant? Thx in advance for any clarification.

I think you've got it backwards: It is correct in the (idealized) example above, but incorrect in the real world.

When calculating the escape velocity of the Earth, the influence of other bodies is neglected. In the real world, that effect must be taken into account to be accurate.
 
  • #3
Originally posted by Cpt. Bob
if the spacecraft was placed stationary any distance from the earth, the maximum velocity it could ever achieve is 11 km/sec. Is this correct
Yes.
and if so why?
Because in this scenario, the ship can only gain kinetic energy from its potential energy in the Earth's gravitational field. And, as the distance earth-ship approaches infinity, the potential energy approaches a certain limit.
Yet we know that meteorites can have much higher velocities than 11 km/s. Which means they carry surplus energy that does not stem from Earth's gravity alone.
Would it be incorrect in the example above, but correct in the real world
I'd put it the other way round: correct in the above example, but incorrect in the real world
because of other more powerful gravitational forces, such as the suns
Yes, a celestial body that is much more massive than earth, but not much farther away (at a certain time), could (have) provide(d) the surplus energy.
 
  • #4
Great, thanks for the help. I hadnt even thought about conservation of energy as it applies here.:smile:
 
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  • #5
Pretty good answers, guys!
 

1. What is escape velocity?

Escape velocity is the minimum velocity required for an object to escape the gravitational pull of a planet or other celestial body. It is the speed at which the object's kinetic energy is equal to its potential energy at that point.

2. How is escape velocity calculated?

Escape velocity can be calculated using the formula v = √(2GM/r), where v is the escape velocity, G is the gravitational constant, M is the mass of the planet, and r is the distance from the center of the planet to the object.

3. What factors affect escape velocity?

Escape velocity is affected by the mass and radius of the planet, as well as the distance from the center of the planet. It is also affected by the gravitational constant, which is a universal value.

4. What is the difference between escape velocity and acceleration from gravity?

Escape velocity is the minimum speed required to escape the gravitational pull of a planet, while acceleration from gravity is the force that causes an object to accelerate towards the planet's center. Escape velocity is a specific speed, while acceleration from gravity is a continuous force.

5. Can escape velocity be achieved in reality?

Yes, escape velocity can be achieved through various means such as rocket propulsion systems. However, the required velocity may differ depending on the specific planet or celestial body, as well as the mass and composition of the object attempting to escape the gravitational pull.

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