Escape velocity of solar system projectile

In summary, the escape velocity for a projectile fired from Earth in the direction of the Earth's motion around the Sun must take into account the Earth's velocity in its orbit and not just the Sun's gravitational pull. This means that the minimum speed required for the projectile to escape the solar system would be higher than the escape velocity calculated for an object at rest with respect to the Sun.
  • #1

Homework Statement


A projectile is fired from the Earth in the direction of the earth’s motion around
the sun. what minimum speed must the projectile have relative to the Earth to escape the
SOLAR SYSTEM? Ignore the earth’s rotation.


Homework Equations



escape velocity = sqt[(2G x mass of sun) / Earth's distance from sun, 1 AU]

The Attempt at a Solution


is the solution that simple? or did I miss some concepts? I think only the sun's gravitation is considered...

thanks
 
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  • #2
The expression you have is the escape velocity for an object placed where the Earth is and at rest with respect to the Sun, i.e. has zero kinetic energy relative to the Sun. This is not the case for a projectile fired from the Earth because the Earth is moving relative to the Sun.
 
  • #3
kuruman said:
The expression you have is the escape velocity for an object placed where the Earth is and at rest with respect to the Sun, i.e. has zero kinetic energy relative to the Sun. This is not the case for a projectile fired from the Earth because the Earth is moving relative to the Sun.

Thanks.. what should i do then? should i add Earth's velocity in its orbit? how exactly will i compute for that? thanks...

i will submit this after 6 hours,, so i really need direct answers.. can't reply anymore.. thanks in advance
 
  • #4
You don't have to reply if you can't, but we don't give direct answers either. Yes, you need to add the Earth's speed because the projectile is fired in the same direction as the Earth is moving. To find the Earth's speed, consider this: how far does the Earth travel in its orbit in one year?
 
  • #5
kuruman said:
You don't have to reply if you can't, but we don't give direct answers either. Yes, you need to add the Earth's speed because the projectile is fired in the same direction as the Earth is moving. To find the Earth's speed, consider this: how far does the Earth travel in its orbit in one year?

ok sorry,,

but,, do i really need to add Earth's speed? I need the escape velocity relative to earth..

thanks
 
  • #6
As I said, the equation that you quoted gives the speed that the projectile must have if it were at rest relative to the Sun. If it were already moving relative to the Sun (as in this case), would it need a higher or lower speed than the equation gives?
 

What is escape velocity?

Escape velocity is the minimum speed that an object needs to achieve in order to break free from the gravitational pull of a larger object, such as a planet or star, and move into space.

How is escape velocity calculated?

The escape velocity of a planet or star can be calculated using the formula:
Ve = √(2GM/R)
Where:
Ve = escape velocity
G = gravitational constant (6.67 x 10^-11 Nm^2/kg^2)
M = mass of the larger object
R = radius of the larger object

What is the escape velocity of Earth?

The escape velocity of Earth is approximately 11.2 km/s (kilometers per second), or 6.95 mi/s (miles per second). This means that an object needs to be traveling at this speed in order to escape Earth's gravitational pull and enter into space.

Can escape velocity be exceeded?

Yes, escape velocity can be exceeded by an object if it has enough energy or propulsion. This is how spacecrafts are able to leave Earth's orbit and travel to other planets and celestial bodies.

Does the escape velocity of a planet or star change?

The escape velocity of a planet or star depends on its mass and radius, so it can vary from object to object. However, the escape velocity of a specific object will not change unless its mass or radius changes significantly, such as in the case of a planet gaining or losing a large amount of mass.

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