Author Question: What is escape velocity from the center of the Earth? (Read 1269 times)

hummingbird

  • Sr. Member
  • ****
  • Posts: 324
Escape velocity on the surface is 11.2 km/s.

If a hole is drilled to the center of the Earth, then what initial velocity should have the projectile launched from the center of the Earth in order to escape to the infinity?



curlz

  • Hero Member
  • *****
  • Posts: 538
An interesting question which I haven't encountered before.  I won't run the numbers, but I'll outline the solution: the total kinetic energy required will be that needed to reach infinity from the surface, plus that required to reach the surface from the center.  The former is easily determined from the stated escape velocity; the latter can be determined by integrating the gravitational force from zero to the surface.  Although the value of this depends on the earth's density at various depths, it is an adequate approximation to assume that the density is constant throughout, and in that case the gravitational pull is simply a linear function of the distance to the center, and the integral will be proportional to the square of that distance.



Related Topics

Need homework help now?

Ask unlimited questions for free

Ask a Question

Sandstorm

  • Sr. Member
  • ****
  • Posts: 268
Brilliant question, simple answer (I think).

First dropping an apple towards the earth's center.  Its velocity should peak at the velocity of low earth orbit which is Escape Velocity/sqr(2).  (This assumes uniform density).

Therefore, using Conservation of Energy
Escape V center of Earth = sqr(Escape V^2 + (EscapeV/sqr(2))^2)
=sqr(1.5) * Escape V



 

Did you know?

Sperm cells are so tiny that 400 to 500 million (400,000,000–500,000,000) of them fit onto 1 tsp.

Did you know?

The most common treatment options for addiction include psychotherapy, support groups, and individual counseling.

Did you know?

The average office desk has 400 times more bacteria on it than a toilet.

Did you know?

Serum cholesterol testing in adults is recommended every 1 to 5 years. People with diabetes and a family history of high cholesterol should be tested even more frequently.

Did you know?

In the United States, an estimated 50 million unnecessary antibiotics are prescribed for viral respiratory infections.

For a complete list of videos, visit our video library