What Is the Escape Speed from the Sun to Mercury at 25 Million Kilometers?

[Mecia22]

Homework Statement

I need to what the escape speed from the sun to mercury would be if the spaceship is 25 mil km away from the sun.

Homework Equations

The Attempt at a Solution

Basically, all need to know is if I can do this:
Gm1m2/radius of sun+ 25 mil km away from sun=1/2 mv^2.

Also, as you get farther away you can decrease your speed. Correct?

 

[voko]

What is "escape speed from the Sun to Mercury"? The escape speed is usually defined from some location near a gravitating body to infinity, not to another body.

 

[Mecia22]

Oh sorry, I meant just from the sun.

 

[voko]

Then your equation is correct.

 

[Nickie]

I would first clarify the term "gravity wells" as referring to the curvature of spacetime caused by massive objects such as planets and stars, which creates a gravitational force that attracts other objects towards it. This is a fundamental concept in the theory of gravity and is responsible for keeping planets in orbit around the sun.

To calculate the escape speed from the sun to Mercury, we can use the formula v = √(2GM/R), where G is the gravitational constant, M is the mass of the sun, and R is the distance between the sun and Mercury. Plugging in the values for the mass of the sun (1.989 x 10^30 kg) and the distance between the sun and Mercury (25 million km or 2.5 x 10^10 m), we get an escape speed of approximately 48.7 km/s.

As for the statement about decreasing speed as you get farther away, this is not entirely accurate. The escape speed is the minimum speed required for an object to escape the gravitational pull of a massive object at a certain distance. As the object moves further away, the gravitational force decreases, but the escape speed remains the same. However, if the object is already moving at a greater speed than the escape speed, it can continue to move away from the massive object. I hope this clarifies your understanding of gravity wells and escape speed.