Solve for Escape Velocity on Mars: Differential Equation Method

Once you have that, you can solve for the velocity by integrating the equation and applying initial conditions. In summary, to determine the velocity of a particle projected outward from Mars and acted upon by gravity, you need to first model the motion into a differential equation and then solve it. Once you have the velocity, you can use it to find the velocity of escape from Mars.
  • #1
verticos
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Homework Statement


The acceleration of gravity on the surface of Mars is 0.38g. The radius of Mars is 2100 miles. Determine the velocity of a particle projected in a radial direction outward from Mars and acted upon by only the gravitational attraction of Mars by first modeling the motion into a differential equation and then solving the differential equation. Use your result to determine the velocity of escape from Mars.


Homework Equations


v^(2) = [2gR^(2) / r] + C


The Attempt at a Solution


g = 0.38
r = 2100 miles
R = ?
I don't understand the differential equation part at all. I'm confused because I'm only given 2 variables...

Any help is appreciated
 
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  • #2
Your differential equation should consist of an expression that relates the acceleration experienced by the projectile with the distance.
 

1. What is escape velocity on Mars?

Escape velocity on Mars is the minimum speed required for an object to escape the gravitational pull of the planet and enter into orbit.

2. How is escape velocity on Mars calculated?

Escape velocity on Mars can be calculated using the following formula:

Ve = √(2GM/R)

Where Ve is the escape velocity, G is the universal gravitational constant, M is the mass of Mars, and R is the radius of Mars.

3. Why is the differential equation method used to solve for escape velocity on Mars?

The differential equation method is used because it takes into account the changing gravitational force as the object moves away from the planet's surface. This makes it a more accurate method compared to using a simple formula.

4. What are the variables involved in the differential equation method for solving escape velocity on Mars?

The variables involved are time, distance, mass of the planet, and the initial velocity of the object.

5. Can the differential equation method be applied to other planets?

Yes, the differential equation method can be applied to other planets as long as the necessary variables are known. However, the values for the variables will be different for each planet.

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