# Calculating Escape Velocity for Earth: Where Am I Going Wrong?

• breid040
In summary, the conversation is about calculating the escape velocity of Earth using the formula vescape = sqrt(2GM/r), but getting incorrect results. After plugging in the constants and solving for r, the correct units for r (meters) are eventually identified, leading to the correct answer. The person expresses gratitude for the help.
breid040
Homework Statement
Find the escape energy of earth. Earth's radius is 6378km, its mass is 5.976x10^24kg, and the universal gravitational constant is 6.67x10^-11
Relevant Equations
vescape=Sqrt(2MG/r)
I really cannot understand where this is going wrong...
Plugging in the constants, I get
vescape=Sqrt(2(6.67x10^-11)(5.976x10^24kg)/6378).

(6.67x10^-11)(5.976x10^24kg) gives me 3.99x10^14, and multiplied by 2 gives me 7.97x10^14.

7.97x10^14/6378=1.25x10^11.
The square root of 1.25x10^11 would give 353541 m/s. I know that this is not right, as the escape velocity of Earth is 11.2 km/s.

If I divide 2MR by 6378000, then it gives me the correct answer... but this is not the radius of the earth. I genuinely am stumped. I've typed this carefully into my calculator many times. Help is greatly appreciated.

When substituting for r, what should be the units for r?

breid040
TSny said:
When substituting for r, what should be the units for r?
Ah. Meters. Thanks so much... can't believe I missed that!

TSny

## 1. How do I calculate the escape velocity for Earth?

To calculate the escape velocity for Earth, you can use the formula: v = √(2GM/R), where v is the escape velocity, G is the gravitational constant (6.67 x 10^-11 m^3/kg/s^2), M is the mass of Earth (5.97 x 10^24 kg), and R is the radius of Earth (6.37 x 10^6 m). Plug in these values and solve for v.

## 2. What is the unit of measurement for escape velocity?

The unit of measurement for escape velocity is meters per second (m/s).

## 3. Can I use the same formula to calculate escape velocity for other planets?

Yes, you can use the same formula to calculate the escape velocity for other planets. However, the values for G, M, and R will be different for each planet, so make sure to use the correct values for the specific planet you are calculating for.

## 4. Why is it important to calculate escape velocity for space missions?

Calculating escape velocity is important for space missions because it helps determine the amount of energy needed to launch a spacecraft into orbit around a planet or to escape its gravitational pull. It also helps determine the trajectory and speed of a spacecraft during its journey.

## 5. What other factors can affect the escape velocity for a planet?

The escape velocity for a planet can be affected by factors such as the planet's mass, radius, and distance from the Sun. It can also be affected by the presence of other celestial bodies, such as moons, which can influence the planet's gravitational pull. Additionally, the planet's rotation and atmospheric conditions can also impact the escape velocity.

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