# What Altitude Above Earth Gives a Gravitational Acceleration of 3.53 m/s²?

• Punchlinegirl
In summary, the question is asking for the altitude above Earth's surface where the gravitational acceleration is 3.53 m/s^2. Using the equation a=GM/r^2 and given G=6.67 x 10^-11 and M=5.98 x 10^24, solving for r gives 1.06 x 10^7 m. However, this is not the correct answer as the question is asking for the altitude above the Earth's surface, not the distance from the center of gravity. To find the correct answer, we need to consider the given value of 'r' as the distance from Earth's center and calculate the altitude above the Earth's surface using that value.
Punchlinegirl
At what altitude above Earth's surface would the gravitational acceleration be 3.53 m/s^2?

I used the equation
a= GM/r^2
G=6.67 x 10^-11 and M= 5.98 x 10^24
Solving for r gives 1.06 x 10^7 m which isn't right... can someone tell me what I'm doing wrong?

Reread the question. You need the altitude above the Earth's surface, not the distance from the center of gravity of the earth.

How would I find that since all I know is the acceleration, mass and radius of the Earth?

You know r = 1.06 x 10^7 m, the problem isn't asking for 'r'.

The problem is asking how far from Earth's surface. You know 'r' of earth, how high above the Earth is r = 1.06 x 10^7m?

## 1. What is gravitational acceleration?

Gravitational acceleration, also known as acceleration due to gravity, is the acceleration experienced by an object in a gravitational field. It is a measure of how quickly an object's velocity changes as it falls towards the surface of a planet or other massive body.

## 2. How is gravitational acceleration calculated?

Gravitational acceleration can be calculated using Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. In the case of gravitational acceleration, the force is the object's weight, and the mass is the object's mass. Therefore, the formula for gravitational acceleration is a = F/m, where a is gravitational acceleration, F is the object's weight, and m is the object's mass.

## 3. What is the value of gravitational acceleration on Earth?

The value of gravitational acceleration on Earth is approximately 9.8 meters per second squared (m/s²). This means that for every second an object falls towards the Earth, its velocity increases by 9.8 m/s.

## 4. Does gravitational acceleration change at different locations on Earth?

Yes, gravitational acceleration can vary slightly at different locations on Earth due to factors such as altitude and the density of the Earth's crust. However, these differences are very small and not noticeable to the average person.

## 5. How does gravitational acceleration differ on other planets?

The value of gravitational acceleration on other planets can vary greatly depending on the planet's mass and radius. For example, on Mars, the gravitational acceleration is only 3.7 m/s², while on Jupiter it is 24.8 m/s². This means that objects will fall at a slower rate on Mars and a faster rate on Jupiter compared to Earth.

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