joel amos said:Given that the Earth has a radius of 6.4x10^6 m, what is the acceleration of a Trojan Badger launched from a catapult when it is 8.5x10^8 m above the surface of the Earth?
I'm not sure how to go about this question. All help is appreciated: formulas, explanations, answers, etc.
Distance between objects? What does that mean in this context?joel amos said:Here's what I've tried.
acceleration of gravity = [Radius of earth/Distance between objects]^2 x 9.8m/s/s
Distance between the Trojan Badger and Earth. In other words, distance from earth.haruspex said:Distance between objects? What does that mean in this context?
Think again. What answer would that give if it were 1mm from the surface of the earth?joel amos said:Distance between the Trojan Badger and Earth. In other words, distance from earth.
joel amos said:The formula I know of is Fg = (G x m1 x m2)/ r^2 . However, I don't have the mass of the badger.
joel amos said:F = ma
But, I don't know why I'd need to use the above equation to calculate distance...I already have distance.
joel amos said:So it'll be...
ma = (G*m*m)/r^s simplified to a = (G*m)/r^2 ?
where...
a = acceleration of gravity
G = gravitational constant
m = mass of earth
r = distance from Earth (8.5x10^8 m)
Is this correct?
And if the above is correct, then why would've my teacher included the radius of the Earth into the problem?
Distance from which bit of earth, exactly? Go back and think about why my 1mm example gave a silly answer.joel amos said:r = distance from Earth (8.5x10^8 m)
Yes.joel amos said:Is it this:
acceleration of gravity = [Radius of earth/(Distance from surface + Radius of earth)]^2 x 9.8m/s/s
The formula for calculating acceleration due to gravity on Earth's surface is g = G * M / r^2, where G is the universal gravitational constant, M is the mass of Earth, and r is the distance from the center of Earth to the object.
Acceleration due to gravity decreases as one moves farther away from Earth's center. This is because the gravitational force between two objects is inversely proportional to the square of the distance between them.
At Earth's surface, the average value of acceleration due to gravity is 9.8 m/s^2. However, this value can vary slightly depending on factors such as altitude, latitude, and the density of Earth's materials.
Earth's radius directly affects the strength of its gravitational pull. The larger the radius, the farther an object is from Earth's center, resulting in a weaker gravitational force.
No, acceleration due to Earth's radius is not the same everywhere on Earth's surface. As mentioned earlier, factors such as altitude and latitude can affect the value of acceleration. Additionally, the density and distribution of Earth's materials can also cause slight variations in acceleration.