The discussion revolves around calculating the acceleration due to gravity at a significant altitude above the Earth's surface, specifically when a Trojan Badger is launched from a catapult at a height of 8.5x10^8 m. The problem involves gravitational concepts and the relationship between distance and gravitational acceleration.
The conversation has progressed with participants offering various interpretations and approaches to the problem. Some have provided formulas and attempted calculations, while others have sought clarification on the assumptions and definitions involved. There is an ongoing exploration of how to correctly incorporate the Earth's radius into the calculations.
Participants note the importance of understanding the separation distance in the context of gravitational calculations, particularly how it affects the results when considering objects at significant altitudes. The original problem statement includes the Earth's radius, which is a point of discussion regarding its relevance to the calculations.
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