Find the acceleration or gravity at an altitude of 1000n
Answers
Answer:
How do you find the acceleration of gravity at a certain altitude?
Vishakh Rajendran's answer to What is acceleration due to gravity, and how do you derive an expression for it?
If you see the expression for acceleration due to gravity, it is dependent upon the distance between the two bodies. The value of 9.81 m/s^2 is at sea level only (that is, the surface of earth).
In the link provided above, you can see that the expression for g is g = G M / r^2.
As can be seen, the value of ‘g’ is independent of the mass of the object. But the altitude (distance between the bodies) plays a significant effect.
‘g’ will vary with altitude (the portions above the earth’s surf
Using a to represent acceleration,
a=G*M/r^2, where G is the gravitational constant, r is the distances to the center of the Earth, and M is the mass of the Earth.
This can written as
a=G*M/(R+h)^2, where R is the radius of the Earth and h is the altitude (and r from the first equation is r = R+h). Note that you could use this formula, as is, and this formula is essentially exact (in Newtonian physics).
This can be written as
a=g*(R/(R+h))^2 where g is the acceleration of gravity at sea level (this formula is also essentially exact in Newtonian physics).
As an aside, the above formulas are approxima
Newton’s law of Universal Gravitation states that two masses whose centers are a distance r apart will exert a force on each other equal to
F = GM1M2/r^2
the force of gravity exerted on a mass M2 by the earth is called it’s weight and is equal to
w=M2g
if you set the description of weight given by universal gravity formula equal to the expression with acceleration of gravity g you get
GMearthM2/r^2 = M2g
the m2’s cancel leaving
g=GMearth/r^2
You can write r as:
r=radius of the earth + height above the earth’s surface