Calculate the effective value of g, the acceleration of gravity, at 6400m , above the Earth's surface.
Calculate the effective value of g , the acceleration of gravity, at 6200km , above the Earth's surface
To calculate the effective value of the acceleration of gravity, g, at a given height above the Earth's surface, you can use the formula:
g' = g * ( R / (R + h) )^2
Where:
g' is the effective value of g at the height h,
g is the acceleration of gravity at the Earth's surface (approximately 9.8 m/s^2),
R is the radius of the Earth (approximately 6,371 km), and
h is the height above the Earth's surface.
For the first scenario, where the height is 6400m above the Earth's surface, we need to convert this to kilometers.
6400m = 6400m / 1000 = 6.4km
Now we can calculate the effective value of g at this height:
g' = 9.8 * ( 6,371 / (6,371 + 6.4) )^2
Solving this equation will give us the effective value of g at 6400m above the Earth's surface.
For the second scenario, where the height is given as 6200km above the Earth's surface, we can directly use the formula to calculate the effective value of g:
g' = 9.8 * ( 6,371 / (6,371 + 6200) )^2
Solving this equation will give us the effective value of g at 6200km above the Earth's surface.
To calculate the effective value of g, the acceleration of gravity, at a certain height above the Earth's surface, we can use the equation:
g' = (g * re^2) / (r^2)
Where:
g' is the effective value of gravity at the given height
g is the acceleration of gravity at the Earth's surface, approximately 9.8 m/s^2
re is the radius of the Earth, approximately 6400 km or 6,400,000 m
r is the distance (height) above the Earth's surface
1. For a height of 6400 m:
g' = (9.8 * (6,400,000)^2) / ((6,400,000 + 6400)^2)
= (9.8 * 40,960,000,000) / (40,960,000,000)
= 9.8 m/s^2
Therefore, at a height of 6400 m above the Earth's surface, the effective value of g (acceleration of gravity) is approximately 9.8 m/s^2.
2. For a height of 6200 km:
First, convert km to m: 6200 km = 6,200,000 m
g' = (9.8 * (6,400,000)^2) / ((6,400,000 + 6,200,000)^2)
= (9.8 * 40,960,000,000) / (246,400,000,000)
≈ 1.620746 m/s^2
Therefore, at a height of 6200 km above the Earth's surface, the effective value of g (acceleration of gravity) is approximately 1.620746 m/s^2.
Use Newtons equation...
g'=GMe/(re+r) where r is the distance above the earth's surface.