An artificial satellite placed into earth's orbit has a mass of 1250kg. It travels at an average distance of 222.5km above the surface of the earth. The radius of the earth is 6370km. What acceleration due to gravity does the earth give the satellite?
I know to find the distance you add both the kms together.
a=g
a=6.593x10^6 m?
thanks in advance
acceleration=GMe/(re+alt)^2
acceleration=[(6.67x10^-11)(1250kg)]/(6.593x10^6)^2=1.92x10^-21
Are the numbers plugged in correctly? The answer seems off.
nevermind, got it, thanks.
Well, if you're looking for the acceleration due to gravity that the earth gives the satellite, you can use the formula:
a = (G * M) / r^2
Where:
a = acceleration due to gravity
G = gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2)
M = mass of the earth (approximately 5.972 × 10^24 kg)
r = distance between the satellite and the center of the earth (in meters)
Now, since the distance given is the average distance above the surface of the earth, you'll need to add the radius of the earth (6370 km) to the distance traveled by the satellite (222.5 km).
So, in meters, the total distance would be (6370 km + 222.5 km) * 1000 = 6,592,500 meters.
Now you can substitute the values into the formula:
a = (6.674 × 10^-11 N m^2/kg^2 * 5.972 × 10^24 kg) / (6,592,500 m)^2
After crunching the numbers, you'll find that the acceleration due to gravity that the earth gives the satellite is approximately 0.3114 m/s^2.
And remember, it's not just any gravity, it's Earth gravity! It's got that special touch!
To find the acceleration due to gravity that the Earth gives to the satellite, you can use the formula for gravitational acceleration:
a = GM/r^2
Where:
a = acceleration due to gravity (in m/s^2)
G = gravitational constant (approximately 6.67430 × 10^-11 m^3/kg/s^2)
M = mass of the Earth (approximately 5.972 × 10^24 kg)
r = distance between the center of the Earth and the satellite (in meters)
First, convert the distance from kilometers to meters by multiplying by 1000:
Distance = 222.5km * 1000m/km = 222,500m
Next, convert the radius of the Earth from kilometers to meters by multiplying by 1000:
Radius = 6370km * 1000m/km = 6,370,000m
Now, substitute the values into the formula and calculate the acceleration:
a = (6.67430 × 10^-11 m^3/kg/s^2 * 5.972 × 10^24 kg) / (6,370,000m + 222,500m)^2
Simplify the denominator:
a = (6.67430 × 10^-11 m^3/kg/s^2 * 5.972 × 10^24 kg) / (6,592,500m)^2
Calculate the acceleration:
a = 6.593 x 10^6 m/s^2
So, the Earth gives the satellite an acceleration due to gravity of approximately 6.593 x 10^6 m/s^2.