calculate the value of g at a height of 3600 km above the surface of the earth?
😢 i can't solve it .....
To calculate the value of acceleration due to gravity (g) at a height of 3600 km above the surface of the Earth, we need to use the formula for gravitational acceleration:
g =G * (M / R²)
where:
- G is the gravitational constant (approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2)
- M is the mass of the Earth (approximately 5.972 x 10^24 kg)
- R is the distance between the center of the Earth and the object (in this case, the height above the Earth's surface plus the Earth's radius)
First, we need to convert the height from kilometers (km) to meters (m):
3600 km = 3600 * 1000 = 3,600,000 meters
Next, we need to add the Earth's radius to the height to get the value of R. The average radius of the Earth is approximately 6,371 km or 6,371,000 meters:
R = 3,600,000 m + 6,371,000 m = 9,971,000 meters
Now, we can plug the values into the formula:
g = (6.67430 x 10^-11 m^3 kg^-1 s^-2) * (5.972 x 10^24 kg) / (9,971,000 m)^2
Calculating this expression will give us the value of g at a height of 3600 km above the surface of the Earth.
To calculate the value of acceleration due to gravity (g) at a height of 3600 km above the surface of the Earth, we can use Newton's Law of Universal Gravitation. This law states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The formula for calculating the value of g is:
g = G * (M / r^2)
Where:
- g represents the acceleration due to gravity
- G is the gravitational constant, approximately equal to 6.674 × 10^-11 N(m/kg)^2
- M is the mass of the Earth, approximately equal to 5.972 × 10^24 kg
- r is the distance between the center of the Earth and the height above its surface
In this case, the height above the Earth's surface is 3600 km, which is equivalent to 3,600,000 meters. Therefore, we can substitute the known values into the formula:
g = (6.674 × 10^-11 N(m/kg)^2) * (5.972 × 10^24 kg) / (3,600,000 m)^2
Simplifying the equation, we have:
g = (6.674 × 10^-11 N(m/kg)^2) * (5.972 × 10^24 kg) / (1.296 × 10^13 m^2)
Calculating this expression will give you the value of g at a height of 3600 km above the surface of the Earth.
mg= F =G•m •M/(R+h)²
g= G•M/(R+h)²
the gravitational constant G =6.67•10⁻¹¹ N•m²/kg²,
h=3600000 m=3.6•10⁶ m
Earth’s mass is M = 5.97•10²⁴kg,
Earth’s radius is R = 6.378•10⁶ m.