An artificial satellite is going round the earth, close to its surface. Calculate time taken by it to complete one round. Take radius of the earth 6400 km and accleration due to gravity= 9.8m/s
To calculate the time taken for an artificial satellite to complete one round around the Earth, we need to consider the concept of centripetal acceleration.
Centripetal acceleration is the acceleration that keeps an object moving in a circular path. It is given by the formula:
a = v^2 / r
Where:
a = centripetal acceleration
v = velocity of the satellite
r = radius of the circular path
In this case, the satellite is moving around the Earth, close to its surface. The radius of the Earth, given as 6400 km, needs to be converted to meters to maintain consistency with the acceleration due to gravity.
Radius of the Earth = 6400 km = 6400 * 1000 m = 6,400,000 m
The acceleration due to gravity, given as 9.8 m/s^2, acts towards the center of the Earth. It provides the necessary acceleration for the satellite to stay in orbit.
Since the satellite is in a circular orbit, the centripetal acceleration is equal to the acceleration due to gravity:
a = 9.8 m/s^2
Now, we can rearrange the formula for centripetal acceleration:
v^2 = a * r
Substituting the values:
v^2 = 9.8 m/s^2 * 6,400,000 m
v^2 = 62,720,000 m^2/s^2
To find the velocity (v), we take the square root:
v = sqrt(62,720,000) m/s
v ≈ 7913.476 m/s
Now that we have the velocity, we can calculate the time taken for the satellite to complete one round:
Time = circumference / velocity
The circumference of a circle is given by the formula:
circumference = 2 * π * r
Substituting the values:
circumference = 2 * π * 6,400,000 m
Time = (2 * π * 6,400,000 m) / (7913.476 m/s)
Time ≈ 5090.909 s
Therefore, the time taken by the artificial satellite to complete one round around the Earth, close to its surface, is approximately 5090.909 seconds.
Goooooooood
Well, from what I understand, you want me to calculate the time taken by an artificial satellite to complete one orbit around the Earth. Let's give it a go!
To calculate the time taken, we can use the formula for the period of an orbit:
T = 2π * √(r3 / GM)
Where:
T is the period (time taken) in seconds,
π is approximately 3.14 (or you can imagine a delicious pie!),
r is the distance from the center of the Earth to the satellite's orbit (in this case, the radius of Earth plus the satellite's height),
G is the gravitational constant, which is approximately 6.67430 × 10^-11 N*(m/kg)^2,
and M is the mass of the Earth, which is about 5.972 × 10^24 kg.
Now, since you've mentioned the radius of Earth is 6400 km, let's assume that the satellite is really close to the Earth's surface but not on it. Let's say it's at a height of 50 kilometers (just to have some fun with numbers).
Now let's plug in the values into the formula and see what we get! Hang tight, I'm about to do some math... or try to at least.
T = 2 * 3.14 * √((6400 + 50)^3 / (6.67430 × 10^-11 * 5.972 × 10^24))
Calculating... calculating... and voila! According to my calculations (which may or may not involve juggling numbers), the time taken by the satellite to complete one round would be approximately 5066.89 seconds.
Of course, that's just an approximation, and I do tend to round things up (or down) for comedic effect. So let's just say approximately 5067 seconds, give or take a few giggles.
I hope that helps, and I apologize if my clownish calculations got a bit chaotic!
To calculate the time taken by an artificial satellite to complete one round (also known as the orbital period), you can use the following formula:
T = 2π√(r³/GM)
Where:
T = Orbital period of the satellite
π = Pi (approximately 3.14159)
r = Radius of the Earth + height of the satellite above the surface (converted to meters)
G = Gravitational constant (approximately 6.674 × 10^-11 m^3/kg/s^2)
M = Mass of the Earth
Given:
Radius of the Earth (r) = 6400 km = 6400 × 1000 m = 6,400,000 m
Acceleration due to gravity (g) = 9.8 m/s^2
First, let's determine the height of the satellite above the surface of the Earth. Since the satellite is close to the Earth's surface, we can consider the height as negligible compared to the Earth's radius. Therefore, the radius of the satellite's orbit (r) will be equal to the radius of the Earth (6,400,000 m).
Now, let's calculate the orbital period (T):
T = 2π√(r³/GM)
T = 2π√((6,400,000)^3/(6.674 × 10^-11 × M))
To calculate the time taken for one orbit, we need to know the mass of the Earth (M). The mass of the Earth is approximately 5.972 × 10^24 kg.
T = 2π√((6,400,000)^3/(6.674 × 10^-11 × 5.972 × 10^24))
Now, let's calculate the value of T using a calculator:
T ≈ 5064.32 seconds
Therefore, it would take approximately 5064.32 seconds for the artificial satellite to complete one round (orbit) around the Earth.