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Answer :
The satellite travels approximately 27975.1 miles in 40 minutes ,if the earths radius is 4000 miles at sea level.
We can start by finding the satellite's orbital radius using the fact that it completes one orbit in 120 minutes.
The time it takes for an object to complete one orbit (period) is related to the radius of the orbit (distance from the center of the Earth) by the following equation:
T² = (4π² / GM) * r³
where T is the period in seconds,
G is the gravitational constant,
M is the mass of the Earth, and
r is the radius of the orbit.
We can convert the given period of 120 minutes to seconds:
T = 120 minutes = 120 * 60 seconds = 7200 seconds
Substituting this and the other given values into the equation above, we get:
7200²= (4π² / (6.67430 × 10⁻¹¹ * 5.97 × 10²⁴)) * r³
Solving for r, we get:
r = (GM T² / 4π²)^(1/3)
Plugging in the values, we get:
r = ((6.67430 × 10⁻¹¹ * 5.97 × 10²⁴) * 7200² / 4π²)^(1/3) = 42164.5 miles
This is the distance of the satellite's circular orbit from the center of the Earth. To find the distance the satellite travels in 40 minutes, we can use the fact that it travels a fraction of the circumference of its orbit in that time. The circumference of a circle is given by:
C = 2πr
So the distance the satellite travels in 40 minutes is:
d = (40/120) * 2πr = (1/3) * 2π * 42164.5 miles = 27975.1 miles (rounded to one decimal place)
Therefore, the satellite travels approximately 27975.1 miles in 40 minutes.
To learn more about the 'circular orbit':
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