The luminous star Alnilam in the Orion belt is 1,340 light-years away from Earth. Use the conversion factor 1 parsec = 3.262 lig
ht-years to find the closest conversion of this distance from light-years to parsecs (pc).
2 answers:
Answer:
The distance to the star Alnilam in the Orion belt is 410.8 Pc
Explanation:
The angle due to the change in position of a nearby object against the background stars is known as parallax. This angle is gotten when the position of the object is measured in January and then in July according to the configuration of the Earth with respect to the Sun in those months (see the image below).
The parallax angle can be used to find out the distance by means of triangulation. Making a triangle between the nearby star, the Sun and the Earth(as is shown in the image below), knowing that the distance between the Earth and the Sun (150000000 Km) is defined as 1 astronomical unit:
Where d is the distance to the star.
(1)
Equation (1) can be rewritten in terms of d:
(2)
Equation (2) represents the distance in a unit known as parsec (pc), which is the distance of a star with a parallax angle of 1 arc second.
For the case of the star Alnilam in the Orion belt ( 1340 light-years):
Since 1 parsec is equivalent to 3.262 light-years, therefore:
⇒
Notice how both , Light years and parsecs are units for distance.
Key terms:
Parsec: Parallax of arc second.
Light-year: Distance traveled by light in one year.
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Complete Question:
A hollow cylinder with an inner radius of 4.0mm and an outer radius of 30mm conducts a 3.0-A current flowing parallel to the axis of the cylinder. If the current density is uniform throughout the wire, what is the magnitude of the magnetic field at a point 12mm from its center?
Answer:
The magnitude of the magnetic field = 7.24 μT
Explanation:
Inner radius, a = 4.0 mm = 0.004 m
Outer radius, b = 30 mm = 0.03 m
Radius, r = 12 mm = 0.012 m
let h² = b² - a²
h² = 0.03² - 0.004²
h² = 0.000884
Let d² = r² - a²
d² = 0.012² - 0.004²
d² = 0.000128
Current I = 3A
μ = 4π * 10⁻⁷
The magnitude of the magnetic field is given by:
B = 7.24 * 10⁻⁶T
B = 7.24 μT
Answer:
a
The orbital speed is
b
The escape velocity of the rocket is
Explanation:
Generally angular velocity is mathematically represented as
Where T is the period which is given as 1.6 days =
Substituting the value
At the point when the rocket is on a circular orbit
The gravitational force = centripetal force and this can be mathematically represented as
Where G is the universal gravitational constant with a value
M is the mass of the earth with a constant value of
r is the distance between earth and circular orbit where the rocke is found
Making r the subject
The orbital speed is represented mathematically as
Substituting value
The escape velocity is mathematically represented as
Substituting values