The sun has a mass of 1.99 × 1030 kg and is moving in a circular orbit about the center of our galaxy, the Milky Way. The radius of the orbit is 2.3 × 104 light-years (1 light-year = 9.5 × 1015 m), and the angular speed of the sun is 1.1 × 10-15 rad/s. a) Determine the tangential speed of the sun. b) What is the magnitude of the net force that acts on the sun to keep it moving around the center of the Milky Way?
To find the tangential speed of the sun in its orbit around the Milky Way, you can use the formula:
Tangential speed = Radius × Angular speed
a) To find the tangential speed:
Given:
- Radius of the orbit = 2.3 × 10^4 light-years
- Angular speed of the sun = 1.1 × 10^-15 rad/s
First, convert the radius from light-years to meters:
1 light-year = 9.5 × 10^15 m
Radius = 2.3 × 10^4 light-years × 9.5 × 10^15 m/light-year
Radius = 2.185 × 10^20 m
Now, plug in the values into the formula to calculate the tangential speed:
Tangential speed = 2.185 × 10^20 m × 1.1 × 10^-15 rad/s
Tangential speed = 2.4035 × 10^5 m/s
Therefore, the tangential speed of the sun is 2.4035 × 10^5 m/s.
b) To find the magnitude of the net force that acts on the sun to keep it moving around the center of the Milky Way, you can use the formula:
Centripetal force = (Mass × Tangential speed^2) / Radius
Given:
- Mass of the sun = 1.99 × 10^30 kg
- Tangential speed of the sun = 2.4035 × 10^5 m/s
- Radius of the orbit = 2.185 × 10^20 m
Plug in the values into the formula to calculate the centripetal force:
Centripetal force = (1.99 × 10^30 kg × (2.4035 × 10^5 m/s)^2) / (2.185 × 10^20 m)
Centripetal force = 5.502 × 10^30 N
Therefore, the magnitude of the net force that acts on the sun to keep it moving around the center of the Milky Way is 5.502 × 10^30 Newtons.