You must show your work for full credit.) Calculate the circular speed of an object that orbits the Sun at a distance of 5.2 AU (1 AU = 1.5e+11 meters, the distance between the Earth and the Sun)
To calculate the circular speed of an object orbiting the Sun at a distance of 5.2 AU, we can use the formula for circular velocity.
The formula for circular velocity is:
v = √(G * M / r)
Where:
v is the circular velocity,
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2),
M is the mass of the central body (in this case, the Sun),
and r is the distance between the object and the central body (in this case, 5.2 AU).
First, let's convert the distance from AU to meters:
1 AU = 1.5 × 10^11 meters
So, the distance between the object and the Sun is:
r = 5.2 AU * 1.5 × 10^11 meters/AU
= 7.8 × 10^11 meters
Next, we need to find the mass of the Sun. The mass of the Sun is approximately 1.989 × 10^30 kilograms.
Now, we can substitute these values into the formula to find the circular velocity:
v = √(6.67430 × 10^-11 m^3 kg^-1 s^-2 * 1.989 × 10^30 kg / 7.8 × 10^11 meters)
v = √(1.323 × 10^20)
v ≈ 3.64 × 10^9 meters per second
Therefore, the circular speed of the object orbiting the Sun at a distance of 5.2 AU is approximately 3.64 × 10^9 meters per second.