You must show your work for full credit.) Calculate the circular speed of an object that orbits the Sun at a distance of 0.2 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 given distance, we need to use the formula for circular velocity:
v = √(GM/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 Sun (1.989 × 10^30 kg),
and r is the distance from the center of the Sun to the object.
First, convert the distance from AU to meters:
0.2 AU = 0.2 * 1.5e+11 meters = 3.0e+10 meters
Now, substitute the values into the equation:
v = √((6.67430 × 10^-11 m^3 kg^-1 s^-2) * (1.989 × 10^30 kg) / (3.0e+10 meters))
Simplifying the equation:
v = √(1.25216707 × 10^20 m^2 kg s^-2 / 3.0e+10 meters)
Taking the square root:
v ≈ 2.8808 × 10^4 m/s
Therefore, the circular speed of the object that orbits the Sun at a distance of 0.2 AU is approximately 2.8808 × 10^4 meters per second.