A comet has a mass of 2.2 x 10^14 kg and has an average orbital distance of 1.22 x 10^13 m from the Sun. As it orbits, it experiences a force of 1.89 x 10^10 N. Calculate its average orbital speed.

Answer 1

The average orbital speed can be calculated using the formula:

$v = \sqrt{\frac{GM}{r}}$

Where:
- v is the average orbital speed
- G is the gravitational constant: 6.67 x 10^-11 Nm^2/kg^2
- M is the mass of the Sun: 1.989 x 10^30 kg
- r is the average orbital distance

Plugging in the values:

$v = \sqrt{\frac{(6.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2) \times (1.989 \times 10^{30} \, \text{kg})}{1.22 \times 10^{13} \, \text{m}}}$

$v = \sqrt{1.083 \times 10^{20} \, \text{m}^3/\text{kg}\cdot\text{s}^2}$

$v \approx 3.29 \times 10^5 \, \text{m/s}$

Therefore, the average orbital speed of the comet is approximately 3.29 x 10^5 m/s.