a) The orbital speed of the astronaut is 1.65 * 10³ m/s.
b) The period of the orbit is 1.90h
a) The speed at which an object orbits the barycenter of a system, which is often a large body, is known as its orbital speed.
The phrase can be used to describe the instantaneous speed at a specific location in the orbit as well as the mean orbital speed, which is the average speed throughout a full orbit.
Newton's second law is used to calculate the astronaut's orbital speed, with
∑F =ma : mg(moon) down = mv²/ r down
now, solve for the velocity, and we get
v = ((gmoon)r)¹/²
v = ((1.52m/s²)(1.7 * 10⁶ m + 100 * 10³))¹/²
v = 1.65 * 10³ m/s
b)
For a period, we know that,
v = -2πr/T
T = 2π (1.8 * 10⁶m)/ 1.65 * 10³m/s
T = 6.84 * 10³s
T = 1.90 h
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