Question

What speed should a satellite of mass 4,900 kg moving around
the moon be in order to stay in orbit, if the distance between
them is 4.2% 10ºm and the mass of the moon is 7.36 % 1022 kg?
Estimate G as 6.67 x 10-11 N (m/kg)
X
V = ?
m = 4,900 kg

Answer 1

Based on the calculations, the speed required for this satellite to stay in orbit is equal to 1.8 × 10³ m/s.

Given the following data:

• Gravitational constant = 6.67 × 10⁻¹¹ m/kg²

• Mass of Moon = 7.36 × 10²² kg

• Distance, r = 4.2 × 10⁶ m.

How to determine the speed of this satellite?

In order to determine the speed of this satellite to stay in orbit, the centripetal force acting on it must be sufficient to change its direction.

This ultimately implies that, the centripetal force must be equal to the gravitational force as shown below:

Fc = Fg

mv²/r = GmM/r²

Where:

• m is the mass of the satellite.

• M is mass of the Moon.

Making v the subject of formula, we have;

v = √(GM/r)

Substituting the given parameters into the formula, we have;

v = √(6.67 × 10⁻¹¹ × 7.36 × 10²²/4.2 × 10⁶)

v = √(1,168,838.095)

v = 1,081.13 m/s.

Speed, v = 1.8 × 10³ m/s.

Read more on speed here: https://brainly.com/question/20162935

#SPJ1