Question

Consider formula A to be v = and formula B to be v2 = G. Write the letter of the appropriate formula to use in each scenario. Determine the tangential speed of the moon given the mass of Earth and the distance from Earth to the moon. Determine the tangential speed of a satellite that takes 90 minutes to complete an orbit 150 km above Earth’s surface.

Answer 1

Answer:

Situation one:

The moon will be experiencing gravitational force in the form of centripetal force, so we equate the two formulas.

Gravitational force = GMm /r²

Centripetal force = mv²/r

Equating,

GMm/r² = mv²/r

v² = GM/r

The first scenario will use the formula v² = GM/r

Situation 2:

The second situation will use the simple distance over time formula for velocity, where the distance will be the circumference and the time will be in seconds.

Answer 2

Answer:

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

$v = 7.59 \times 10^3 m/s$

Explanation:

As we know that the moon is at distance "r" from the centre of Earth

So we will have

$\frac{GmM}{r^2} = \frac{mv^2}{r}$

now we have

$v^2 = \frac{GM}{r}$

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

here

M = mass of moon

r = orbital radius of moon

Now we have to find the speed of satellite which complete the circular orbit of height 150 km

now we have

$radius = (6.37 \times 10^6 + 1.50 \times 10^5) meter$

times = 90 minutes

$speed = \frac{distance}{time}$

$v = \frac{2\pi r}{T}$

$v = \frac{2\pi(6.52 \times 10^6)}{90\times 60}$

$v = 7.59 \times 10^3 m/s$