Question

With what orbital speed will a satellite circle Jupiter if placed at a height of 4.40 10 6 m above the surface of the planet? The mass of Jupiter is 1.90 ✕ 1027 kg and the radius of Jupiter is 7.14 ✕ 107 m.

Answer 1

Answer:

$v = 4.1 \times 10^4 m/s$

Explanation:

Here we know that for every satellite we have net force on it given as centripetal force

So it is given as

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

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

now we will have

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

here we know that

r = distance from the center of the planet

$r = 7.14 \times 10^7 + 4.40 \times 10^6$

$r = 7.58 \times 10^7 m$

now we will have

$v^2 = \frac{6.67 \times 10^{-11}(1.90 \times 10^{27})}{7.58 \times 10^7}$

$v^2 = 1.67 \times 10^9$

$v = 4.1 \times 10^4 m/s$