Physics: In 1610, galileo used his telescope to discover four prominent moons around jupiter. their mean orbital radii a and periods t are as follows: (a) io has a mean orbital radius of 4.22 x 108 m and a period of 1.77 days. find the mass of jupiter from this information. (b) europa has a mean orbital radius of 6.71 x 108 m and a period of 3.55 days. find the mass of jupiter from this information. (c) ganymede has a mean orbital radius of 10.7 x 108 m and a period of 7.16 days. find the mass of jupiter

A. Her speed is 4.4 m/s, and her velocity is 0 m/s.Explanation: i took the test on edgenuity...

In 1610, galileo used his telescope to discover

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12.03.2022

Time period of any moon of Jupiter is given by

$T = 2\pi \sqrt{\frac{r^3}{GM}}$

from above formula we can say that mass of Jupiter is given by

$M = \frac{4 \pi^2 r^3}{GT^2}$

now for part a)

r = 4.22 * 10^8 m

T = 1.77 day = 152928 seconds

now by above formula

$M = \frac{4 \pi^2 r^3}{GT^2}$

$M = \frac{4 \pi^2 (4.22 * 10^8)^3}{(6.67 * 10^{-11})(152928)^2}$

$M = 1.9* 10^{27} kg$

Part B)

r = 6.71 * 10^8 m

T = 3.55 day = 306720 seconds

now by above formula

$M = \frac{4 \pi^2 r^3}{GT^2}$

$M = \frac{4 \pi^2 (6.71 * 10^8)^3}{(6.67 * 10^{-11})(306720)^2}$

$M = 1.9* 10^{27} kg$

Part c)

r = 10.7 * 10^8 m

T = 7.16 day = 618624 seconds

now by above formula

$M = \frac{4 \pi^2 r^3}{GT^2}$

$M = \frac{4 \pi^2 (10.7 * 10^8)^3}{(6.67 * 10^{-11})(618624)^2}$

$M = 1.89* 10^{27} kg$

PART D)

r = 18.8 * 10^8 m

T = 16.7 day = 1442880 seconds

now by above formula

$M = \frac{4 \pi^2 r^3}{GT^2}$

$M = \frac{4 \pi^2 (18.8 * 10^8)^3}{(6.67 * 10^{-11})(1442880)^2}$

$M = 1.889* 10^{27} kg$

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