In this problem, be especially wary of round-off; keep 3 sigfigs in each answer

Question

In this problem, be especially wary of round-off; keep 3 sigfigs in each answer and throughout your calculations.

Based on the following data about planet X (which orbits around the Sun):

Planet X's distance from Sun = 3.4*1012 m
Planet X's radius = 1.8*106 m
Planet X's mass = 9*1022 kg

a.) Find gx, the size of the acceleration due to gravity on the surface of Planet X. m/s2

b.) What is the weight of a 10 kg mass on the surface of Planet X?  N
(How does this compare to its weight on Earth?)

c.) How long would it take for a ball dropped from a height of 10 m to hit the ground?  s
(How does this compare to the time it would take on Earth?)

d.) At 1 of Planet X's radii above the planet's surface, what is gx?  m/s2

e.) For Planet X's orbit around the Sun, please find:
its orbital speed:  m/s
its centripetal acceleration:  m/s2

f.) How long is a year on Planet X? Express your answers in both seconds and Earth years:
in seconds
in Earth years

Explanation / Answer

Here ,

a)

acceleration due to gravity = (G * m/R^2)

acceleration due to gravity = 6.626 *10^-34 * 9*10^22/(1.8 *10^6)^2

acceleration due to gravity = 1.856 m/s^2

the acceleration due to gravity is 1.856 m/s^2

b)

for a 10 kg mass

weight = m * g

weight = 10 * 1.856

weight = 18.6 N

the weight of 10 Kg mass is 18.6 N

c)
as the time taken for the ball to fall

t = sqrt(2 * h/g)

t = sqrt(2 * 10/1.856)

t = 3.28 s

the time taken for the ball to fall is 3.28 s

d)

as r = R + R

r = 2 * R

acceleration due to gravity = (G * m/(2R)^2)

acceleration due to gravity = 6.626 *10^-34 * 9*10^22/(2 * 1.8 *10^6)^2

acceleration due to gravity = 0.464 m/s^2

the acceleration due to gravity is 0.464 m/s^2

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