1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
jek_recluse [69]
3 years ago
15

In 1610, galileo used his telescope to discover four prominent moons around jupiter. their mean orbital radii a and periods t ar

e 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 from this information. (d) callisto has a mean orbital radius of 18.8 x 108 m and a period of 16.7 days. find the mass of jupiter from this information
Physics
1 answer:
katrin2010 [14]3 years ago
6 0

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

You might be interested in
How to find weight in science
Kaylis [27]

There are several different methods, depending on the particular situation.  A few that might occasionally be useful include:

-- Read the label on the package.

-- Measure the mass and multiply by the local acceleration of gravity.

-- Measure the mass AND the local acceleration of gravity, then multiply.

-- Place the object or sample on a bathroom scale.

-- Place the object on one end of a symmetrical see-saw.  Through trial and error, determine the weight required on the other end to balance the system.

8 0
3 years ago
Which elements will have chemical properties similar to NE (neon)?
gregori [183]
Elements that have similar properties are in the same column(group).  Neon is in group 18 (or VIIIA depending on your table).  So look for an element that is in the same column.

O - Group 16
Ar - Group 18
N - Group 15

The one that matches is Ar (both 18)
6 0
3 years ago
A box has a length of 18 cm, a height of 19 cm, and a width of 20 cm. What is its volume?
OLEGan [10]
To find the volume, multiply them all together: (height x width x length)

18 x 19 x 20 = 6840cm³
3 0
3 years ago
Read 2 more answers
A diver who is 10.0 meters underwater experience has a pressure of 202 kPa. If the diver’s surface area is 1.50 meters squared,
erastova [34]

Force = 202,200 x 1.5 ms.q
Force = 303,000 newtons 

4 0
3 years ago
Please can someone solve this physics question with a good explenation.
zimovet [89]

Answer:

The coefficient of dynamic friction is 0.025.

Explanation:

Given:

Initial speed after the push is 'v' as seen in the graph.

Final speed of the stone is 0 m/s as it comes to rest.

Total distance traveled is, D=29.8\ m

Total time taken is, t_{total}=17.5\ s

Time interval for deceleration is 3.5 to 17.5 s which is for 14 s.

Now, average speed of the stone is given as:

v_{avg}=\frac{D}{t_{total}}=\frac{29.8}{17.5}=1.703\ m/s

Now, we know that, average speed can also be expressed as:

v_{avg}=\frac{v_i+v_f}{2}\\1.703=\frac{v+0}{2}\\v=2\times 1.703=3.41\ m/s

Now, from the graph, the vertical height of the triangles is, v=3.41\ m/s

The deceleration is given as the slope of the line from time 3.5 s to 17.5 s.

Therefore, deceleration is:

a=\frac{\textrm{Vertical height}}{\textrm{Time interval}}\\a=\frac{v-0}{17.5-3.5}\\a=\frac{3.41}{14}=0.244\ m/s^2

Frictional force is the net force acting on the stone. Frictional force is given as:

f=\mu_dN\\Where, \mu_d\rightarrow \textrm{coefficient of dynamic friction}\\N\rightarrow \textrm{Normal force}\\N=mg\\\therefore f=\mu_dmg

Now, from Newton's second law, net force is equal to the product of mass and acceleration.

Therefore,

\mu_dmg=ma\\\mu_d=\frac{a}{g}

Plug in 0.244 for 'a' and 9.8 for 'g'. This gives,

\mu_d=\frac{a}{g}=\frac{0.244}{9.8}=0.025

Therefore, the coefficient of dynamic friction is 0.025.

3 0
3 years ago
Other questions:
  • Bode's Law: correctly predicted the location of Jupiter, uses a number sequence to determine planetary distances, incorrectly pr
    7·1 answer
  • What type of wave requires a medium to transfer energy
    8·2 answers
  • A 2.0 kg arrow is fired at 10 m/s into a stationary 10kg block of ice what is the velocity of the arrow / ice combination after
    5·1 answer
  • Which of the following is the most important skill for a human resource
    5·1 answer
  • If a gas has an absolute pressure of 319 kPa, its gage pressure is A. 419 kPa. B. 219 kPa. C. 439 kPa. D. 199 kPa.
    15·1 answer
  • Helpppppp please!!!!!
    15·2 answers
  • Our planet heats unevenly, explain how this affects wind patterns. Use the words sea breeze and land breeze please :)
    11·2 answers
  • A basketball referee tosses the ball straight up for the starting tip-off. At what velocity must a basketball player leave the g
    8·1 answer
  • Where does solar energy wastes go
    8·1 answer
  • A huge block of stone has a mass of 650kg and gains 70000j of gpe. how high has it been raised? (g = 10m/s2 )
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!