Time period of any moon of Jupiter is given by

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

now for part a)

T = 1.77 day = 152928 seconds
now by above formula



Part B)

T = 3.55 day = 306720 seconds
now by above formula



Part c)

T = 7.16 day = 618624 seconds
now by above formula



PART D)

T = 16.7 day = 1442880 seconds
now by above formula



Hello. You did not inform the experiment that Arthur is conducting, which makes it impossible for your question to be answered accurately. However, I will try to help you in the best possible way.
The hypothesis is an assumption that is made before the experiment is carried out. This hypothesis is formed with the observation of some phenomenon of nature where the researcher believes that two or more elements interact to form a result. In this case, the experiment is carried out to determine whether the assumption, that is, the hypothesis is false or true. In the event that an experiment determines that the hypothesis is false, two things may have occurred: (a) the experiment was set up, or analyzed incorrectly, (b) the elements tested have no relation to the observed phenomenon.
Explanation:
LD₁ = 10⁵ mm⁻²
LD₂ = 10⁴mm⁻²
V = 1000 mm³
Distance = (LD)(V)
Distance₁ = (10⁵mm⁻²)(1000mm³) = 10×10⁷mm = 10×10⁴m
Distance₂ = (10⁹mm⁻²)(1000mm³) = 1×10¹² mm = 1×10⁹ m
Conversion to miles:
Distance₁ = 10×10⁴ m / 1609m = 62 miles
Distance₂ = 10×10⁹m / 1609 m = 621,504 miles.
Answer:
The new Coulomb force is q₁q₂/9πε₀r²
Explanation
The coulomb force between the two charges q₁ and q₂ at a distance r in air is given by F = q₁q₂/4πε₀r².
Now, let us assume the material of dielectric constant κ = 9 is placed between them on the side of the q₁ charge. The value of its effective charge is now q₃ = q₁/κ at a distance of d = r/2 from the q₂ charge.
Since we have air between q₂ and q₃, the coulomb force between them is
F' = q₂q₃/4πε₀d²
= q₂(q₁/κ)/4πε₀(r/2)²
= 4q₂q₁/κ4πε₀r²
= 4/κ(q₂q₁/4πε₀r²)
= 4/9 × (q₂q₁/4πε₀r²)
= q₁q₂/9πε₀r²
So, the new Coulomb force is q₁q₂/9πε₀r²