Question

In: Physics

Suppose the Earth had two Moons instead of one, with the second moon (let’s call it...

Suppose the Earth had two Moons instead of one, with the second moon (let’s call it Althea) orbiting in a 2:1 resonance inside of the Moon’s orbit. This means Althea orbits twice for each lunar sidereal period of 27.3 days. The mass and radius of Althea are Ma=5.34*10 ˆ 21 kg and Ra= 869 km.

(a) (1 pt) Draw and label a diagram showing ‘from above’, the possible configuration(s) of Earth and its two moons when tides on Earth would be the strongest.

(b) (2 pts) Find the orbital distance of Althea from Earth, in km.

(c) (2 pts) Which appears larger in Earth’s sky, Moon or Althea? (If you didn’t get an answer for part (b), assume r = 2.40*10 ˆ 5 km.)

(d) (3 pts) Tidal forces of a body (1) on another body (2) have a magnitude equal to Ftidal =4GM1M2R2/r^3 where M1 and M2 are the masses of the two bodies, R2 is radius of body (2), and r is their physical separation. What is the relative strength of Althea’s tides on Earth, compared to the Moon’s tides on Earth?

(e) (3 pts) If Althea is in a retrograde orbit (clockwise from above), tidal friction would cause it to slowly spiral inwards. Standing on Earth’s surface, what would Althea’s apparent angular size be just before it is ripped apart by tidal forces? (Recall that the Roche limit is rc = RA(2ME/MA )^1/3. How does this compare to the angular size of the Sun?

Solutions

Expert Solution


Related Solutions

What would the electric force of the Moon on the Earth be if the Moon had...
What would the electric force of the Moon on the Earth be if the Moon had 10^52 electrons attracting an equal number of protons in the Earth? The Earth-Moon distance is 400,000km. Given the value you got (compare to gravity between the Earth & Moon), why do we ignore electrical forces at astronomical distances? -What is the principle in this problem? -Step by Step solution. Pictures help.
Suppose two people (let’s call them Julio and Karina) agree to meet for lunch at a...
Suppose two people (let’s call them Julio and Karina) agree to meet for lunch at a certain restaurant, each person’s arrival time, in minutes after noon, follows a normal distribution with mean 30 and standard deviation 10. Assume that they arrive independently of each other and that they agree to wait for 15 minutes. If each person agrees to wait exactly fifteen minutes for the other before giving up and leaving. h) Report the probability distribution of the difference (not...
Estimate the initial rotation period of the Earth if the Moon had been torn from it,...
Estimate the initial rotation period of the Earth if the Moon had been torn from it, as suggested by the fission theory. Compare your answer to the estimated rate of spin of the early Earth (5 hours or so). Is the fission theory a viable theory?
Explain the difference between mass and weight. Why is your weight on the Moon one-sixth that on Earth?
Explain the difference between mass and weight. Why is your weight on the Moon one-sixth that on Earth?
what is the one way light time from moon to earth, calculate with general relativity effect....
what is the one way light time from moon to earth, calculate with general relativity effect. Please explain each step.
Estimate the number of Solar neutrinos passing through a detector on the Earth in one second....
Estimate the number of Solar neutrinos passing through a detector on the Earth in one second. Assume that the detector has a surface area of 1.0 square meters and is aligned so that it faces directly towards the centre of the Sun. Assume that every neutrino travels without any change (i.e. none are absorbed or converted to a different particle). Also assume that the energy carried out of the Sun by the neutrinos is negligible
This is the full question Consider a‘‘duel’’ between two players. Let’s call these players H and...
This is the full question Consider a‘‘duel’’ between two players. Let’s call these players H and D.Now,we have historical information on each because this is not their first duel. H will kill at long range with probability 0.3 and at short range with probability 0.8. D will kill at long range with probability 0.4 and at short range with probability 0.6. Let’s consider a system that awards 10 points for a kill for each player. Build a payoff matrix by...
... Instead of two blocks and one pulley, let
... Instead of two blocks and one pulley, let
You’ve been examining two enzymes (let’s call them Enzyme A and Enzyme B) . For enzyme...
You’ve been examining two enzymes (let’s call them Enzyme A and Enzyme B) . For enzyme A the Km=1000mM and Vmax = 1000 mmol/min. For Enzyme B, Km= 10mM and Vmax= 100 mmol/min. Showing your work, and explain your reasoning, determine which enzyme works faster at substrate concentrations of 5mM, 100mM, and 2000mM.
There are two call options for the same underlying asset and same maturity. One call option...
There are two call options for the same underlying asset and same maturity. One call option C1 has exercise price of $120 and the other call option C2 has exercise price of $150. Also, one call sells for $8 and the other sells for $10. Select the prices of C1 and C2 from the given two values. Explain the reason/s for your price selection reflecting on the payoff and profit diagrams of the call options.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT