What happens to the strength of the gravitational attraction if you do not alter the distance, but you double both masses?

[1] Short answer questions (2 points for each lettered subheading):

(a) What happens to the strength of the gravitational attraction between two masses if you reduce
the distance between them by half?

Gravitational Force: 𝐹=! #! ##
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What happens to the strength of the gravitational attraction if you do not alter the distance, but
you double both masses?

Hint: You should be able to answer these two questions by inspecting the form of Newton’s
gravitational force equation (above). Imagine making the requested changes to the variable(s)
and then observing the resultant effect on F. You can make it easier on yourself by imagining
that the original values of all the variables (letters) are equal to one.

(b) How many astronomical units are there between the Earth and the Sun?

What is the numerical value of an astronomical unit in kilometers?

(c) How long does it take light to travel from the Sun to the Earth?

How long does it take light to travel from the Sun to Jupiter? (Do not Google!)
Hint: There are 5.2 astronomical units between the Sun and Jupiter.

(d) What time does the last quarter moon set?

What is the phase of the moon if it rises at Noon?

(e) What is the ecliptic plane?

For the Sun, Earth, Moon system define the line of nodes?

[2] Long answer exercise (10 points): Describe in some detail the important telescopic observations that
Galileo about Venus. Why were these observations so important?

[3] Long answer exercise (10 points) Giordano Bruno 1548—1600 was burned at the stake for heresy by
the inquisition. Describe at least three of his astronomical speculations that led him to this horrible fate.

[4] Long answer exercise (10 points) State clearly Kepler’s three laws. Explain the essential meaning of
the second and third law to an interested non-scientific friend without making a mess.

[5] Conversions (10 points; 2 points each only if you show your work.
(See Canvas/ Modules/Conversions)

[a] Convert Saturn’s average distance from the sun 9.54 au into kilometers (show work).

[b] Convert the distance to Andromeda galaxy 2,540,000 light years into parsecs (show work).

[c] Convert 6×10$ kiloparsecs (kpc) into Megaparsecs (Mpc) (show work).

[d] Convert 7 degrees into radians (See Canvas/Modules/Arclength) (show work).

[e] The Milky Way has around one hundred billion stars. If you were to count these stars at a rate of
one every second, how long in years would it take you to finish the task (assuming no breaks).
Hint: (Number of stars) = (Rate of count) X (Time of count).
So, (Time of count in seconds) = (Number of Stars), since (Rate of count) = 1. The problem
therefore, reduces to a conversion of seconds to years. (show work).

Extra points: (8 points)
Explain the difference between inertial mass and weight.

If forces come in equal and opposite pairs (Newton’s third law), is the gravitational force on Newton’s
apple (due the Earth), the same strength as the gravitational force on the Earth (due to the apple)?

Why does the apple fall to the Earth rather than the Earth fall to the apple?
(Hint: Think of Newton’s second law and inertial mass).

For the Earth-Moon system. Who orbits whom? (Not as obvious as it seems).