So easy, but I just can't grasp this.

[takoma]

For the following hypothetical changes in astronomical bodies answer whether the change would make the specified property L - Larger, S - Smaller, or N - Not changed. (If the first is L and the rest S, enter
LSSSS).

A) If the mass of an object dropped on the surface of Mercury were increased, the acceleration of the object would be ...
B) If the radius of the Earth were larger, the force of gravity on objects on its surface would be ...
C) If the distance between two planets is increased, the force of gravity is ...
D) If the mass of Mars were greater, the acceleration due to gravity on its surface would be ...
E) If the mass of the Sun were doubled and the Earth kept the same distance, the period of the Earth's orbit would be ...

What am I tripping up on?

I've tried:

SSSSN
SSSNN
SSSLN
SSSSS
SLSSN

But apparently all of these combinations are incorrect. Can anyone help? This should be so easy, but I don't understand what I'm missing.

 

[FeynmanMH42]

A) If the mass of an object dropped on the surface of Mercury were increased, the acceleration of the object would be ...
NOT CHANGED. Acceleration due to gravity is a constant, despite the mass. (Remember Galileo and his two weights?) Mercury is the only planet without an atmosphere, so there'd be no air resistance to slow things down.
B) If the radius of the Earth were larger, the force of gravity on objects on its surface would be ...
Depends. If the mass also increased, the force would be larger. But if the mass remained the same, the force would be smaller as the Earth would be less dense (think of a black hole, the mass of a star squeezed into an infinitesimally small speck.)
C) If the distance between two planets is increased, the force of gravity is ...
SMALLER. Gravity between two planets is larger the larger the planets are and the closer they are to each other. The planets are further apart, so smaller.
D) If the mass of Mars were greater, the acceleration due to gravity on its surface would be ...
LARGER. The larger the planet, the greater the pull of gravity.
E) If the mass of the Sun were doubled and the Earth kept the same distance, the period of the Earth's orbit would be ...
SMALLER. The bigger mass would cause there to be a stronger gravity pull on the Earth, making it need to go faster in order to stop it crashing into the Sun.

 

[neophysique]

A) acceleration would be greater. Just like in D.

 

[Doc Al]

A) acceleration would be greater. Just like in D.

Nonsense. The acceleration of an object due to gravity is independent of mass (as FeynmanMH42 explained).

 

[neophysique]

Nonsense. The acceleration of an object due to gravity is independent of mass (as FeynmanMH42 explained).

That's like saying the Earth's moon and Mars accelerate toward the
Earth at the same rate.

 

[Checkfate]

The radius length between the moon and Mars is significantly differant. Thank god radius matters or else all the stars would start running towards each other. lol

This is all shown by the following equation. $$g=\frac{GM_{e}}{r^{2}}$$ where G is the gravitational constant, $$M_{e}$$ is the mass of the earth, and r is the radius between the centres of the two celestial bodies. (notice no mention of mass of other object) As galileo proved, the gravitational acceleratiion is not affected by the mass of the falling object, only on the mass of the planet and the radius between their centres.


also, Even though Jupiter has a mass 10000x greater than us, it is so huge that if you were to stand on it's outer layer(if it were solid), it's gravitational acceleration would only just greater then twice that felt on earth.

That should answer some of your questions as well as set the debate over whether mass plays a part

 

[drpizza]

It seems that all of your questions relate to $$F_g = \frac{G m_1 m_2}{r^2}$$

Keep in mind that if you divide the force by one of the masses, you get the acceleration (as checkpoint has pointed out). Later, you may get questions that not only ask if these quantities increase, but by what degree. i.e. if the distance from the center (radius) is doubled, what happens to the force? (1/4'd) Or, you may get a combination of effects - what if the planet's mass is multiplied by 5, but it's radius only doubles...

 

[LURCH]

I agree with Neo about A), though I'm certain that "N" (not canged) is the answer the author of the question was looking for, the truth is that if we increase the total mass of the system, acceleration due to gravity increases. If their were an "NM" option (Not Much Change), that would be the best answer. The "correct" answer (the one that will get counted as correct on a standardised test) is N, but the true answer is L.

 

[OlderDan]

I agree with Neo about A), though I'm certain that "N" (not canged) is the answer the author of the question was looking for, the truth is that if we increase the total mass of the system, acceleration due to gravity increases. If their were an "NM" option (Not Much Change), that would be the best answer. The "correct" answer (the one that will get counted as correct on a standardised test) is N, but the true answer is L.

Are you talking about the acceleration of the object in an inertial reference frame, or the apparent acceleration of the relative velocity between the object and Mercury? Increasing the mass of the object should have no effect on its acceleration in the center of mass frame. The acceleration of Mercury would increase slightly because of the increased mass of the object. So there will be a slight effect on the relative acceleration, but not on the acceleration of the object.

 

[Doc Al]

OlderDan has it exactly right, of course. Realize that the correction to the relative acceleration is extremely small. See the discussion here: https://www.physicsforums.com/showpost.php?p=343562&postcount=16

 

[ritwik06]

Nonsense. The acceleration of an object due to gravity is independent of mass (as FeynmanMH42 explained).

I absolutely agree with you. Sir Richard P. Feynman stated that gravitational pull is independent of mass. According to Albert Einstein, gravity is a distortion in space. It depends on density, isn't it??