Question

1. if the earth were four times as massive but had the same radius, then what would happe the strength of the gravitational field upon earths surface?

a: it would be 2x larger.
b: it would be 2x smaller.
c: it would be 4x larger.
d: it would be 4x smaller.

1. if the earth had three times the radius but the same mass, then what would happen to the strength of the gravitational field upon earths surface?

a: it would be 3x larger.
b: it would be 3x smaller.
c: it would be 9x larger.
d: it would be 9x smaller.

1. a planet and its moon are gravitationally attracted to each other. which picture be the smallest gravitational force?

1. a 320 n gravitational force causes satellite a (2000 kg) to orbit 50,000 km from e satellite b (400kg) shares the same orbit.

what is the force of gravity between satellite b and earth? justify your

alternate credit: describe or explain 1 orbit - related concept or skill you learned tha

alternate credit: describe / explain 1 gravity - related concept / skill you learned t

Explanation:

Step1: Recall gravitational field formula

The gravitational field strength at a planet's surface is $g = \frac{GM}{r^2}$, where $G$ is the gravitational constant, $M$ is the planet's mass, and $r$ is its radius.
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For Question 15:

Step1: Set initial and new values

Initial: $g_1 = \frac{GM}{r^2}$; New: $M_2=4M$, $r_2=r$

Step2: Calculate new gravitational field

$g_2 = \frac{G(4M)}{r^2} = 4\times\frac{GM}{r^2}=4g_1$
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For Question 16:

Step1: Set initial and new values

Initial: $g_1 = \frac{GM}{r^2}$; New: $M_2=M$, $r_2=3r$

Step2: Calculate new gravitational field

$g_2 = \frac{GM}{(3r)^2} = \frac{GM}{9r^2}=\frac{1}{9}g_1$
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For Question 17:

Step1: Recall gravitational force formula

Gravitational force is $F = \frac{GMm}{d^2}$, where $d$ is the distance between masses.

Step2: Compare forces for each option

• A: $F_A = \frac{GMm}{d^2}$
• B: $F_B = \frac{G(2M)m}{d^2}=2F_A$
• C: $F_C = \frac{GM(2m)}{d^2}=2F_A$
• D: (Assuming $d$ is larger, or masses smaller; based on standard setup, A has the smallest product of masses and same distance, so smallest force)

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For Question 18:

Step1: Recall gravitational force for satellites

Gravitational force on a satellite is $F = \frac{GM_E m_s}{r^2}$, where $M_E$ is Earth's mass, $m_s$ is satellite mass, $r$ is orbit radius.

Step2: Relate forces for Satellite A and B

Orbit radius $r$ is same, so $F \propto m_s$. $\frac{F_B}{F_A} = \frac{m_B}{m_A}$

Step3: Calculate $F_B$

$F_B = F_A \times \frac{m_B}{m_A} = 320\ \text{N} \times \frac{400\ \text{kg}}{2000\ \text{kg}} = 320\ \text{N} \times 0.2 = 64\ \text{N}$
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Answer:

1. C. It would be 4x larger.
2. D. It would be 9x smaller.
3. A (the pair with masses $M$ and $m$, distance $d$)
4. 64 N; The gravitational force on a satellite in the same orbit is directly proportional to the satellite's mass, so scaling the mass by $\frac{400}{2000}=0.2$ scales the force by the same factor.