Question

1. based on the gravitational field model, use the word list to complete the passage by placing the correct terms on the lines below to describe the effects of earth’s gravitational field on the motion of hst and the moon. 1

word list

a	b	c
greater	greater	greater

compared to the average distance from earth to the moon, the distance from earth to hst is a. as a result, earth’s gravitational field strength at the location of hst is b than earth’s gravitational field strength at any location of the moon’s orbit. therefore, in order to remain in a stable orbit, the orbital period of hst must be c than the orbital period of the moon.
a: ______
b: ______
c: ______

1. based on the model and kepler’s laws, which graph correctly represents the relative orbital speeds of hst and the moon as the two satellites orbit earth twice?

(graphs: four graphs with speed vs time, hst and moon labeled, options (1), (3), (2), (4))

Explanation:

Step1: Analyze distance for blank A

The Hubble Space Telescope (HST) orbits much closer to Earth than the Moon. So the distance from Earth to HST is less than Earth-Moon distance.

Step2: Analyze gravitational field for blank B

Gravitational field strength follows $g=\frac{GM}{r^2}$, where $r$ is distance from Earth's center. Smaller $r$ means greater $g$. So HST's location has greater gravitational field strength.

Step3: Analyze orbital period for blank C

From Kepler's 3rd Law, $T^2 \propto r^3$. Smaller $r$ means smaller $T$. So HST's orbital period is less than the Moon's.

Step4: Analyze orbital speed graph

Orbital speed is $v=\sqrt{\frac{GM}{r}}$. For circular orbits, speed is constant. HST has smaller $r$, so greater constant speed than the Moon.

Answer:

For Question 5:

A: less
B: greater
C: less

For Question 6:

(2) HST has a constant, higher speed; Moon has a constant, lower speed over time