Satellite Energy and Orbits Quiz

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What is the total energy of a satellite orbiting close to the Earth's surface?

$rac{GMm}{2R_e}$
$-rac{GMm}{2R_e}$ (correct)
$0$
$-rac{GMm}{R_e}$

Which of the following describes the kinetic energy of a satellite in orbit?

$K = -rac{GMm}{R_e + h}$
$K = rac{mv^2}{R_e}$
$K = rac{GMm}{R_e + h}$
$K = rac{1}{2}mv^2$ (correct)

At which height does a geostationary satellite orbit?

24,000 km
55,000 km
36,000 km (correct)
12,000 km

What type of satellite maintains a constant position relative to the Earth's surface?

Geostationary satellite (D) Signup and view all the answers

What is the primary reason an astronaut experiences weightlessness in a satellite?

The astronaut is in free fall. (A) Signup and view all the answers

Which of the following statements about the total energy of a satellite is true?

Total energy is equal to the sum of potential energy and kinetic energy. (B) Signup and view all the answers

What is the characteristic of a polar satellite's orbit?

Passes through both poles (B) Signup and view all the answers

What best describes the binding energy of a satellite?

Energy required to remove the satellite from its orbit (C) Signup and view all the answers

Which orbital pathway is most commonly used for Earth observation satellites?

Polar orbits (B) Signup and view all the answers

What is the formula for the escape speed needed to leave Earth's gravitational field?

$v_e = rac{GM}{R}$ (C) Signup and view all the answers

If a body of mass m is raised through a height h, how is the change in gravitational potential energy expressed?

$ riangle U = mgh$ (A) Signup and view all the answers

At the center of a solid sphere, what is the gravitational potential energy formula?

$V(r) = rac{3GM}{2R}$ (A) Signup and view all the answers

What happens to the acceleration due to gravity as altitude increases?

It decreases as the altitude increases (C) Signup and view all the answers

Which of the following equations represents the gravitational potential energy of a body at the surface of the Earth?

$U = -rac{GMm}{R_E}$ (A) Signup and view all the answers

How does the gravitational potential vary outside a uniform spherical shell?

$V(r) = rac{GM}{r}$ (D) Signup and view all the answers

At what point is the acceleration due to gravity highest?

At the poles (B) Signup and view all the answers

Which variable represents the mass of the Earth in the formulas for gravitational acceleration?

M (C) Signup and view all the answers

What happens to the gravitational potential energy as a body moves away from the Earth?

It increases steadily (A) Signup and view all the answers

What is the expression for the orbital speed of a satellite located at a height h above the Earth's surface?

$v_o = rac{GM_E}{R_E + h}$ (C) Signup and view all the answers

How does the acceleration due to gravity change with depth?

It decreases until the center is reached, then increases (A) Signup and view all the answers

What is the gravitational potential of a body located on the surface of a shell?

$V(r) = rac{GM}{R}$ (C) Signup and view all the answers

Which factor has the least effect on acceleration due to gravity?

Density of the atmosphere (D) Signup and view all the answers

Which factor does NOT affect the value of escape speed from a planet?

Weight of the object (D) Signup and view all the answers

What is the significance of the angular speed ($ ext{ω}$) in the gravity formula at latitude?

It affects the net gravitational pull at different latitudes (B) Signup and view all the answers

What is the gravitational potential formula for a distance $r$ inside a solid sphere?

$V(r) = rac{GM}{2R}(3 - rac{r^2}{R^2})$ (B) Signup and view all the answers

Which location would experience the lowest acceleration due to gravity?

At the equator (B) Signup and view all the answers

What does the gravitational potential indicate?

The work done in bringing a unit mass from infinity to a point (B) Signup and view all the answers

What is the effect of the Earth's shape on gravitational acceleration?

It causes gravity to be weaker at the equator and stronger at the poles (D) Signup and view all the answers

Which formula correctly describes the change in gravity at a height $h$ above the Earth's surface?

$g(h) = rac{GM}{(R+h)^2}$ (D) Signup and view all the answers

Which of the following statements best describes the Law of Areas in Kepler's Laws?

The line connecting a planet to the Sun sweeps out equal areas in equal times. (D) Signup and view all the answers

What does Newton's law of gravitation imply about the gravitational force between two masses?

The force depends on the product of their masses and the square of the distance between them. (D) Signup and view all the answers

Which of the following characteristics is true regarding gravitational force?

It is always attractive between two masses. (B) Signup and view all the answers

In the context of Kepler's Laws, what does the term 'semi-major axis' refer to?

The longest diameter of an ellipse. (C) Signup and view all the answers

What revolutionary concept did Tycho Brahe contribute to our understanding of planetary motion?

Accurate observational data of planetary positions. (B) Signup and view all the answers

Which equation represents the gravitational force between two point masses?

$F=rac{Gm_1m_2}{r^2}$ (B) Signup and view all the answers

What role did Johannes Kepler play in the development of gravitational theory?

He formulated the laws that describe planetary motion. (B) Signup and view all the answers

What does it mean that gravitational force is a conservative force?

The work done by gravitational force is the same regardless of the path taken. (C) Signup and view all the answers

How did Henry Cavendish contribute to gravitational science?

He discovered the gravitational constant G. (C) Signup and view all the answers

What does the equation $T^2 ext{ is proportional to } R^3$ in Kepler's Laws signify?

The relationship between the distance of a planet from the Sun and its orbit time. (A) Signup and view all the answers

Kepler's Laws

Three laws describing planetary motion around the Sun. These laws were derived from observations, supported Newton's work, and laid groundwork for understanding gravitation.

Law of Orbits

Planets orbit the Sun in elliptical paths, with the Sun at one focus.