Question

In: Physics

The mass of Earth is 5.972 * 1024 kg, and the radius of Earth is 6,371...

The mass of Earth is 5.972 * 10²⁴ kg, and the radius of Earth is 6,371 km. The mass of the moon is 7.348 * 10²² kg, and the radius of the moon is 1,737 km. The centers of the Earth and the moon are separated by 384,400 km.
(3A) What is the magnitude of the gravitational acceleration (in m/s²) due to the moon at the near-side surface of Earth? (Hint: The correct answer is between 0.000001 and 5).
(3B) How does the gravitational acceleration due to the moon at the near-side surface of Earth compare to the gravitational acceleration due to Earth at the surface of Earth (i.e., what value is g_{moon at surface of
Earth} / g_{Earth at surface of Earth})?
(3C) What is the magnitude of the gravitational acceleration (in m/s²) due to the moon at the surface of the moon? (Hint: The correct answer is between 0.1 and 50).
(3D) What is the magnitude of the gravitational acceleration (in m/s²) due to Earth at the near-side surface of the moon? (Hint: The correct answer is between 0.0001 and 5).
(3E) How does the gravitational acceleration due to Earth at the near-side surface of the moon compare to the gravitational acceleration due to the moon at the surface of the moon (i.e., what value is g_{Earth at
surface of moon} / g_{moon at surface of moon})? (Hint: The correct answer is between 0.00001 and 5).
(3F) Which force is stronger, the gravitational force due to the moon at the near-side surface of Earth, or the gravitational force due to Earth at the near-side surface of the moon?

Expert Solution

Radius of earth , Radius of moon , Distance between the center of earth and moon

Mass of earth , mass of moon

2)

Gravitational acceleration due to moon at the near side surface of earth is

3)

Gravitational acceleration due to earth at the surface of earth is

4)

Gravitational acceleration due to moon at the surface of moon is

5)

Gravitational acceleration due to earth at the near side surface of moon is

6)

7)

That is , the gravitational force due to Earth at the near-side surface of the moon is stronger.

genius_generous answered 2 years ago

A planet of mass 7 × 1024 kg is at location <2 × 1011, -4 ×...

A planet of mass 7 × 1024 kg is at location <2 × 1011, -4 × 1011, 0> m. A star of mass 4 × 1030 kg is at location <-6 ×1011, 6 × 1011, 0> m. It will be useful to draw a diagram of the situation, including the relevant vectors. (a) What is the relative position vector r→ pointing from the planet to the star? r→= < , , > m (b) What is the distance between the planet...

The following information will aid you in your calculations: Mass of Earth: 5.97 x 1024...

The following information will aid you in your calculations: Mass of Earth: 5.97 x 1024 kg Mass of Moon: 7.35 x 1022 kg Mass of Sun: 1.99 x 1030 kg Earth-Moon Distance: 3.84 x 105 km Earth-Sun Distance: 1.496 x 108 km a) Calculate the altitude necessary for a satellite to be in a geostationary (geosynchronous) orbit about the Moon. You may need to look up the term geostationary or geosynchronous and some additional information before...

A satellite of mass mS orbits the Earth (with mass m_E and radius R_E) with a...

A satellite of mass mS orbits the Earth (with mass m_E and radius R_E) with a velocity v and an altitude h. The gravitational force F_G and the centripetal force F_C are given by: F_G = G(m_S · m_E)/(R_E + h)^2 , F_C =(m_S · v^2)/(R_E + h) , G = const. (a) Find an equation for the kinetic energy E_kin(h) of a satellite with an altitude h. (b) Based on the kinetic energy, how much liquid hydrogen (energy density:...

Planet X has a mass of 6 times the mass of Earth, and its radius is...

Planet X has a mass of 6 times the mass of Earth, and its radius is 8 times the radius of Earth. A rocket takes off from Planet X's surface, with a velocity that is 1/3 vesc, where vesc is the escape velocity of the planet. How high from the center of Planet X does the rocket reach in meters?

The space shuttle orbits the earth 16 times per day. mearth = 5.975 x 1024 kg ...

The space shuttle orbits the earth 16 times per day. mearth = 5.975 x 1024 kg rearth = 6.371 x 106 m G = 6.67 x 10-11 N.m2/kg2 How high (in miles) above the earth does it orbit? Height “h” above the Earth’s surface? What is the acceleration due to gravity at this height? aCentrip = aGrav What is the period (in hours) of revolution? T = ? 1/f f Þ rev/hr w = 16 rev/dy =...

A) The mass of Jupiter is 317.8000 times that of earth, and its radius is 10.960...

A) The mass of Jupiter is 317.8000 times that of earth, and its radius is 10.960 times that of earth. Calculate the acceleration of gravity at the surface of Jupiter. Express your answer in g's (i.e. as a ratio to our acceleration of gravity) B) Then calculate the average density of Jupiter (in kg/m3) given the earth's density is 5.52×103 kg/m3

A satellite with Mass m is in orbit with a constant radius around the earth r0...

A satellite with Mass m is in orbit with a constant radius around the earth r0 (RE=6370km, Mass ME = 5,98*1024kg) a) Show that the satellite moves with uniform circular motion and calculate the velocity v0 in dependance of G,M E and R E . b) At which height h above the earth's surface is the geostationary orbit found? Which linear velocity does a satellite have at this height? c) Compare this to the linear velocity on earth's surface as...

A disk of mass 2.5 kg and radius 70 cm with a small mass of 0.09...

A disk of mass 2.5 kg and radius 70 cm with a small mass of 0.09 kg attached at the edge is rotating at 1.8 rev/s. The small mass suddenly flies off of the disk. What is the disk's final rotation rate (in rev/s)?

A solid cylinder with a mass of 3 kg, a radius of 25 cm, and a...

A solid cylinder with a mass of 3 kg, a radius of 25 cm, and a length of 40 cm is rolling across a horizontal floor with a linear speed of 12 m/s. The cylinder then comes to a ramp, and, as it is rolling up this ramp without slipping, it is slowing down. When the cylinder finally comes to a stop and begins rolling back down the ramp, how high is it above the floor?

A satellite of mass 220 kg is placed into Earth orbit at a height of 150...

A satellite of mass 220 kg is placed into Earth orbit at a height of 150 km above the surface. (a) Assuming a circular orbit, how long does the satellite take to complete one orbit? h (b) What is the satellite's speed? m/s (c) Starting from the satellite on the Earth's surface, what is the minimum energy input necessary to place this satellite in orbit? Ignore air resistance but include the effect of the planet's daily rotation. J