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# Masses in Equilateral Triangle and Net Forces Exerted

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Problem 12.16
Part A
What is the acceleration due to Earth's gravity at a distance from the center of the Earth equal to the orbital radius of the Moon?

Problem 12.12
Suppose that three astronomical objects (1, 2, and 3) are observed to lie on a line, and that the distance from object 1 to object 3 is .

Part A
Given that object 1 has four times the mass of object 3 and seven times the mass of object 2, find the distance between objects 1 and 2 for which the net force on object 2 is zero.

Problem 12.10
IP
Three 6.60- masses are at the corners of an equilateral triangle and located in space far from any other masses.

Part A
If the sides of the triangle are 1.80 long, find the magnitude of the net force exerted on each of the three masses.

Part B
How does your answer to part A change if the sides of the triangle are doubled in length?

Problem 12.64
IP Suppose a planet is discovered that has the same total mass as the Earth, but its radius is 1/4 .
Part A
Is the acceleration due to gravity on this planet more than, less than, or the same as the acceleration due to gravity on the Earth?
a)The acceleration due to gravity on this planet is more than the acceleration due to gravity on the Earth.
B)The acceleration due to gravity on this planet is less than the acceleration due to gravity on the Earth.
C)The acceleration due to gravity on this planet is the sama as the acceleration due to gravity on the Earth.

Part B
Part not displayed

Part C
Calculate the acceleration due to gravity on this planet.

Problem 12.3
A communications satellite with a mass of 400 is in a circular orbit about the Earth. The radius of the orbit is 3.1Ã—104 as measured from the center of the Earth.
Part A
Calculate the weight of the satellite on the surface of the Earth.

Part B
Calculate the gravitational force exerted on the satellite by the Earth when it is in orbit.

Problem 12.14
Part A
At what altitude above the Earth's surface is the acceleration due to gravity equal to 8?

Problem 12.26
Phobos, one of the moons of Mars, orbits at a distance of 9378 from the center of the red planet.
Part A
What is the orbital period of Phobos?

Problem 12.29: GPS Satellites
GPS (Global Positioning System) satellites orbit at an altitude of 3.0Ã—107 .

Part A
Find the orbital period.

Part B
Find the orbital speed of such a satellite.

Problem 12.30
IP Two satellites orbit the Earth, with satellite 1 at a greater altitude than satellite 2.
Part A
Which satellite has the greater orbital speed?
Satellite 2

Part B
Part not displayed

Part C
Calculate the orbital speed of a satellite that orbits at an altitude of 3 above the surface of the Earth.

Part D
Calculate the orbital speed of a satellite that orbits at an altitude of 6 above the surface of the Earth.

Problem 12.39
Part A
Find the minimum kinetic energy needed for a 4.2Ã—104- rocket to escape the Moon.

Part B
Find the minimum kinetic energy needed for a 4.2Ã—104- rocket to escape the Earth.

Problem 12.76: Sampling Comet Wild 2
The spacecraft Stardust flew to within 147 miles of Comet Wild 2 on January 2, 2004, snapping pictures and collecting tiny specks of dust in its glistening halo to be returned to the Earth. The roughly spherical comet has a radius of 2.7 , and the acceleration due to gravity on its surface is 0.00010 .
Part A
Find the mass of the comet.

Part B
Find the speed needed to escape from its surface. (Note: It is easy for a person to jump upward with a speed of 3 .)

Problem 12.43
Part A
What is the launch speed of a projectile that rises vertically above the Earth to an altitude equal to 14 before coming to rest momentarily?

Problem 12.47: The End of the Lunar Module
On Apollo Moon missions, the lunar module would blast off from the Moon's surface and dock with the command module in lunar orbit. After docking, the lunar module would be jettisoned and allowed to crash back onto the lunar surface. Seismometers placed on the Moon's surface by the astronauts would then pick up the resulting seismic waves.
Part A
Find the impact speed of the lunar module, given that it is jettisoned from an orbit 110 above the lunar surface moving with a speed of 1600 .

Problem 12.58
An astronaut exploring a distant solar system lands on an unnamed planet with a radius of 3500 . When the astronaut jumps upward with an initial speed of 3.10 , she rises to a height of 0.600 .
Part A
What is the mass of the planet?

Problem 12.74
Part A
Find the kinetic energy of a 1400- satellite in a circular orbit about the Earth, given that the radius of the orbit is 1.20Ã—104 miles.

Part B
How much energy is required to move this satellite to a circular orbit with a radius of 2.70Ã—104 miles?