The International Space Station (ISS) orbits the Earth in a nearly circular orbit that is 345 km above the Earths surface. (a) How many hours does it take for the ISS to make each orbit? (b) Some of the experiments performed by astronauts in the ISS involve the effects of “weightlessness” on objects. What gravitational force does the Earth exert on a 10 kg object in the ISS? Express your answer in newtons and as a fraction of the force that Earth would exert on the object at Earth’s surface. (c) Considering your answer in part 2(b) above, how can an object be considered weightless in the ISS? 3. Two planets, both of mass m, are separated by a distance d. Their relative velocity is negligible, and there is an inertial frame in which both planets are essentially at rest. The gravitational potential u(r) at the position r in the presence of the two planets, located at R1 and R2, is given as u(r) = − Gm R1 −r − Gm R2 −r . This problem takes place far out in space and there are no other massive objects in the vicinity of the two planets. (a) Draw a graph of u as a function of position (r) along the line between the two planets. (b) There are space stations Alpha and Beta located on the line between the planets. Both space stations are at rest with respect to the planets. Alpha is at distance d 4 from planet 1 and Beta is at distance d 3 from planet 2. A projectile of mass m is fired from station Alpha, with its velocity v pointing directly at planet 2. What is the minimum speed v

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Chapter1: Units, Trigonometry. And Vectors
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The International Space Station (ISS) orbits the Earth in a nearly circular orbit that is 345

km above the Earths surface.

(a) How many hours does it take for the ISS to make each orbit?

(b) Some of the experiments performed by astronauts in the ISS involve the effects of

“weightlessness” on objects. What gravitational force does the Earth exert on a 10 kg

object in the ISS? Express your answer in newtons and as a fraction of the force that

Earth would exert on the object at Earth’s surface.

(c) Considering your answer in part 2(b) above, how can an object be considered weightless

in the ISS?

3. Two planets, both of mass m, are separated by a distance d. Their relative velocity is negligible, and there is an inertial frame in which both planets are essentially at rest. The gravitational potential u(r) at the position r in the presence of the two planets, located at R1 and

R2, is given as

u(r) = −

Gm

R1 −r

Gm

R2 −r

.

This problem takes place far out in space and there are no other massive objects in the vicinity

of the two planets.

(a) Draw a graph of u as a function of position (r) along the line between the two planets.

(b) There are space stations Alpha and Beta located on the line between the planets. Both

space stations are at rest with respect to the planets. Alpha is at distance d

4

from planet

1 and Beta is at distance d

3

from planet 2. A projectile of mass m is fired from station

Alpha, with its velocity v pointing directly at planet 2. What is the minimum speed v

 

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