worksheet_19.doc

19 Worksheet (A2) Data needed to answer questions can be found in the Data, formulae and relationships sheet. 1

Define gravitational field strength at  at a point in space.

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Show that the gravitational constant G has the unit N m 2 g!2.

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"he gravitational field strength on the surface of the #oon is 1.$ N g !1. %hat %hat is the the wei weigh ghtt of of an an astr astron onau autt of of mass mass &' g stan standi ding ng on the the sur surfa face ce of the the #oo #oon( n(

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)alculate the magnitude of the gravitational force between the ob*ects des cribed below. +ou +ou ma assume that the ob*ects are -point masses. a

b

c

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two protons separated b a distance of /.' 0 1' !1 m mass of a proton 3 1.4 0 1' !24 g  g5

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two binar stars, each of mass /.' 0 1' 2& g, with a separation of &.' 0 1' 12 m

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two 1/'' g elephants separated b a distance of /.' m

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"he diagram shows the #oon and an artificial satellite orbiting round the 7arth. "he radius of the 7arth is  R.

a b c

%rite an equation for the gravitational field s trength  g at a distance r from the centre of an isolated ob*ect of mass  M . 8 what factor would the gravitational field decrease if the distance from the centre of the mass were doubled( "he satellite orbits at a distance of / R from the 7arths centre and the #oon is at a distance of /9 R. )alculate the ratio: gravitational field strength at position of  satellite gravitational field strength at position of  #oon

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6 "he planet Neptune has a mass of 1.' × 1'2$ g and a radius of 2.2 × 1'4 m.

)alculate the surface gravitational field strength of Neptune.

;S and ; riginal material ? )ambridge @niversit =ress 2'1'

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19 Worksheet (A2)

7 )alculate the radius of =luto, given its mass is /.' × 1'26 g and its surface gravitational field strength has been estimated to be .' N g !1.

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8 ; space probe of mass 1&'' g is travelling from 7arth to the planet #ars. "he space probe is midwa between the planets. @se the data given t o calculate: a the gravitational force on the space probe due to the 7arth b the gravitational force on the space probe due to #ars c the acceleration of the probe due to the gravitational force acting on it.

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Data

separation between 7arth and #ars = 4.& × 1'1' m mass of 7arth = $.' × 1'2 g

mass of #ars = $. × 1'26 g

9 ;n artificial satellite orbits the 7arth at a height of '' m above its surface . "he satellite has a mass /''' g, the radius of the 7arth is $'' m and the mass of the 7arth is $.' × 1'2 g. Aor this satellite, calculate: a b c 10 a b c d

the gravitational force eBperienced its centripetal acceleration its orbital speed.

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7Bplain what is meant b the term gravitational potential  at  at a point. %rite down the gravitational potential energ of a bod of mass 1 g when it is at an infinite distance from another bod. "he radius of the 7arth is $. × 1'$ m and the mass of the 7arth = $.' × 1'2 g. )alculate the potential energ of the 1 g mass at the 7arths surface. %rite down the minimum energ required to remove the bod  totall from the 7arths gravitational field.

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11 "he planets in our solar sstem orbit the Sun in almost circular orbits. a Show that the orbital speed v of a planet at a distance r from the centre of the Sun is given b: v3 b

GM 

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r 

"he mean distance between the Sun and the 7arth is 1./ × 1'11 m and the mass of the Sun is 2.' × 1'6' g. )alculate the orbital speed of the 7arth as it travels round the Sun.

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12 "here is a point between the 7arth and the #oon where the net gravitational field strength is Cero. ;t this point the 7arths gravitational field strength is equal in magnitude but opposite in direction to the gravitational field strength of the #oon. iven that: mass of  7arth mass of  #oon

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calculate how far this point is from the centre of the #oon in terms of  R, where R is the separation between the centres of the 7arth and the #oon.

"otal:

;S and ; riginal material ? )ambridge @niversit =ress 2'1'

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