(a) Determine the amount of work (injoules) that must be done on a 98 kg payload

Question

(a) Determine the amount of work (injoules) that must be done on a 98 kg payload to elevate it to aheight of 991 km above the Earth's surface.
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(b) Determine the amount of additional work that is required to putthe payload into circular orbit at this elevation. ---------J (a) Determine the amount of work (injoules) that must be done on a 98 kg payload to elevate it to aheight of 991 km above the Earth's surface.
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(b) Determine the amount of additional work that is required to putthe payload into circular orbit at this elevation. ---------J

Explanation / Answer

a ) U= GmM/R R= REarth + 991,000 G= 6.67x10-11 N m2/kg2 Let REarth=6.37 x 106 m M =   5.9742 × 1024kilograms U= 6.67x10-11 x 98 x 5.97 ×1024 /( 6.37 x 106 +0.991x106) U= 5.30x10 9 J b) Since F=ma a= F/m ; F= GmM/R2 and a also is equal to a = V2/R Additional energy is required to achive an orbital velocityV Ke= 0.5mV2 since V2=aR= (F/m)R = [(GmM/R2 )/ m]R V2 =  GM/R Ke= 0.5 m GM/R Ke= 0.5 x 98 x 6.67x10-11 x 5.97 ×1024 /( 6.37 x 106 +0.991x106) Ke= 27.0 x106 J That should do it Ke= 27.0 x106 J That should do it

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