The moons mass and radius are 00123 me and 0273 re e earth...

Name: the moons mass and radius are 00123 me and 0273 re e earth for jupiter the corresponding figures are 318 me and 110 re find in each case the gravitational acceleration at the surface and the escape ve
Uploaded: 2021-11-09T19:08:38-08:00
Duration: 4 min 2 s
Channel: Mahipal Kumawat
Description: the moons mass and radius are 00123 me and 0273 re e earth for jupiter the corresponding figures are 318 me and 110 re find in each case the gravitational acceleration at the surface and the escape ve

The Moon’s mass and radius are 0.0123 ME and 0.273 RE (E = Earth). For Jupiter the corresponding figures are 318 ME and 11.0 RE. Find in each case the gravitational acceleration at the surface and the escape velocity

Transcript

00:01 That the gravitational acceleration at the surface of the earth is given by g e is equal to capital g mass of the earth gm e divide r e square and its value is approximately 9 .8 meter per second square now if you want to write the gravitational acceleration at the surface of moon that is g moon that can be written as capital g mass of the moon divide the radius of the moon and its square in the question it is given that the mass of the moon is 0 .0 .0 .123 times the mass of the earth and the radius is 0 .273 times of the radius of the earth and it's square now if you solve this we get 0 .165 g and m e r e square g m e divide r e square can be written as ge so we can write it as 0 .165 g e or we can write it as put the value of g e that is 9 .8 meter per second square and we get 1 .617 meter per second square meter per second square now we will talk about the s -c -f velocity so s -c -f velocity ve at the earth surface is given by under root 2 gere gere if you put the values of g e and r e then we get approximately 11 .2 kilometer per second this is the escape velocity at the earth surface so escape velocity at the surface of the moon vm can be written as to gm and rm now put the value of gm and rm to multiply the gm is 0 .165 multiply g e multiply rm is 0 .273 multiply r e it can be written as 0 .212 multiply vee where v e is the escape velocity at the earth surface under root this 2 g e and r e that is vee now put the value of v that is 11 .2 kilometer second we get around 2 .37 kilometers per second this is the escape velocity at the surface of the moon now at jupiter surface the gravitational acceleration j g j can be written as capital g the mass of the jupiter divide the radius of jupiter and its square now put the values g multiply it is given in the cution 318 times of the mass of the earth and the radius is 11 times of the earth square.

03:03 Put the values we get around 2 .62 multiply gme divide re square.

03:09 Now further solve this, we get around 2 .62 multiply ge and put the value of g .e...

Question

The Moon’s mass and radius are 0.0123 ME and 0.273 RE (E = Earth). For Jupiter the corresponding figures are 318 ME and 11.0 RE. Find in each case the gravitational acceleration at the surface and the escape velocity

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