Give reason ?

The mass of Jupiter is 319 times more than the mass of the earth and the gravity of Jupiter is 25 ms^-2 and earth is 9.8 ms^-2 which is only 2.5 times more than the gravity of earth. What may be the reason?

2 Answers
May 2, 2018

The radius of Jupiter is several times bigger than that of Earth's.

Explanation:

I'll include a calculation just to prove that,

g=(Gm)/r^2, where:

  • g = acceleration due to free fall (ms^-2)
  • G = gravitational constant (6.67*10^-11Nm^2 kg^-2)
  • m = mass of object (kg)
  • r = distance between a point and center of mass of the object (m)

Since G is a constant, we can say that:
(g_Er_E""^2)/(m_E)=(g_Jr_J""^2)/(m_J)

(9.8r_E""^2)/(m_E)=(25(ar_E)^2)/(319m_E)

9.8=(25a^2)/319

a^2=(9.8*319)/25

a=sqrt((9.8*319)/25)~~11.2

Radius of Jupiter is approximately 11.2 times that of Earth.

An increase in mass results in an increase in acceleration due to free fall, but an increase in distance decreases acceleration. Since DeltaM>Deltar^2, acceleration will be greater.

May 2, 2018

We define acceleration due to gravity at the surface of the earth as

g-=GM_e/R_e^2 .........(1)
where G is Universal Gravitational Constant, M_eand R_e are mass and radius of earth respectively. After inserting varius values we have g=9.81\ ms^-2

Similarly acceleration due to gravity at the surface of Jupiter would be

g_j=(GM_j)/R_j^2 .......(2)

Dividing (2) by (1) and inserting given values we get

g_j/g=M_j/M_e R_e^2/R_j^2
=>25/9.8=319xxR_e^2/R_j^2
=>R_e/R_j=sqrt(25/9.8xx1/319)
=>R_e/R_j=0.089

Radius of earth =6,371\ km
Radius of Jupiter =69,911\ km

=>R_e/R_j=6371/69911=0.091

We see that both ratios match well.

Therefore, we can say that gravity of Jupiter is only 2.5times that of earth due to larger radius of Jupiter which appears in the inverse square expression of gravity.