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Sum

**Solve the following problem.**

Calculate the value of acceleration due to gravity on the surface of Mars if the radius of Mars = 3.4 × 10^{3} km and its mass is 6.4 × 10^{23} kg.

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#### Solution

**Given: **M = 6.4 × 10^{23} kg, R = 3.4 × 10^{3} km = 3.4 × 10^{6} m,

**To find:** Acceleration due to gravity on the surface of the Mars (g_{M})

**Formula: **g = `"GM"/"R"^2`

**Calculation: **As, G = 6.67 × 10^{-11} Nm^{2}/kg^{2}

From formula,

`"g"_"M" = (6.67 xx 10^-11 xx 6.4 xx 10^23)/(3.4 xx 10^6)^2 = (6.67 xx 6.4)/(3.4 xx 3.4)`

= antilog{log(6.67) + log(6.4) - log(3.4) - log(3.4)}

= antilog{(0.8241) + (0.8062) - (0.5315) - (0.5315)}

= antilog {0.5673}

= 3.693 m/s^{2}

Acceleration due to gravity on the surface of Mars is **3.693 m/s ^{2}**.

Concept: Earth Satellites

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