Mars, which has a radius of 3.4 × 106 m and a mass of 6.4 × 1023 kg, orbits the Sun, which has a mass of 2.0 × 1030 kg at a distance of 2.3 × 1011m. Mar’s revolution around the sun is 687 days. It takes 24 hours and 37 minutes to complete one revolution. Which is greater, the tangential speed of Mars’s rotation or revolution?

Tangential speed of Mass revolution is greater

Explanation:

In the above question, we are given the following values:

Radius of Mars = 3.4 × 10^6 m

Mass of Mars = 6.4 × 10^23 kg

Mass of the sun = 2.0 × 10^30 kg at a distance of 2.3 × 10^11m.

Mar’s revolution around the sun = 687 days.

Time of Revolution = 24 hours and 37 minutes to complete one revolution.

Step 1

Find the tangential speed of rotation of Mars

Rotation of Mars = 2 × π × r

Radius of Mars = 3.4 × 10^6 m

Rotation of Mars = 2 × π × 3.4 × 10^6 m

Rotation of Mars = 21362830.044m

= 21.4 × 10^6 m

Tangential Speed of rotation for Mars = Rotation of Mars/ time

Time = 24 hrs 37 minutes

Converting to seconds = 88620s

Tangential Speed of rotation = 21.4 × 10^6 m/ 88620s

= 241.48047845m/s

= 241.5 m/s

Step 2

revolution of Mars = 2 × π × d

d = 2.3 × 10^11m.

= 2 × π × 2.3 × 10^11m = 1.45 × 10^12m

Revolution of Mars = 687 days

Converting 687 days to seconds = 59356800s

Tangential Speed of Revolution of Mars = Revolution of Mars/ times

Tangential Speed of Revolution = 1.45 × 10^12m/595356800s

Tangential Speed of Revolution = 24420m/s

Comparing the Tangential Speed of Rotation with the Tangential speed of Revolution, we can see the GREATER ONE IS THE TANGENTIAL SPEED OF REVOLUTION.

inverse v=i*r

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