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In March 1999 the Mars Global Surveyor (GS) entered its final orbit about Mars, sending data back to Earth. Assume a circular orbit with a period of 7.08 × 103 s and orbital speed of 3.40 × 103 m/s . The mass of the GS is 930 kg and the radius of Mars is 3.43 × 106 m. Calculate the mass of Mars.
In March 1999 the Mars Global Surveyor (GS) entered its final orbit about Mars, sending data back to Earth. Assume a circular orbit with a period of 7.08 × 103 s and orbital speed of 3.40 × 103 m/s . The mass of the GS is 930 kg and the radius of Mars is 3.43 × 106 m. Calculate the mass of Mars.
Final answer:Combining gravitational and centripetal forces, Mars' mass is estimated to be 6.42 × 10²³ kg based on the spacecraft's orbit and speed.Explanation:Here's how to calculate the mass of Mars () using the given information:1. Gravitational force on the spacecraft:The gravitational force () acting on the Mars Global Surveyor (GS) is:= G **/ r²2. Centripetal force on the spacecraft:The centripetal force () required for the GS to maintain its circular orbit is:=* v² / r3. Equilibrium condition:For the GS to maintain its circular orbit, the gravitational force acting on it must be balanced by the centripetal force:Substitute the expressions for each force:G **/ r² =* v² / r4. Solve for:Rearrange the equation to isolate M_mars:= (* v² * r) / (G *)5. Plug in the values:= (930 kg * (3.40 × 10³ m/s)² * 3.43 × 10⁶ m) / (6.6743 × 10⁻¹¹ N * m²/kg² * 930 kg)6. Calculate the mass of Mars:≈ 6.42 × 10²³ kgTherefore, the estimated mass of Mars is 6.42 × 10²³ kg....