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Question

You pilot the interstellar craft Bellerophon to the fourth planet orbiting the star Altair. The radius of the planet is measured to be 5350000 m. When you land on the planet, you find the strength of the gravitational field is 5.91 m/s². What is the mass of the planet? (You can enter your answer similar to the following format: 1.99*10^30 kg)

Answer 1

Zac, this is a simple application of (1) Newton's gravitational law and (2) second law of motion:

(1) F = GMm/R² is the gravitational force on a mass, m, exerted by a planet of mass, M and radius, R.

G is the gravitational constant.

(2) The force on a mass, m, is F = ma

==> a = F/m

= (GMm/R²)/m . . . . . . from eqn (1)

= GM/R² . . . . . . . most conveniently, m cancels out!

Therefore, 5.91 = GM/(5.35 x10⁶)² . . . . . . . with all units in MKS

=> M = 5.91 x (5.35 x 10⁶)² / 6.67 x 10⁻¹¹

I leave you to do the arithmetic! Be sure the answer is in proper scientific notation, as requested in the question.

Note, that we show G only to decimal places - because the other numbers in the question are given to 2 decimal places.